id	sid	tid	token	lemma	pos
cana-6095	1	1	communications	communication	NOUN
cana-6095	1	2	on	on	ADP
cana-6095	1	3	applied	apply	VERB
cana-6095	1	4	nonlinear	nonlinear	ADJ
cana-6095	1	5	analysis	analysis	NOUN
cana-6095	1	6	issn	issn	NOUN
cana-6095	1	7	:	:	PUNCT
cana-6095	1	8	1074	1074	NUM
cana-6095	1	9	-	-	PUNCT
cana-6095	1	10	133x	133x	NUM
cana-6095	1	11	vol	vol	NOUN
cana-6095	1	12	30	30	NUM
cana-6095	1	13	no	no	NOUN
cana-6095	1	14	.	.	NOUN
cana-6095	1	15	3	3	NUM
cana-6095	1	16	(	(	PUNCT
cana-6095	1	17	2023	2023	NUM
cana-6095	1	18	)	)	PUNCT
cana-6095	1	19	56	56	NUM
cana-6095	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	1	21	uncertainty	uncertainty	NOUN
cana-6095	1	22	quantification	quantification	NOUN
cana-6095	1	23	in	in	ADP
cana-6095	1	24	numerical	numerical	ADJ
cana-6095	1	25	methods	method	NOUN
cana-6095	1	26	using	use	VERB
cana-6095	1	27	deep	deep	ADJ
cana-6095	1	28	bayesian	bayesian	NOUN
cana-6095	1	29	neural	neural	ADJ
cana-6095	1	30	networks	network	NOUN
cana-6095	1	31	shobhankumar	shobhankumar	VERB
cana-6095	1	32	d.m1	d.m1	NOUN
cana-6095	1	33	,	,	PUNCT
cana-6095	1	34	machhindranath	machhindranath	ADJ
cana-6095	1	35	m.	m.	NOUN
cana-6095	1	36	dhane2	dhane2	PROPN
cana-6095	1	37	*	*	PROPN
cana-6095	1	38	,	,	PUNCT
cana-6095	1	39	vanaja	vanaja	PROPN
cana-6095	1	40	v3	v3	PROPN
cana-6095	1	41	,	,	PUNCT
cana-6095	1	42	ramesh	ramesh	PROPN
cana-6095	1	43	t4	t4	PROPN
cana-6095	1	44	.	.	PROPN
cana-6095	1	45	1	1	NUM
cana-6095	1	46	associate	associate	NOUN
cana-6095	1	47	professor	professor	NOUN
cana-6095	1	48	,	,	PUNCT
cana-6095	1	49	department	department	NOUN
cana-6095	1	50	of	of	ADP
cana-6095	1	51	mathematics	mathematics	PROPN
cana-6095	1	52	,	,	PUNCT
cana-6095	1	53	maharani	maharani	PROPN
cana-6095	1	54	’s	’s	PROPN
cana-6095	1	55	science	science	PROPN
cana-6095	1	56	college	college	PROPN
cana-6095	1	57	for	for	ADP
cana-6095	1	58	women	woman	NOUN
cana-6095	1	59	,	,	PUNCT
cana-6095	1	60	palace	palace	NOUN
cana-6095	1	61	road	road	NOUN
cana-6095	1	62	,	,	PUNCT
cana-6095	1	63	bengaluru	bengaluru	PROPN
cana-6095	1	64	,	,	PUNCT
cana-6095	1	65	karnataka	karnataka	PROPN
cana-6095	1	66	,	,	PUNCT
cana-6095	1	67	india	india	PROPN
cana-6095	1	68	;	;	PUNCT
cana-6095	1	69	email	email	NOUN
cana-6095	1	70	:	:	PUNCT
cana-6095	2	1	shobhankumardm@gmail.com	shobhankumardm@gmail.com	X
cana-6095	2	2	2*associate	2*associate	NUM
cana-6095	2	3	professor	professor	NOUN
cana-6095	2	4	,	,	PUNCT
cana-6095	2	5	department	department	NOUN
cana-6095	2	6	of	of	ADP
cana-6095	2	7	mathematics	mathematics	PROPN
cana-6095	2	8	,	,	PUNCT
cana-6095	2	9	gfgc	gfgc	PROPN
cana-6095	2	10	,	,	PUNCT
cana-6095	2	11	yelahanka	yelahanka	PROPN
cana-6095	2	12	,	,	PUNCT
cana-6095	2	13	bengaluru	bengaluru	PROPN
cana-6095	2	14	,	,	PUNCT
cana-6095	2	15	karnataka	karnataka	PROPN
cana-6095	2	16	,	,	PUNCT
cana-6095	2	17	india	india	PROPN
cana-6095	2	18	;	;	PUNCT
cana-6095	2	19	email	email	NOUN
cana-6095	2	20	:	:	PUNCT
cana-6095	2	21	drdhani.99dce@gmail.com	drdhani.99dce@gmail.com	NOUN
cana-6095	2	22	3associate	3associate	NUM
cana-6095	2	23	professor	professor	NOUN
cana-6095	2	24	,	,	PUNCT
cana-6095	2	25	department	department	NOUN
cana-6095	2	26	of	of	ADP
cana-6095	2	27	mathematics	mathematics	PROPN
cana-6095	2	28	,	,	PUNCT
cana-6095	2	29	gfgc	gfgc	PROPN
cana-6095	2	30	,	,	PUNCT
cana-6095	2	31	yelahanka	yelahanka	PROPN
cana-6095	2	32	,	,	PUNCT
cana-6095	2	33	bengaluru	bengaluru	PROPN
cana-6095	2	34	,	,	PUNCT
cana-6095	2	35	karnataka	karnataka	PROPN
cana-6095	2	36	,	,	PUNCT
cana-6095	2	37	india	india	PROPN
cana-6095	2	38	;	;	PUNCT
cana-6095	2	39	email	email	NOUN
cana-6095	2	40	:	:	PUNCT
cana-6095	3	1	vanajaksr94@yahoo.com	vanajaksr94@yahoo.com	PROPN
cana-6095	3	2	4associate	4associate	PROPN
cana-6095	3	3	professor	professor	NOUN
cana-6095	3	4	,	,	PUNCT
cana-6095	3	5	department	department	NOUN
cana-6095	3	6	of	of	ADP
cana-6095	3	7	mathematics	mathematics	PROPN
cana-6095	3	8	,	,	PUNCT
cana-6095	3	9	cambridge	cambridge	PROPN
cana-6095	3	10	institute	institute	PROPN
cana-6095	3	11	of	of	ADP
cana-6095	3	12	technology	technology	PROPN
cana-6095	3	13	,	,	PUNCT
cana-6095	3	14	k	k	PROPN
cana-6095	3	15	r	r	PROPN
cana-6095	3	16	puram	puram	PROPN
cana-6095	3	17	,	,	PUNCT
cana-6095	3	18	bengaluru	bengaluru	PROPN
cana-6095	3	19	,	,	PUNCT
cana-6095	3	20	karnataka	karnataka	PROPN
cana-6095	3	21	,	,	PUNCT
cana-6095	3	22	india	india	PROPN
cana-6095	3	23	;	;	PUNCT
cana-6095	3	24	email	email	NOUN
cana-6095	3	25	:	:	PUNCT
cana-6095	4	1	rameshgollahally@gmail.com	rameshgollahally@gmail.com	X
cana-6095	4	2	*	*	PUNCT
cana-6095	4	3	corresponding	correspond	VERB
cana-6095	4	4	author	author	NOUN
cana-6095	4	5	:	:	PUNCT
cana-6095	4	6	drdhani.99dce@gmail.com	drdhani.99dce@gmail.com	X
cana-6095	4	7	email	email	NOUN
cana-6095	4	8	of	of	ADP
cana-6095	4	9	co-author:shobhankumardm@gmail.com	co-author:shobhankumardm@gmail.com	NOUN
cana-6095	4	10	article	article	NOUN
cana-6095	4	11	history	history	NOUN
cana-6095	4	12	:	:	PUNCT
cana-6095	4	13	received	receive	VERB
cana-6095	4	14	:	:	PUNCT
cana-6095	4	15	06	06	NUM
cana-6095	4	16	-	-	SYM
cana-6095	4	17	03	03	NUM
cana-6095	4	18	-	-	PUNCT
cana-6095	4	19	2023	2023	NUM
cana-6095	4	20	revised	revise	VERB
cana-6095	4	21	:	:	PUNCT
cana-6095	4	22	27	27	NUM
cana-6095	4	23	-	-	PUNCT
cana-6095	4	24	04	04	NUM
cana-6095	4	25	-	-	PUNCT
cana-6095	4	26	2023	2023	NUM
cana-6095	4	27	accepted	accept	VERB
cana-6095	4	28	:	:	PUNCT
cana-6095	4	29	26	26	NUM
cana-6095	4	30	-	-	SYM
cana-6095	4	31	05	05	NUM
cana-6095	4	32	-	-	PUNCT
cana-6095	4	33	2023	2023	NUM
cana-6095	4	34	abstract	abstract	NOUN
cana-6095	4	35	:	:	PUNCT
cana-6095	4	36	grammar	grammar	NOUN
cana-6095	4	37	plays	play	VERB
cana-6095	4	38	a	a	DET
cana-6095	4	39	pivotal	pivotal	ADJ
cana-6095	4	40	role	role	NOUN
cana-6095	4	41	in	in	ADP
cana-6095	4	42	second	second	ADJ
cana-6095	4	43	language	language	NOUN
cana-6095	4	44	acquisition	acquisition	NOUN
cana-6095	4	45	(	(	PUNCT
cana-6095	4	46	sla	sla	PROPN
cana-6095	4	47	)	)	PUNCT
cana-6095	4	48	,	,	PUNCT
cana-6095	4	49	especially	especially	ADV
cana-6095	4	50	during	during	ADP
cana-6095	4	51	the	the	DET
cana-6095	4	52	formative	formative	ADJ
cana-6095	4	53	middle	middle	ADJ
cana-6095	4	54	school	school	NOUN
cana-6095	4	55	years	year	NOUN
cana-6095	4	56	when	when	SCONJ
cana-6095	4	57	students	student	NOUN
cana-6095	4	58	are	be	AUX
cana-6095	4	59	developing	develop	VERB
cana-6095	4	60	foundational	foundational	ADJ
cana-6095	4	61	language	language	NOUN
cana-6095	4	62	skills	skill	NOUN
cana-6095	4	63	.	.	PUNCT
cana-6095	5	1	this	this	DET
cana-6095	5	2	abstract	abstract	ADJ
cana-6095	5	3	explores	explore	VERB
cana-6095	5	4	the	the	DET
cana-6095	5	5	intersection	intersection	NOUN
cana-6095	5	6	of	of	ADP
cana-6095	5	7	grammar	grammar	NOUN
cana-6095	5	8	instruction	instruction	NOUN
cana-6095	5	9	and	and	CCONJ
cana-6095	5	10	sla	sla	PROPN
cana-6095	5	11	,	,	PUNCT
cana-6095	5	12	highlighting	highlight	VERB
cana-6095	5	13	its	its	PRON
cana-6095	5	14	impact	impact	NOUN
cana-6095	5	15	on	on	ADP
cana-6095	5	16	linguistic	linguistic	ADJ
cana-6095	5	17	proficiency	proficiency	NOUN
cana-6095	5	18	,	,	PUNCT
cana-6095	5	19	cognitive	cognitive	ADJ
cana-6095	5	20	development	development	NOUN
cana-6095	5	21	,	,	PUNCT
cana-6095	5	22	and	and	CCONJ
cana-6095	5	23	communicative	communicative	ADJ
cana-6095	5	24	competence	competence	NOUN
cana-6095	5	25	.	.	PUNCT
cana-6095	6	1	drawing	draw	VERB
cana-6095	6	2	from	from	ADP
cana-6095	6	3	research	research	NOUN
cana-6095	6	4	and	and	CCONJ
cana-6095	6	5	classroom	classroom	NOUN
cana-6095	6	6	observations	observation	NOUN
cana-6095	6	7	,	,	PUNCT
cana-6095	6	8	the	the	DET
cana-6095	6	9	chapter	chapter	NOUN
cana-6095	6	10	examines	examine	VERB
cana-6095	6	11	how	how	SCONJ
cana-6095	6	12	middle	middle	ADJ
cana-6095	6	13	school	school	NOUN
cana-6095	6	14	students	student	NOUN
cana-6095	6	15	internalize	internalize	VERB
cana-6095	6	16	grammatical	grammatical	ADJ
cana-6095	6	17	structures	structure	NOUN
cana-6095	6	18	to	to	PART
cana-6095	6	19	enhance	enhance	VERB
cana-6095	6	20	their	their	PRON
cana-6095	6	21	speaking	speaking	NOUN
cana-6095	6	22	,	,	PUNCT
cana-6095	6	23	writing	writing	NOUN
cana-6095	6	24	,	,	PUNCT
cana-6095	6	25	reading	reading	NOUN
cana-6095	6	26	,	,	PUNCT
cana-6095	6	27	and	and	CCONJ
cana-6095	6	28	listening	listening	NOUN
cana-6095	6	29	skills	skill	NOUN
cana-6095	6	30	.	.	PUNCT
cana-6095	7	1	it	it	PRON
cana-6095	7	2	delves	delve	VERB
cana-6095	7	3	into	into	ADP
cana-6095	7	4	the	the	DET
cana-6095	7	5	importance	importance	NOUN
cana-6095	7	6	of	of	ADP
cana-6095	7	7	age	age	NOUN
cana-6095	7	8	-	-	PUNCT
cana-6095	7	9	appropriate	appropriate	ADJ
cana-6095	7	10	methods	method	NOUN
cana-6095	7	11	that	that	PRON
cana-6095	7	12	balance	balance	VERB
cana-6095	7	13	explicit	explicit	ADJ
cana-6095	7	14	grammar	grammar	NOUN
cana-6095	7	15	teaching	teaching	NOUN
cana-6095	7	16	with	with	ADP
cana-6095	7	17	implicit	implicit	ADJ
cana-6095	7	18	language	language	NOUN
cana-6095	7	19	exposure	exposure	NOUN
cana-6095	7	20	,	,	PUNCT
cana-6095	7	21	ensuring	ensure	VERB
cana-6095	7	22	that	that	SCONJ
cana-6095	7	23	students	student	NOUN
cana-6095	7	24	build	build	VERB
cana-6095	7	25	a	a	DET
cana-6095	7	26	robust	robust	ADJ
cana-6095	7	27	understanding	understanding	NOUN
cana-6095	7	28	of	of	ADP
cana-6095	7	29	syntax	syntax	NOUN
cana-6095	7	30	,	,	PUNCT
cana-6095	7	31	morphology	morphology	NOUN
cana-6095	7	32	,	,	PUNCT
cana-6095	7	33	and	and	CCONJ
cana-6095	7	34	semantics	semantic	NOUN
cana-6095	7	35	.	.	PUNCT
cana-6095	8	1	furthermore	furthermore	ADV
cana-6095	8	2	,	,	PUNCT
cana-6095	8	3	the	the	DET
cana-6095	8	4	chapter	chapter	NOUN
cana-6095	8	5	evaluates	evaluate	VERB
cana-6095	8	6	the	the	DET
cana-6095	8	7	influence	influence	NOUN
cana-6095	8	8	of	of	ADP
cana-6095	8	9	socio	socio	NOUN
cana-6095	8	10	-	-	PUNCT
cana-6095	8	11	cultural	cultural	ADJ
cana-6095	8	12	factors	factor	NOUN
cana-6095	8	13	on	on	ADP
cana-6095	8	14	grammar	grammar	NOUN
cana-6095	8	15	learning	learning	NOUN
cana-6095	8	16	,	,	PUNCT
cana-6095	8	17	emphasizing	emphasize	VERB
cana-6095	8	18	the	the	DET
cana-6095	8	19	importance	importance	NOUN
cana-6095	8	20	of	of	ADP
cana-6095	8	21	tailored	tailor	VERB
cana-6095	8	22	pedagogical	pedagogical	ADJ
cana-6095	8	23	approaches	approach	NOUN
cana-6095	8	24	that	that	PRON
cana-6095	8	25	resonate	resonate	VERB
cana-6095	8	26	with	with	ADP
cana-6095	8	27	diverse	diverse	ADJ
cana-6095	8	28	student	student	NOUN
cana-6095	8	29	populations	population	NOUN
cana-6095	8	30	.	.	PUNCT
cana-6095	9	1	by	by	ADP
cana-6095	9	2	integrating	integrate	VERB
cana-6095	9	3	theoretical	theoretical	ADJ
cana-6095	9	4	perspectives	perspective	NOUN
cana-6095	9	5	and	and	CCONJ
cana-6095	9	6	practical	practical	ADJ
cana-6095	9	7	insights	insight	NOUN
cana-6095	9	8	,	,	PUNCT
cana-6095	9	9	this	this	DET
cana-6095	9	10	discussion	discussion	NOUN
cana-6095	9	11	aims	aim	VERB
cana-6095	9	12	to	to	PART
cana-6095	9	13	underscore	underscore	VERB
cana-6095	9	14	grammar	grammar	NOUN
cana-6095	9	15	’s	’s	PART
cana-6095	9	16	essential	essential	ADJ
cana-6095	9	17	role	role	NOUN
cana-6095	9	18	in	in	ADP
cana-6095	9	19	equipping	equip	VERB
cana-6095	9	20	students	student	NOUN
cana-6095	9	21	with	with	ADP
cana-6095	9	22	the	the	DET
cana-6095	9	23	tools	tool	NOUN
cana-6095	9	24	necessary	necessary	ADJ
cana-6095	9	25	for	for	ADP
cana-6095	9	26	effective	effective	ADJ
cana-6095	9	27	second	second	ADJ
cana-6095	9	28	language	language	NOUN
cana-6095	9	29	communication	communication	NOUN
cana-6095	9	30	.	.	PUNCT
cana-6095	10	1	keywords	keyword	NOUN
cana-6095	10	2	:	:	PUNCT
cana-6095	10	3	second	second	ADJ
cana-6095	10	4	language	language	NOUN
cana-6095	10	5	acquisition	acquisition	NOUN
cana-6095	10	6	,	,	PUNCT
cana-6095	10	7	grammar	grammar	NOUN
cana-6095	10	8	instruction	instruction	NOUN
cana-6095	10	9	,	,	PUNCT
cana-6095	10	10	middle	middle	ADJ
cana-6095	10	11	school	school	NOUN
cana-6095	10	12	education	education	NOUN
cana-6095	10	13	,	,	PUNCT
cana-6095	10	14	linguistic	linguistic	ADJ
cana-6095	10	15	proficiency	proficiency	NOUN
cana-6095	10	16	,	,	PUNCT
cana-6095	10	17	socio	socio	NOUN
cana-6095	10	18	-	-	PUNCT
cana-6095	10	19	cultural	cultural	ADJ
cana-6095	10	20	factors	factor	NOUN
cana-6095	10	21	and	and	CCONJ
cana-6095	10	22	cognitive	cognitive	ADJ
cana-6095	10	23	development	development	NOUN
cana-6095	10	24	.	.	PUNCT
cana-6095	11	1	abstract	abstract	ADJ
cana-6095	11	2	uncertainty	uncertainty	NOUN
cana-6095	11	3	quantification	quantification	NOUN
cana-6095	11	4	(	(	PUNCT
cana-6095	11	5	uq	uq	NOUN
cana-6095	11	6	)	)	PUNCT
cana-6095	11	7	represents	represent	VERB
cana-6095	11	8	a	a	DET
cana-6095	11	9	critical	critical	ADJ
cana-6095	11	10	challenge	challenge	NOUN
cana-6095	11	11	in	in	ADP
cana-6095	11	12	numerical	numerical	ADJ
cana-6095	11	13	computation	computation	NOUN
cana-6095	11	14	,	,	PUNCT
cana-6095	11	15	particularly	particularly	ADV
cana-6095	11	16	as	as	ADP
cana-6095	11	17	complex	complex	ADJ
cana-6095	11	18	scientific	scientific	ADJ
cana-6095	11	19	and	and	CCONJ
cana-6095	11	20	engineering	engineering	NOUN
cana-6095	11	21	systems	system	NOUN
cana-6095	11	22	demand	demand	VERB
cana-6095	11	23	robust	robust	ADJ
cana-6095	11	24	error	error	NOUN
cana-6095	11	25	estimation	estimation	NOUN
cana-6095	11	26	and	and	CCONJ
cana-6095	11	27	reliability	reliability	NOUN
cana-6095	11	28	assessment	assessment	NOUN
cana-6095	11	29	.	.	PUNCT
cana-6095	12	1	this	this	DET
cana-6095	12	2	comprehensive	comprehensive	ADJ
cana-6095	12	3	review	review	NOUN
cana-6095	12	4	examines	examine	VERB
cana-6095	12	5	the	the	DET
cana-6095	12	6	integration	integration	NOUN
cana-6095	12	7	of	of	ADP
cana-6095	12	8	deep	deep	ADJ
cana-6095	12	9	bayesian	bayesian	NOUN
cana-6095	12	10	neural	neural	ADJ
cana-6095	12	11	networks	network	NOUN
cana-6095	12	12	(	(	PUNCT
cana-6095	12	13	bnns	bnns	PROPN
cana-6095	12	14	)	)	PUNCT
cana-6095	12	15	with	with	ADP
cana-6095	12	16	traditional	traditional	ADJ
cana-6095	12	17	numerical	numerical	ADJ
cana-6095	12	18	methods	method	NOUN
cana-6095	12	19	to	to	PART
cana-6095	12	20	enhance	enhance	VERB
cana-6095	12	21	uncertainty	uncertainty	NOUN
cana-6095	12	22	quantification	quantification	NOUN
cana-6095	12	23	across	across	ADP
cana-6095	12	24	various	various	ADJ
cana-6095	12	25	computational	computational	ADJ
cana-6095	12	26	domains	domain	NOUN
cana-6095	12	27	.	.	PUNCT
cana-6095	13	1	we	we	PRON
cana-6095	13	2	explore	explore	VERB
cana-6095	13	3	fundamental	fundamental	ADJ
cana-6095	13	4	theoretical	theoretical	ADJ
cana-6095	13	5	concepts	concept	NOUN
cana-6095	13	6	,	,	PUNCT
cana-6095	13	7	including	include	VERB
cana-6095	13	8	bayesian	bayesian	NOUN
cana-6095	13	9	inference	inference	NOUN
cana-6095	13	10	,	,	PUNCT
cana-6095	13	11	probabilistic	probabilistic	ADJ
cana-6095	13	12	numerics	numeric	NOUN
cana-6095	13	13	,	,	PUNCT
cana-6095	13	14	and	and	CCONJ
cana-6095	13	15	neural	neural	ADJ
cana-6095	13	16	network	network	NOUN
cana-6095	13	17	architectures	architecture	NOUN
cana-6095	13	18	,	,	PUNCT
cana-6095	13	19	demonstrating	demonstrate	VERB
cana-6095	13	20	how	how	SCONJ
cana-6095	13	21	bnns	bnns	PROPN
cana-6095	13	22	can	can	AUX
cana-6095	13	23	capture	capture	VERB
cana-6095	13	24	both	both	CCONJ
cana-6095	13	25	aleatoric	aleatoric	ADJ
cana-6095	13	26	and	and	CCONJ
cana-6095	13	27	epistemic	epistemic	ADJ
cana-6095	13	28	uncertainties	uncertainty	NOUN
cana-6095	13	29	in	in	ADP
cana-6095	13	30	numerical	numerical	ADJ
cana-6095	13	31	computations	computation	NOUN
cana-6095	13	32	.	.	PUNCT
cana-6095	14	1	through	through	ADP
cana-6095	14	2	detailed	detailed	ADJ
cana-6095	14	3	analysis	analysis	NOUN
cana-6095	14	4	of	of	ADP
cana-6095	14	5	applications	application	NOUN
cana-6095	14	6	in	in	ADP
cana-6095	14	7	partial	partial	ADJ
cana-6095	14	8	differential	differential	NOUN
cana-6095	14	9	equation	equation	NOUN
cana-6095	14	10	solving	solving	NOUN
cana-6095	14	11	,	,	PUNCT
cana-6095	14	12	numerical	numerical	ADJ
cana-6095	14	13	integration	integration	NOUN
cana-6095	14	14	,	,	PUNCT
cana-6095	14	15	materials	material	NOUN
cana-6095	14	16	modeling	modeling	NOUN
cana-6095	14	17	,	,	PUNCT
cana-6095	14	18	and	and	CCONJ
cana-6095	14	19	scientific	scientific	ADJ
cana-6095	14	20	machine	machine	NOUN
cana-6095	14	21	learning	learning	NOUN
cana-6095	14	22	,	,	PUNCT
cana-6095	14	23	we	we	PRON
cana-6095	14	24	show	show	VERB
cana-6095	14	25	that	that	SCONJ
cana-6095	14	26	bayesian	bayesian	NOUN
cana-6095	14	27	approaches	approach	NOUN
cana-6095	14	28	provide	provide	VERB
cana-6095	14	29	principled	principled	ADJ
cana-6095	14	30	uncertainty	uncertainty	NOUN
cana-6095	14	31	estimates	estimate	NOUN
cana-6095	14	32	while	while	SCONJ
cana-6095	14	33	maintaining	maintain	VERB
cana-6095	14	34	computational	computational	ADJ
cana-6095	14	35	efficiency	efficiency	NOUN
cana-6095	14	36	.	.	PUNCT
cana-6095	15	1	the	the	DET
cana-6095	15	2	paper	paper	NOUN
cana-6095	15	3	also	also	ADV
cana-6095	15	4	addresses	address	VERB
cana-6095	15	5	mailto:shobhankumardm@gmail.com	mailto:shobhankumardm@gmail.com	X
cana-6095	16	1	mailto:drdhani.99dce@gmail.com	mailto:drdhani.99dce@gmail.com	X
cana-6095	16	2	mailto:vanajaksr94@yahoo.com	mailto:vanajaksr94@yahoo.com	PROPN
cana-6095	16	3	mailto:rameshgollahally@gmail.com	mailto:rameshgollahally@gmail.com	X
cana-6095	17	1	mailto:drdhani.99dce@gmail.com	mailto:drdhani.99dce@gmail.com	X
cana-6095	17	2	mailto:shobhankumardm@gmail.com	mailto:shobhankumardm@gmail.com	PROPN
cana-6095	17	3	communications	communication	NOUN
cana-6095	17	4	on	on	ADP
cana-6095	17	5	applied	apply	VERB
cana-6095	17	6	nonlinear	nonlinear	ADJ
cana-6095	17	7	analysis	analysis	NOUN
cana-6095	17	8	issn	issn	NOUN
cana-6095	17	9	:	:	PUNCT
cana-6095	17	10	1074	1074	NUM
cana-6095	17	11	-	-	PUNCT
cana-6095	17	12	133x	133x	NUM
cana-6095	17	13	vol	vol	NOUN
cana-6095	17	14	30	30	NUM
cana-6095	17	15	no	no	NOUN
cana-6095	17	16	.	.	NOUN
cana-6095	17	17	3	3	NUM
cana-6095	17	18	(	(	PUNCT
cana-6095	17	19	2023	2023	NUM
cana-6095	17	20	)	)	PUNCT
cana-6095	18	1	57	57	NUM
cana-6095	18	2	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-6095	18	3	significant	significant	ADJ
cana-6095	18	4	challenges	challenge	NOUN
cana-6095	18	5	in	in	ADP
cana-6095	18	6	scalability	scalability	NOUN
cana-6095	18	7	,	,	PUNCT
cana-6095	18	8	multi	multi	ADJ
cana-6095	18	9	-	-	ADJ
cana-6095	18	10	modal	modal	ADJ
cana-6095	18	11	posterior	posterior	ADJ
cana-6095	18	12	distributions	distribution	NOUN
cana-6095	18	13	,	,	PUNCT
cana-6095	18	14	evaluation	evaluation	NOUN
cana-6095	18	15	metrics	metric	NOUN
cana-6095	18	16	,	,	PUNCT
cana-6095	18	17	and	and	CCONJ
cana-6095	18	18	distribution	distribution	NOUN
cana-6095	18	19	shifts	shift	NOUN
cana-6095	18	20	,	,	PUNCT
cana-6095	18	21	while	while	SCONJ
cana-6095	18	22	outlining	outline	VERB
cana-6095	18	23	promising	promise	VERB
cana-6095	18	24	research	research	NOUN
cana-6095	18	25	directions	direction	NOUN
cana-6095	18	26	for	for	ADP
cana-6095	18	27	scalable	scalable	ADJ
cana-6095	18	28	inference	inference	NOUN
cana-6095	18	29	methods	method	NOUN
cana-6095	18	30	,	,	PUNCT
cana-6095	18	31	advanced	advanced	ADJ
cana-6095	18	32	architectures	architecture	NOUN
cana-6095	18	33	,	,	PUNCT
cana-6095	18	34	integrated	integrated	ADJ
cana-6095	18	35	uq	uq	NOUN
cana-6095	18	36	frameworks	framework	NOUN
cana-6095	18	37	,	,	PUNCT
cana-6095	18	38	and	and	CCONJ
cana-6095	18	39	enhanced	enhance	VERB
cana-6095	18	40	theoretical	theoretical	ADJ
cana-6095	18	41	foundations	foundation	NOUN
cana-6095	18	42	.	.	PUNCT
cana-6095	19	1	by	by	ADP
cana-6095	19	2	bridging	bridge	VERB
cana-6095	19	3	bayesian	bayesian	NOUN
cana-6095	19	4	methods	method	NOUN
cana-6095	19	5	with	with	ADP
cana-6095	19	6	numerical	numerical	ADJ
cana-6095	19	7	computation	computation	NOUN
cana-6095	19	8	,	,	PUNCT
cana-6095	19	9	deep	deep	ADJ
cana-6095	19	10	bnns	bnn	NOUN
cana-6095	19	11	offer	offer	VERB
cana-6095	19	12	a	a	DET
cana-6095	19	13	transformative	transformative	ADJ
cana-6095	19	14	approach	approach	NOUN
cana-6095	19	15	to	to	ADP
cana-6095	19	16	uncertainty	uncertainty	NOUN
cana-6095	19	17	-	-	PUNCT
cana-6095	19	18	aware	aware	ADJ
cana-6095	19	19	scientific	scientific	ADJ
cana-6095	19	20	computing	computing	NOUN
cana-6095	19	21	.	.	PUNCT
cana-6095	20	1	keywords	keyword	NOUN
cana-6095	20	2	:	:	PUNCT
cana-6095	20	3	uncertainty	uncertainty	NOUN
cana-6095	20	4	quantification	quantification	NOUN
cana-6095	20	5	,	,	PUNCT
cana-6095	20	6	bayesian	bayesian	NOUN
cana-6095	20	7	neural	neural	ADJ
cana-6095	20	8	networks	network	NOUN
cana-6095	20	9	,	,	PUNCT
cana-6095	20	10	numerical	numerical	ADJ
cana-6095	20	11	methods	method	NOUN
cana-6095	20	12	,	,	PUNCT
cana-6095	20	13	scientific	scientific	ADJ
cana-6095	20	14	machine	machine	NOUN
cana-6095	20	15	learning	learning	NOUN
cana-6095	20	16	,	,	PUNCT
cana-6095	20	17	probabilistic	probabilistic	ADJ
cana-6095	20	18	numerics	numeric	NOUN
cana-6095	20	19	,	,	PUNCT
cana-6095	20	20	epistemic	epistemic	ADJ
cana-6095	20	21	uncertainty	uncertainty	NOUN
cana-6095	20	22	,	,	PUNCT
cana-6095	20	23	bayesian	bayesian	NOUN
cana-6095	20	24	inference	inference	NOUN
cana-6095	20	25	.	.	PUNCT
cana-6095	21	1	1.introduction	1.introduction	NUM
cana-6095	21	2	numerical	numerical	ADJ
cana-6095	21	3	methods	method	NOUN
cana-6095	21	4	form	form	VERB
cana-6095	21	5	the	the	DET
cana-6095	21	6	foundation	foundation	NOUN
cana-6095	21	7	of	of	ADP
cana-6095	21	8	scientific	scientific	ADJ
cana-6095	21	9	computing	computing	NOUN
cana-6095	21	10	,	,	PUNCT
cana-6095	21	11	enabling	enable	VERB
cana-6095	21	12	the	the	DET
cana-6095	21	13	solution	solution	NOUN
cana-6095	21	14	of	of	ADP
cana-6095	21	15	complex	complex	ADJ
cana-6095	21	16	mathematical	mathematical	ADJ
cana-6095	21	17	problems	problem	NOUN
cana-6095	21	18	that	that	PRON
cana-6095	21	19	arise	arise	VERB
cana-6095	21	20	in	in	ADP
cana-6095	21	21	engineering	engineering	NOUN
cana-6095	21	22	,	,	PUNCT
cana-6095	21	23	physics	physics	NOUN
cana-6095	21	24	,	,	PUNCT
cana-6095	21	25	economics	economic	NOUN
cana-6095	21	26	,	,	PUNCT
cana-6095	21	27	and	and	CCONJ
cana-6095	21	28	countless	countless	ADJ
cana-6095	21	29	other	other	ADJ
cana-6095	21	30	disciplines	discipline	NOUN
cana-6095	21	31	.	.	PUNCT
cana-6095	22	1	traditional	traditional	ADJ
cana-6095	22	2	numerical	numerical	ADJ
cana-6095	22	3	approaches	approach	NOUN
cana-6095	22	4	including	include	VERB
cana-6095	22	5	finite	finite	ADJ
cana-6095	22	6	element	element	NOUN
cana-6095	22	7	methods	method	NOUN
cana-6095	22	8	,	,	PUNCT
cana-6095	22	9	finite	finite	ADJ
cana-6095	22	10	difference	difference	NOUN
cana-6095	22	11	schemes	scheme	NOUN
cana-6095	22	12	,	,	PUNCT
cana-6095	22	13	and	and	CCONJ
cana-6095	22	14	numerical	numerical	ADJ
cana-6095	22	15	integration	integration	NOUN
cana-6095	22	16	techniques	technique	NOUN
cana-6095	22	17	provide	provide	VERB
cana-6095	22	18	point	point	NOUN
cana-6095	22	19	estimates	estimate	NOUN
cana-6095	22	20	of	of	ADP
cana-6095	22	21	solutions	solution	NOUN
cana-6095	22	22	but	but	CCONJ
cana-6095	22	23	often	often	ADV
cana-6095	22	24	lack	lack	VERB
cana-6095	22	25	comprehensive	comprehensive	ADJ
cana-6095	22	26	uncertainty	uncertainty	NOUN
cana-6095	22	27	quantification	quantification	NOUN
cana-6095	22	28	(	(	PUNCT
cana-6095	22	29	uq	uq	NOUN
cana-6095	22	30	)	)	PUNCT
cana-6095	22	31	capabilities	capability	NOUN
cana-6095	22	32	.	.	PUNCT
cana-6095	23	1	as	as	SCONJ
cana-6095	23	2	computational	computational	ADJ
cana-6095	23	3	models	model	NOUN
cana-6095	23	4	increasingly	increasingly	ADV
cana-6095	23	5	inform	inform	VERB
cana-6095	23	6	critical	critical	ADJ
cana-6095	23	7	decisions	decision	NOUN
cana-6095	23	8	in	in	ADP
cana-6095	23	9	areas	area	NOUN
cana-6095	23	10	such	such	ADJ
cana-6095	23	11	as	as	ADP
cana-6095	23	12	climate	climate	NOUN
cana-6095	23	13	science	science	NOUN
cana-6095	23	14	,	,	PUNCT
cana-6095	23	15	healthcare	healthcare	PROPN
cana-6095	23	16	,	,	PUNCT
cana-6095	23	17	and	and	CCONJ
cana-6095	23	18	infrastructure	infrastructure	NOUN
cana-6095	23	19	design	design	NOUN
cana-6095	23	20	,	,	PUNCT
cana-6095	23	21	understanding	understand	VERB
cana-6095	23	22	the	the	DET
cana-6095	23	23	reliability	reliability	NOUN
cana-6095	23	24	and	and	CCONJ
cana-6095	23	25	limitations	limitation	NOUN
cana-6095	23	26	of	of	ADP
cana-6095	23	27	these	these	DET
cana-6095	23	28	numerical	numerical	ADJ
cana-6095	23	29	approximations	approximation	NOUN
cana-6095	23	30	becomes	become	VERB
cana-6095	23	31	paramount	paramount	ADJ
cana-6095	23	32	9,10	9,10	NUM
cana-6095	23	33	.	.	PUNCT
cana-6095	24	1	the	the	DET
cana-6095	24	2	field	field	NOUN
cana-6095	24	3	of	of	ADP
cana-6095	24	4	uncertainty	uncertainty	NOUN
cana-6095	24	5	quantification	quantification	NOUN
cana-6095	24	6	has	have	AUX
cana-6095	24	7	emerged	emerge	VERB
cana-6095	24	8	to	to	PART
cana-6095	24	9	address	address	VERB
cana-6095	24	10	these	these	DET
cana-6095	24	11	challenges	challenge	NOUN
cana-6095	24	12	,	,	PUNCT
cana-6095	24	13	seeking	seek	VERB
cana-6095	24	14	to	to	PART
cana-6095	24	15	characterize	characterize	VERB
cana-6095	24	16	,	,	PUNCT
cana-6095	24	17	quantify	quantify	ADJ
cana-6095	24	18	,	,	PUNCT
cana-6095	24	19	and	and	CCONJ
cana-6095	24	20	propagate	propagate	VERB
cana-6095	24	21	uncertainties	uncertainty	NOUN
cana-6095	24	22	through	through	ADP
cana-6095	24	23	computational	computational	ADJ
cana-6095	24	24	models	model	NOUN
cana-6095	24	25	.	.	PUNCT
cana-6095	25	1	traditional	traditional	ADJ
cana-6095	25	2	uq	uq	NOUN
cana-6095	25	3	methods	method	NOUN
cana-6095	25	4	often	often	ADV
cana-6095	25	5	rely	rely	VERB
cana-6095	25	6	on	on	ADP
cana-6095	25	7	sampling	sample	VERB
cana-6095	25	8	-	-	PUNCT
cana-6095	25	9	based	base	VERB
cana-6095	25	10	approaches	approach	NOUN
cana-6095	25	11	such	such	ADJ
cana-6095	25	12	as	as	ADP
cana-6095	25	13	monte	monte	PROPN
cana-6095	25	14	carlo	carlo	PROPN
cana-6095	25	15	simulations	simulation	NOUN
cana-6095	25	16	,	,	PUNCT
cana-6095	25	17	which	which	PRON
cana-6095	25	18	can	can	AUX
cana-6095	25	19	be	be	AUX
cana-6095	25	20	computationally	computationally	ADV
cana-6095	25	21	prohibitive	prohibitive	ADJ
cana-6095	25	22	for	for	ADP
cana-6095	25	23	complex	complex	ADJ
cana-6095	25	24	systems	system	NOUN
cana-6095	25	25	,	,	PUNCT
cana-6095	25	26	or	or	CCONJ
cana-6095	25	27	polynomial	polynomial	ADJ
cana-6095	25	28	chaos	chaos	NOUN
cana-6095	25	29	expansions	expansion	NOUN
cana-6095	25	30	,	,	PUNCT
cana-6095	25	31	which	which	PRON
cana-6095	25	32	may	may	AUX
cana-6095	25	33	struggle	struggle	VERB
cana-6095	25	34	with	with	ADP
cana-6095	25	35	high	high	ADJ
cana-6095	25	36	-	-	PUNCT
cana-6095	25	37	dimensional	dimensional	ADJ
cana-6095	25	38	problems	problem	NOUN
cana-6095	25	39	9	9	NUM
cana-6095	25	40	.	.	PUNCT
cana-6095	26	1	these	these	DET
cana-6095	26	2	limitations	limitation	NOUN
cana-6095	26	3	have	have	AUX
cana-6095	26	4	motivated	motivate	VERB
cana-6095	26	5	the	the	DET
cana-6095	26	6	integration	integration	NOUN
cana-6095	26	7	of	of	ADP
cana-6095	26	8	machine	machine	NOUN
cana-6095	26	9	learning	learn	VERB
cana-6095	26	10	techniques	technique	NOUN
cana-6095	26	11	,	,	PUNCT
cana-6095	26	12	particularly	particularly	ADV
cana-6095	26	13	deep	deep	ADJ
cana-6095	26	14	neural	neural	ADJ
cana-6095	26	15	networks	network	NOUN
cana-6095	26	16	,	,	PUNCT
cana-6095	26	17	with	with	ADP
cana-6095	26	18	established	establish	VERB
cana-6095	26	19	numerical	numerical	ADJ
cana-6095	26	20	methods	method	NOUN
cana-6095	26	21	to	to	PART
cana-6095	26	22	develop	develop	VERB
cana-6095	26	23	more	more	ADV
cana-6095	26	24	efficient	efficient	ADJ
cana-6095	26	25	and	and	CCONJ
cana-6095	26	26	expressive	expressive	ADJ
cana-6095	26	27	uq	uq	NOUN
cana-6095	26	28	frameworks	framework	NOUN
cana-6095	26	29	.	.	PUNCT
cana-6095	27	1	bayesian	bayesian	NOUN
cana-6095	27	2	neural	neural	ADJ
cana-6095	27	3	networks	network	NOUN
cana-6095	27	4	(	(	PUNCT
cana-6095	27	5	bnns	bnns	ADJ
cana-6095	27	6	)	)	PUNCT
cana-6095	27	7	represent	represent	VERB
cana-6095	27	8	a	a	DET
cana-6095	27	9	particularly	particularly	ADV
cana-6095	27	10	promising	promising	ADJ
cana-6095	27	11	approach	approach	NOUN
cana-6095	27	12	for	for	ADP
cana-6095	27	13	uq	uq	PROPN
cana-6095	27	14	in	in	ADP
cana-6095	27	15	numerical	numerical	ADJ
cana-6095	27	16	methods	method	NOUN
cana-6095	27	17	.	.	PUNCT
cana-6095	28	1	by	by	ADP
cana-6095	28	2	treating	treat	VERB
cana-6095	28	3	network	network	NOUN
cana-6095	28	4	weights	weight	NOUN
cana-6095	28	5	as	as	ADP
cana-6095	28	6	probability	probability	NOUN
cana-6095	28	7	distributions	distribution	NOUN
cana-6095	28	8	rather	rather	ADV
cana-6095	28	9	than	than	ADP
cana-6095	28	10	point	point	NOUN
cana-6095	28	11	estimates	estimate	NOUN
cana-6095	28	12	,	,	PUNCT
cana-6095	28	13	bnns	bnns	PROPN
cana-6095	28	14	naturally	naturally	ADV
cana-6095	28	15	capture	capture	VERB
cana-6095	28	16	both	both	DET
cana-6095	28	17	aleatoric	aleatoric	ADJ
cana-6095	28	18	uncertainty	uncertainty	NOUN
cana-6095	28	19	(	(	PUNCT
cana-6095	28	20	inherent	inherent	ADJ
cana-6095	28	21	randomness	randomness	NOUN
cana-6095	28	22	in	in	ADP
cana-6095	28	23	data	datum	NOUN
cana-6095	28	24	)	)	PUNCT
cana-6095	28	25	and	and	CCONJ
cana-6095	28	26	epistemic	epistemic	ADJ
cana-6095	28	27	uncertainty	uncertainty	NOUN
cana-6095	28	28	(	(	PUNCT
cana-6095	28	29	model	model	NOUN
cana-6095	28	30	uncertainty	uncertainty	NOUN
cana-6095	28	31	due	due	ADJ
cana-6095	28	32	to	to	ADP
cana-6095	28	33	limited	limited	ADJ
cana-6095	28	34	data	datum	NOUN
cana-6095	28	35	)	)	PUNCT
cana-6095	28	36	1,8	1,8	NOUN
cana-6095	28	37	.	.	PUNCT
cana-6095	29	1	this	this	DET
cana-6095	29	2	bayesian	bayesian	NOUN
cana-6095	29	3	framework	framework	NOUN
cana-6095	29	4	provides	provide	VERB
cana-6095	29	5	a	a	DET
cana-6095	29	6	principled	principled	ADJ
cana-6095	29	7	approach	approach	NOUN
cana-6095	29	8	to	to	ADP
cana-6095	29	9	uncertainty	uncertainty	NOUN
cana-6095	29	10	estimation	estimation	NOUN
cana-6095	29	11	that	that	PRON
cana-6095	29	12	can	can	AUX
cana-6095	29	13	be	be	AUX
cana-6095	29	14	integrated	integrate	VERB
cana-6095	29	15	with	with	ADP
cana-6095	29	16	various	various	ADJ
cana-6095	29	17	numerical	numerical	ADJ
cana-6095	29	18	techniques	technique	NOUN
cana-6095	29	19	,	,	PUNCT
cana-6095	29	20	from	from	ADP
cana-6095	29	21	solving	solve	VERB
cana-6095	29	22	partial	partial	ADJ
cana-6095	29	23	differential	differential	ADJ
cana-6095	29	24	equations	equation	NOUN
cana-6095	29	25	to	to	ADP
cana-6095	29	26	computing	compute	VERB
cana-6095	29	27	complex	complex	ADJ
cana-6095	29	28	integrals	integral	NOUN
cana-6095	29	29	5,10	5,10	NUM
cana-6095	29	30	.	.	PUNCT
cana-6095	30	1	the	the	DET
cana-6095	30	2	convergence	convergence	NOUN
cana-6095	30	3	of	of	ADP
cana-6095	30	4	bayesian	bayesian	NOUN
cana-6095	30	5	methods	method	NOUN
cana-6095	30	6	with	with	ADP
cana-6095	30	7	deep	deep	ADJ
cana-6095	30	8	learning	learning	NOUN
cana-6095	30	9	and	and	CCONJ
cana-6095	30	10	numerical	numerical	ADJ
cana-6095	30	11	computation	computation	NOUN
cana-6095	30	12	has	have	AUX
cana-6095	30	13	created	create	VERB
cana-6095	30	14	new	new	ADJ
cana-6095	30	15	opportunities	opportunity	NOUN
cana-6095	30	16	for	for	ADP
cana-6095	30	17	advancing	advance	VERB
cana-6095	30	18	scientific	scientific	ADJ
cana-6095	30	19	computing	computing	NOUN
cana-6095	30	20	.	.	PUNCT
cana-6095	31	1	physics	physics	NOUN
cana-6095	31	2	-	-	PUNCT
cana-6095	31	3	informed	inform	VERB
cana-6095	31	4	neural	neural	ADJ
cana-6095	31	5	networks	network	NOUN
cana-6095	31	6	(	(	PUNCT
cana-6095	31	7	pinns	pinns	ADJ
cana-6095	31	8	)	)	PUNCT
cana-6095	31	9	incorporate	incorporate	VERB
cana-6095	31	10	physical	physical	ADJ
cana-6095	31	11	constraints	constraint	NOUN
cana-6095	31	12	into	into	ADP
cana-6095	31	13	the	the	DET
cana-6095	31	14	learning	learning	NOUN
cana-6095	31	15	process	process	NOUN
cana-6095	31	16	,	,	PUNCT
cana-6095	31	17	while	while	SCONJ
cana-6095	31	18	bayesian	bayesian	NOUN
cana-6095	31	19	probabilistic	probabilistic	ADJ
cana-6095	31	20	numerical	numerical	ADJ
cana-6095	31	21	methods	method	NOUN
cana-6095	31	22	reformulate	reformulate	VERB
cana-6095	31	23	traditional	traditional	ADJ
cana-6095	31	24	numerical	numerical	ADJ
cana-6095	31	25	problems	problem	NOUN
cana-6095	31	26	as	as	ADP
cana-6095	31	27	statistical	statistical	ADJ
cana-6095	31	28	inference	inference	NOUN
cana-6095	31	29	tasks	task	NOUN
cana-6095	31	30	9,10	9,10	NUM
cana-6095	31	31	.	.	PUNCT
cana-6095	32	1	these	these	DET
cana-6095	32	2	approaches	approach	NOUN
cana-6095	32	3	enable	enable	VERB
cana-6095	32	4	not	not	PART
cana-6095	32	5	only	only	ADV
cana-6095	32	6	more	more	ADV
cana-6095	32	7	efficient	efficient	ADJ
cana-6095	32	8	computation	computation	NOUN
cana-6095	32	9	but	but	CCONJ
cana-6095	32	10	also	also	ADV
cana-6095	32	11	richer	rich	ADJ
cana-6095	32	12	uncertainty	uncertainty	NOUN
cana-6095	32	13	characterization	characterization	NOUN
cana-6095	32	14	than	than	ADP
cana-6095	32	15	traditional	traditional	ADJ
cana-6095	32	16	numerical	numerical	ADJ
cana-6095	32	17	methods	method	NOUN
cana-6095	32	18	.	.	PUNCT
cana-6095	33	1	this	this	DET
cana-6095	33	2	paper	paper	NOUN
cana-6095	33	3	provides	provide	VERB
cana-6095	33	4	a	a	DET
cana-6095	33	5	comprehensive	comprehensive	ADJ
cana-6095	33	6	examination	examination	NOUN
cana-6095	33	7	of	of	ADP
cana-6095	33	8	uq	uq	PROPN
cana-6095	33	9	in	in	ADP
cana-6095	33	10	numerical	numerical	ADJ
cana-6095	33	11	methods	method	NOUN
cana-6095	33	12	using	use	VERB
cana-6095	33	13	deep	deep	ADJ
cana-6095	33	14	bayesian	bayesian	NOUN
cana-6095	33	15	neural	neural	ADJ
cana-6095	33	16	networks	network	NOUN
cana-6095	33	17	.	.	PUNCT
cana-6095	34	1	we	we	PRON
cana-6095	34	2	review	review	VERB
cana-6095	34	3	theoretical	theoretical	ADJ
cana-6095	34	4	foundations	foundation	NOUN
cana-6095	34	5	,	,	PUNCT
cana-6095	34	6	architectural	architectural	ADJ
cana-6095	34	7	considerations	consideration	NOUN
cana-6095	34	8	,	,	PUNCT
cana-6095	34	9	inference	inference	NOUN
cana-6095	34	10	techniques	technique	NOUN
cana-6095	34	11	,	,	PUNCT
cana-6095	34	12	and	and	CCONJ
cana-6095	34	13	application	application	NOUN
cana-6095	34	14	domains	domain	NOUN
cana-6095	34	15	,	,	PUNCT
cana-6095	34	16	highlighting	highlight	VERB
cana-6095	34	17	both	both	PRON
cana-6095	34	18	current	current	ADJ
cana-6095	34	19	capabilities	capability	NOUN
cana-6095	34	20	and	and	CCONJ
cana-6095	34	21	persistent	persistent	ADJ
cana-6095	34	22	challenges	challenge	NOUN
cana-6095	34	23	.	.	PUNCT
cana-6095	35	1	through	through	ADP
cana-6095	35	2	this	this	DET
cana-6095	35	3	synthesis	synthesis	NOUN
cana-6095	35	4	,	,	PUNCT
cana-6095	35	5	we	we	PRON
cana-6095	35	6	aim	aim	VERB
cana-6095	35	7	to	to	PART
cana-6095	35	8	provide	provide	VERB
cana-6095	35	9	researchers	researcher	NOUN
cana-6095	35	10	and	and	CCONJ
cana-6095	35	11	practitioners	practitioner	NOUN
cana-6095	35	12	with	with	ADP
cana-6095	35	13	a	a	DET
cana-6095	35	14	foundation	foundation	NOUN
cana-6095	35	15	for	for	ADP
cana-6095	35	16	leveraging	leverage	VERB
cana-6095	35	17	bayesian	bayesian	NOUN
cana-6095	35	18	deep	deep	ADJ
cana-6095	35	19	learning	learning	NOUN
cana-6095	35	20	to	to	PART
cana-6095	35	21	enhance	enhance	VERB
cana-6095	35	22	uncertainty	uncertainty	NOUN
cana-6095	35	23	awareness	awareness	NOUN
cana-6095	35	24	in	in	ADP
cana-6095	35	25	numerical	numerical	ADJ
cana-6095	35	26	computation	computation	NOUN
cana-6095	35	27	while	while	SCONJ
cana-6095	35	28	identifying	identify	VERB
cana-6095	35	29	promising	promising	ADJ
cana-6095	35	30	directions	direction	NOUN
cana-6095	35	31	for	for	ADP
cana-6095	35	32	future	future	ADJ
cana-6095	35	33	research	research	NOUN
cana-6095	35	34	.	.	PUNCT
cana-6095	36	1	2.theoretical	2.theoretical	NUM
cana-6095	36	2	foundations	foundation	NOUN
cana-6095	36	3	2.1	2.1	NUM
cana-6095	36	4	bayesian	bayesian	NOUN
cana-6095	36	5	inference	inference	NOUN
cana-6095	36	6	and	and	CCONJ
cana-6095	36	7	probability	probability	NOUN
cana-6095	36	8	theory	theory	NOUN
cana-6095	36	9	bayesian	bayesian	NOUN
cana-6095	36	10	inference	inference	NOUN
cana-6095	36	11	provides	provide	VERB
cana-6095	36	12	a	a	DET
cana-6095	36	13	coherent	coherent	ADJ
cana-6095	36	14	probabilistic	probabilistic	ADJ
cana-6095	36	15	framework	framework	NOUN
cana-6095	36	16	for	for	ADP
cana-6095	36	17	updating	update	VERB
cana-6095	36	18	beliefs	belief	NOUN
cana-6095	36	19	based	base	VERB
cana-6095	36	20	on	on	ADP
cana-6095	36	21	observed	observed	ADJ
cana-6095	36	22	data	datum	NOUN
cana-6095	36	23	.	.	PUNCT
cana-6095	37	1	given	give	VERB
cana-6095	37	2	a	a	DET
cana-6095	37	3	prior	prior	ADJ
cana-6095	37	4	distribution	distribution	NOUN
cana-6095	37	5	p(ω	p(ω	PROPN
cana-6095	37	6	)	)	PUNCT
cana-6095	37	7	over	over	ADP
cana-6095	37	8	model	model	NOUN
cana-6095	37	9	parameters	parameter	NOUN
cana-6095	37	10	ω	ω	PROPN
cana-6095	37	11	and	and	CCONJ
cana-6095	37	12	a	a	DET
cana-6095	37	13	likelihood	likelihood	NOUN
cana-6095	37	14	function	function	NOUN
cana-6095	37	15	p(d|ω	p(d|ω	NOUN
cana-6095	37	16	)	)	PUNCT
cana-6095	37	17	representing	represent	VERB
cana-6095	37	18	the	the	DET
cana-6095	37	19	probability	probability	NOUN
cana-6095	37	20	of	of	ADP
cana-6095	37	21	observing	observe	VERB
cana-6095	37	22	data	datum	NOUN
cana-6095	37	23	d	d	NOUN
cana-6095	37	24	given	give	VERB
cana-6095	37	25	parameters	parameter	NOUN
cana-6095	37	26	ω	ω	PROPN
cana-6095	37	27	,	,	PUNCT
cana-6095	37	28	bayes	bayes	PROPN
cana-6095	37	29	'	'	PART
cana-6095	37	30	theorem	theorem	ADJ
cana-6095	37	31	yields	yield	NOUN
cana-6095	37	32	the	the	DET
cana-6095	37	33	posterior	posterior	ADJ
cana-6095	37	34	distribution	distribution	NOUN
cana-6095	37	35	:	:	PUNCT
cana-6095	37	36	p(ω|d	p(ω|d	NUM
cana-6095	37	37	)	)	PUNCT
cana-6095	37	38	=	=	SYM
cana-6095	37	39	p(d|ω)p(ω	p(d|ω)p(ω	NOUN
cana-6095	37	40	)	)	PUNCT
cana-6095	37	41	/	/	SYM
cana-6095	37	42	p(d	p(d	NOUN
cana-6095	37	43	)	)	PUNCT
cana-6095	37	44	where	where	SCONJ
cana-6095	37	45	p(d	p(d	NOUN
cana-6095	37	46	)	)	PUNCT
cana-6095	37	47	is	be	AUX
cana-6095	37	48	the	the	DET
cana-6095	37	49	marginal	marginal	ADJ
cana-6095	37	50	likelihood	likelihood	NOUN
cana-6095	37	51	or	or	CCONJ
cana-6095	37	52	evidence	evidence	NOUN
cana-6095	37	53	1,8	1,8	ADJ
cana-6095	37	54	.	.	PUNCT
cana-6095	38	1	this	this	DET
cana-6095	38	2	bayesian	bayesian	NOUN
cana-6095	38	3	approach	approach	NOUN
cana-6095	38	4	naturally	naturally	ADV
cana-6095	38	5	quantifies	quantify	VERB
cana-6095	38	6	uncertainty	uncertainty	NOUN
cana-6095	38	7	through	through	ADP
cana-6095	38	8	the	the	DET
cana-6095	38	9	entire	entire	ADJ
cana-6095	38	10	posterior	posterior	ADJ
cana-6095	38	11	distribution	distribution	NOUN
cana-6095	38	12	rather	rather	ADV
cana-6095	38	13	than	than	ADP
cana-6095	38	14	providing	provide	VERB
cana-6095	38	15	single	single	ADJ
cana-6095	38	16	point	point	NOUN
cana-6095	38	17	estimates	estimate	NOUN
cana-6095	38	18	.	.	PUNCT
cana-6095	39	1	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	39	2	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	NOUN
cana-6095	39	3	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	39	4	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	PROPN
cana-6095	39	5	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	39	6	https://arxiv.org/abs/2305.13248	https://arxiv.org/abs/2305.13248	PROPN
cana-6095	39	7	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	PROPN
cana-6095	39	8	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	39	9	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	NOUN
cana-6095	39	10	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	40	1	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	40	2	communications	communication	NOUN
cana-6095	40	3	on	on	ADP
cana-6095	40	4	applied	apply	VERB
cana-6095	40	5	nonlinear	nonlinear	ADJ
cana-6095	40	6	analysis	analysis	NOUN
cana-6095	40	7	issn	issn	NOUN
cana-6095	40	8	:	:	PUNCT
cana-6095	40	9	1074	1074	NUM
cana-6095	40	10	-	-	PUNCT
cana-6095	40	11	133x	133x	NUM
cana-6095	40	12	vol	vol	NOUN
cana-6095	40	13	30	30	NUM
cana-6095	40	14	no	no	NOUN
cana-6095	40	15	.	.	NOUN
cana-6095	40	16	3	3	NUM
cana-6095	40	17	(	(	PUNCT
cana-6095	40	18	2023	2023	NUM
cana-6095	40	19	)	)	PUNCT
cana-6095	41	1	58	58	NUM
cana-6095	41	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	41	3	in	in	ADP
cana-6095	41	4	the	the	DET
cana-6095	41	5	context	context	NOUN
cana-6095	41	6	of	of	ADP
cana-6095	41	7	neural	neural	ADJ
cana-6095	41	8	networks	network	NOUN
cana-6095	41	9	,	,	PUNCT
cana-6095	41	10	the	the	DET
cana-6095	41	11	parameters	parameter	NOUN
cana-6095	41	12	ω	ω	PROPN
cana-6095	41	13	represent	represent	VERB
cana-6095	41	14	weights	weight	NOUN
cana-6095	41	15	and	and	CCONJ
cana-6095	41	16	biases	bias	NOUN
cana-6095	41	17	,	,	PUNCT
cana-6095	41	18	and	and	CCONJ
cana-6095	41	19	the	the	DET
cana-6095	41	20	posterior	posterior	ADJ
cana-6095	41	21	p(ω|d	p(ω|d	NOUN
cana-6095	41	22	)	)	PUNCT
cana-6095	41	23	captures	capture	VERB
cana-6095	41	24	uncertainty	uncertainty	NOUN
cana-6095	41	25	about	about	ADP
cana-6095	41	26	these	these	DET
cana-6095	41	27	parameters	parameter	NOUN
cana-6095	41	28	after	after	ADP
cana-6095	41	29	observing	observe	VERB
cana-6095	41	30	data	datum	NOUN
cana-6095	41	31	d.	d.	NOUN
cana-6095	41	32	predictions	prediction	NOUN
cana-6095	41	33	for	for	ADP
cana-6095	41	34	new	new	ADJ
cana-6095	41	35	inputs	input	NOUN
cana-6095	41	36	x	x	PRON
cana-6095	41	37	are	be	AUX
cana-6095	41	38	made	make	VERB
cana-6095	41	39	through	through	ADP
cana-6095	41	40	bayesian	bayesian	NOUN
cana-6095	41	41	model	model	NOUN
cana-6095	41	42	averaging	averaging	NOUN
cana-6095	41	43	:	:	PUNCT
cana-6095	41	44	p(y|x	p(y|x	NOUN
cana-6095	41	45	,	,	PUNCT
cana-6095	41	46	d	d	NOUN
cana-6095	41	47	)	)	PUNCT
cana-6095	41	48	=	=	SYM
cana-6095	41	49	∫	∫	PROPN
cana-6095	41	50	p(y|x	p(y|x	PROPN
cana-6095	41	51	,	,	PUNCT
cana-6095	41	52	ω	ω	NOUN
cana-6095	41	53	)	)	PUNCT
cana-6095	41	54	p(ω|d	p(ω|d	NUM
cana-6095	41	55	)	)	PUNCT
cana-6095	41	56	dω	dω	ADP
cana-6095	41	57	this	this	DET
cana-6095	41	58	integral	integral	ADJ
cana-6095	41	59	accounts	account	NOUN
cana-6095	41	60	for	for	ADP
cana-6095	41	61	all	all	DET
cana-6095	41	62	possible	possible	ADJ
cana-6095	41	63	models	model	NOUN
cana-6095	41	64	weighted	weight	VERB
cana-6095	41	65	by	by	ADP
cana-6095	41	66	their	their	PRON
cana-6095	41	67	posterior	posterior	ADJ
cana-6095	41	68	probabilities	probability	NOUN
cana-6095	41	69	,	,	PUNCT
cana-6095	41	70	providing	provide	VERB
cana-6095	41	71	a	a	DET
cana-6095	41	72	complete	complete	ADJ
cana-6095	41	73	predictive	predictive	ADJ
cana-6095	41	74	distribution	distribution	NOUN
cana-6095	41	75	that	that	PRON
cana-6095	41	76	incorporates	incorporate	VERB
cana-6095	41	77	both	both	CCONJ
cana-6095	41	78	aleatoric	aleatoric	ADJ
cana-6095	41	79	and	and	CCONJ
cana-6095	41	80	epistemic	epistemic	ADJ
cana-6095	41	81	uncertainties	uncertainty	NOUN
cana-6095	41	82	1,6	1,6	NUM
cana-6095	41	83	.	.	PUNCT
cana-6095	42	1	2.2	2.2	NUM
cana-6095	42	2	neural	neural	ADJ
cana-6095	42	3	networks	network	NOUN
cana-6095	42	4	as	as	ADP
cana-6095	42	5	function	function	NOUN
cana-6095	42	6	approximators	approximator	NOUN
cana-6095	42	7	deep	deep	ADJ
cana-6095	42	8	neural	neural	ADJ
cana-6095	42	9	networks	network	NOUN
cana-6095	42	10	(	(	PUNCT
cana-6095	42	11	dnns	dnn	NOUN
cana-6095	42	12	)	)	PUNCT
cana-6095	42	13	are	be	AUX
cana-6095	42	14	powerful	powerful	ADJ
cana-6095	42	15	function	function	NOUN
cana-6095	42	16	approximators	approximator	NOUN
cana-6095	42	17	that	that	PRON
cana-6095	42	18	can	can	AUX
cana-6095	42	19	learn	learn	VERB
cana-6095	42	20	complex	complex	ADJ
cana-6095	42	21	mappings	mapping	NOUN
cana-6095	42	22	from	from	ADP
cana-6095	42	23	inputs	input	NOUN
cana-6095	42	24	to	to	ADP
cana-6095	42	25	outputs	output	NOUN
cana-6095	42	26	.	.	PUNCT
cana-6095	43	1	a	a	DET
cana-6095	43	2	neural	neural	ADJ
cana-6095	43	3	network	network	NOUN
cana-6095	43	4	f(x	f(x	PROPN
cana-6095	43	5	;	;	PUNCT
cana-6095	43	6	ω	ω	NUM
cana-6095	43	7	)	)	PUNCT
cana-6095	43	8	with	with	ADP
cana-6095	43	9	parameters	parameter	NOUN
cana-6095	43	10	ω	ω	PROPN
cana-6095	43	11	transforms	transform	VERB
cana-6095	43	12	input	input	NOUN
cana-6095	43	13	x	x	PUNCT
cana-6095	43	14	through	through	ADP
cana-6095	43	15	a	a	DET
cana-6095	43	16	series	series	NOUN
cana-6095	43	17	of	of	ADP
cana-6095	43	18	layered	layered	ADJ
cana-6095	43	19	transformations	transformation	NOUN
cana-6095	43	20	,	,	PUNCT
cana-6095	43	21	typically	typically	ADV
cana-6095	43	22	using	use	VERB
cana-6095	43	23	nonlinear	nonlinear	ADJ
cana-6095	43	24	activation	activation	NOUN
cana-6095	43	25	functions	function	NOUN
cana-6095	43	26	.	.	PUNCT
cana-6095	44	1	the	the	DET
cana-6095	44	2	universal	universal	ADJ
cana-6095	44	3	approximation	approximation	NOUN
cana-6095	44	4	theorem	theorem	NOUN
cana-6095	44	5	guarantees	guarantee	NOUN
cana-6095	44	6	that	that	SCONJ
cana-6095	44	7	sufficiently	sufficiently	ADV
cana-6095	44	8	large	large	ADJ
cana-6095	44	9	neural	neural	ADJ
cana-6095	44	10	networks	network	NOUN
cana-6095	44	11	can	can	AUX
cana-6095	44	12	approximate	approximate	VERB
cana-6095	44	13	any	any	DET
cana-6095	44	14	continuous	continuous	ADJ
cana-6095	44	15	function	function	NOUN
cana-6095	44	16	to	to	ADP
cana-6095	44	17	arbitrary	arbitrary	ADJ
cana-6095	44	18	accuracy	accuracy	NOUN
cana-6095	44	19	8,9	8,9	NUM
cana-6095	44	20	.	.	PUNCT
cana-6095	45	1	however	however	ADV
cana-6095	45	2	,	,	PUNCT
cana-6095	45	3	traditional	traditional	ADJ
cana-6095	45	4	dnns	dnn	NOUN
cana-6095	45	5	are	be	AUX
cana-6095	45	6	trained	train	VERB
cana-6095	45	7	using	use	VERB
cana-6095	45	8	optimization	optimization	NOUN
cana-6095	45	9	procedures	procedure	NOUN
cana-6095	45	10	that	that	PRON
cana-6095	45	11	find	find	VERB
cana-6095	45	12	point	point	NOUN
cana-6095	45	13	estimates	estimate	NOUN
cana-6095	45	14	of	of	ADP
cana-6095	45	15	parameters	parameter	NOUN
cana-6095	45	16	ω	ω	PROPN
cana-6095	45	17	,	,	PUNCT
cana-6095	45	18	providing	provide	VERB
cana-6095	45	19	no	no	DET
cana-6095	45	20	inherent	inherent	ADJ
cana-6095	45	21	uncertainty	uncertainty	NOUN
cana-6095	45	22	quantification	quantification	NOUN
cana-6095	45	23	.	.	PUNCT
cana-6095	46	1	these	these	DET
cana-6095	46	2	models	model	NOUN
cana-6095	46	3	often	often	ADV
cana-6095	46	4	produce	produce	VERB
cana-6095	46	5	overconfident	overconfident	ADJ
cana-6095	46	6	predictions	prediction	NOUN
cana-6095	46	7	on	on	ADP
cana-6095	46	8	outof	outof	NOUN
cana-6095	46	9	-	-	PUNCT
cana-6095	46	10	distribution	distribution	NOUN
cana-6095	46	11	data	datum	NOUN
cana-6095	46	12	and	and	CCONJ
cana-6095	46	13	may	may	AUX
cana-6095	46	14	fail	fail	VERB
cana-6095	46	15	to	to	PART
cana-6095	46	16	indicate	indicate	VERB
cana-6095	46	17	when	when	SCONJ
cana-6095	46	18	their	their	PRON
cana-6095	46	19	predictions	prediction	NOUN
cana-6095	46	20	are	be	AUX
cana-6095	46	21	unreliable	unreliable	ADJ
cana-6095	46	22	1,8	1,8	NOUN
cana-6095	46	23	.	.	PUNCT
cana-6095	47	1	bayesian	bayesian	NOUN
cana-6095	47	2	neural	neural	ADJ
cana-6095	47	3	networks	network	NOUN
cana-6095	47	4	address	address	VERB
cana-6095	47	5	these	these	DET
cana-6095	47	6	limitations	limitation	NOUN
cana-6095	47	7	by	by	ADP
cana-6095	47	8	maintaining	maintain	VERB
cana-6095	47	9	probability	probability	NOUN
cana-6095	47	10	distributions	distribution	NOUN
cana-6095	47	11	over	over	ADP
cana-6095	47	12	parameters	parameter	NOUN
cana-6095	47	13	rather	rather	ADV
cana-6095	47	14	than	than	ADP
cana-6095	47	15	point	point	NOUN
cana-6095	47	16	estimates	estimate	NOUN
cana-6095	47	17	.	.	PUNCT
cana-6095	48	1	2.3	2.3	NUM
cana-6095	48	2	uncertainty	uncertainty	NOUN
cana-6095	48	3	quantification	quantification	NOUN
cana-6095	48	4	principles	principle	NOUN
cana-6095	48	5	in	in	ADP
cana-6095	48	6	numerical	numerical	ADJ
cana-6095	48	7	methods	method	NOUN
cana-6095	48	8	,	,	PUNCT
cana-6095	48	9	uncertainty	uncertainty	NOUN
cana-6095	48	10	arises	arise	VERB
cana-6095	48	11	from	from	ADP
cana-6095	48	12	various	various	ADJ
cana-6095	48	13	sources	source	NOUN
cana-6095	48	14	including	include	VERB
cana-6095	48	15	approximation	approximation	NOUN
cana-6095	48	16	errors	error	NOUN
cana-6095	48	17	(	(	PUNCT
cana-6095	48	18	discretization	discretization	NOUN
cana-6095	48	19	,	,	PUNCT
cana-6095	48	20	truncation	truncation	NOUN
cana-6095	48	21	)	)	PUNCT
cana-6095	48	22	,	,	PUNCT
cana-6095	48	23	input	input	NOUN
cana-6095	48	24	uncertainties	uncertainty	NOUN
cana-6095	48	25	(	(	PUNCT
cana-6095	48	26	parameter	parameter	NOUN
cana-6095	48	27	variability	variability	NOUN
cana-6095	48	28	,	,	PUNCT
cana-6095	48	29	measurement	measurement	NOUN
cana-6095	48	30	noise	noise	NOUN
cana-6095	48	31	)	)	PUNCT
cana-6095	48	32	,	,	PUNCT
cana-6095	48	33	and	and	CCONJ
cana-6095	48	34	model	model	NOUN
cana-6095	48	35	discrepancies	discrepancy	NOUN
cana-6095	48	36	(	(	PUNCT
cana-6095	48	37	simplified	simplified	ADJ
cana-6095	48	38	physics	physics	NOUN
cana-6095	48	39	,	,	PUNCT
cana-6095	48	40	missing	miss	VERB
cana-6095	48	41	processes	process	NOUN
cana-6095	48	42	)	)	PUNCT
cana-6095	48	43	9	9	NUM
cana-6095	48	44	.	.	X
cana-6095	49	1	uq	uq	NOUN
cana-6095	49	2	seeks	seek	VERB
cana-6095	49	3	to	to	PART
cana-6095	49	4	characterize	characterize	VERB
cana-6095	49	5	these	these	DET
cana-6095	49	6	uncertainties	uncertainty	NOUN
cana-6095	49	7	and	and	CCONJ
cana-6095	49	8	their	their	PRON
cana-6095	49	9	impact	impact	NOUN
cana-6095	49	10	on	on	ADP
cana-6095	49	11	computational	computational	ADJ
cana-6095	49	12	results	result	NOUN
cana-6095	49	13	.	.	PUNCT
cana-6095	50	1	aleatoric	aleatoric	ADJ
cana-6095	50	2	uncertainty	uncertainty	NOUN
cana-6095	50	3	represents	represent	VERB
cana-6095	50	4	inherent	inherent	ADJ
cana-6095	50	5	randomness	randomness	NOUN
cana-6095	50	6	in	in	ADP
cana-6095	50	7	the	the	DET
cana-6095	50	8	system	system	NOUN
cana-6095	50	9	being	be	AUX
cana-6095	50	10	modeled	model	VERB
cana-6095	50	11	,	,	PUNCT
cana-6095	50	12	such	such	ADJ
cana-6095	50	13	as	as	ADP
cana-6095	50	14	stochastic	stochastic	ADJ
cana-6095	50	15	forcing	forcing	NOUN
cana-6095	50	16	in	in	ADP
cana-6095	50	17	physical	physical	ADJ
cana-6095	50	18	systems	system	NOUN
cana-6095	50	19	or	or	CCONJ
cana-6095	50	20	measurement	measurement	NOUN
cana-6095	50	21	noise	noise	NOUN
cana-6095	50	22	in	in	ADP
cana-6095	50	23	experimental	experimental	ADJ
cana-6095	50	24	data	datum	NOUN
cana-6095	50	25	.	.	PUNCT
cana-6095	51	1	this	this	DET
cana-6095	51	2	uncertainty	uncertainty	NOUN
cana-6095	51	3	is	be	AUX
cana-6095	51	4	irreducible	irreducible	ADJ
cana-6095	51	5	with	with	ADP
cana-6095	51	6	more	more	ADJ
cana-6095	51	7	data	datum	NOUN
cana-6095	51	8	but	but	CCONJ
cana-6095	51	9	can	can	AUX
cana-6095	51	10	be	be	AUX
cana-6095	51	11	characterized	characterize	VERB
cana-6095	51	12	statistically	statistically	ADV
cana-6095	51	13	1,6	1,6	NUM
cana-6095	51	14	.	.	PUNCT
cana-6095	52	1	epistemic	epistemic	ADJ
cana-6095	52	2	uncertainty	uncertainty	NOUN
cana-6095	52	3	arises	arise	VERB
cana-6095	52	4	from	from	ADP
cana-6095	52	5	limited	limited	ADJ
cana-6095	52	6	knowledge	knowledge	NOUN
cana-6095	52	7	or	or	CCONJ
cana-6095	52	8	data	datum	NOUN
cana-6095	52	9	about	about	ADP
cana-6095	52	10	the	the	DET
cana-6095	52	11	system	system	NOUN
cana-6095	52	12	.	.	PUNCT
cana-6095	53	1	this	this	PRON
cana-6095	53	2	includes	include	VERB
cana-6095	53	3	uncertainty	uncertainty	NOUN
cana-6095	53	4	about	about	ADP
cana-6095	53	5	model	model	NOUN
cana-6095	53	6	parameters	parameter	NOUN
cana-6095	53	7	,	,	PUNCT
cana-6095	53	8	appropriate	appropriate	ADJ
cana-6095	53	9	model	model	NOUN
cana-6095	53	10	structure	structure	NOUN
cana-6095	53	11	,	,	PUNCT
cana-6095	53	12	or	or	CCONJ
cana-6095	53	13	boundary	boundary	ADJ
cana-6095	53	14	conditions	condition	NOUN
cana-6095	53	15	.	.	PUNCT
cana-6095	54	1	unlike	unlike	ADP
cana-6095	54	2	aleatoric	aleatoric	ADJ
cana-6095	54	3	uncertainty	uncertainty	NOUN
cana-6095	54	4	,	,	PUNCT
cana-6095	54	5	epistemic	epistemic	ADJ
cana-6095	54	6	uncertainty	uncertainty	NOUN
cana-6095	54	7	can	can	AUX
cana-6095	54	8	be	be	AUX
cana-6095	54	9	reduced	reduce	VERB
cana-6095	54	10	with	with	ADP
cana-6095	54	11	additional	additional	ADJ
cana-6095	54	12	information	information	NOUN
cana-6095	54	13	or	or	CCONJ
cana-6095	54	14	data	datum	NOUN
cana-6095	54	15	1,6	1,6	NUM
cana-6095	54	16	.	.	PUNCT
cana-6095	55	1	uncertainty	uncertainty	NOUN
cana-6095	55	2	type	type	VERB
cana-6095	55	3	nature	nature	NOUN
cana-6095	55	4	reducibility	reducibility	NOUN
cana-6095	55	5	representation	representation	NOUN
cana-6095	55	6	in	in	ADP
cana-6095	55	7	bnns	bnns	PROPN
cana-6095	55	8	aleatoric	aleatoric	ADJ
cana-6095	55	9	inherent	inherent	ADJ
cana-6095	55	10	randomness	randomness	NOUN
cana-6095	55	11	in	in	ADP
cana-6095	55	12	data	datum	NOUN
cana-6095	55	13	irreducible	irreducible	ADJ
cana-6095	55	14	likelihood	likelihood	NOUN
cana-6095	55	15	function	function	NOUN
cana-6095	55	16	epistemic	epistemic	ADJ
cana-6095	55	17	model	model	NOUN
cana-6095	55	18	uncertainty	uncertainty	NOUN
cana-6095	55	19	due	due	ADJ
cana-6095	55	20	to	to	ADP
cana-6095	55	21	limited	limited	ADJ
cana-6095	55	22	knowledge	knowledge	NOUN
cana-6095	55	23	reducible	reducible	ADJ
cana-6095	55	24	with	with	ADP
cana-6095	55	25	more	more	ADJ
cana-6095	55	26	data	datum	NOUN
cana-6095	55	27	posterior	posterior	ADJ
cana-6095	55	28	over	over	ADP
cana-6095	55	29	parameters	parameter	NOUN
cana-6095	55	30	approximation	approximation	NOUN
cana-6095	55	31	discretization	discretization	NOUN
cana-6095	55	32	and	and	CCONJ
cana-6095	55	33	truncation	truncation	NOUN
cana-6095	55	34	errors	error	NOUN
cana-6095	55	35	reducible	reducible	ADJ
cana-6095	55	36	with	with	ADP
cana-6095	55	37	finer	fine	ADJ
cana-6095	55	38	resolution	resolution	NOUN
cana-6095	55	39	model	model	NOUN
cana-6095	55	40	discrepancy	discrepancy	NOUN
cana-6095	55	41	terms	term	VERB
cana-6095	55	42	parametric	parametric	ADJ
cana-6095	55	43	uncertainty	uncertainty	NOUN
cana-6095	55	44	in	in	ADP
cana-6095	55	45	input	input	NOUN
cana-6095	55	46	parameters	parameter	NOUN
cana-6095	55	47	reducible	reducible	ADJ
cana-6095	55	48	with	with	ADP
cana-6095	55	49	better	well	ADJ
cana-6095	55	50	characterization	characterization	NOUN
cana-6095	55	51	prior	prior	ADJ
cana-6095	55	52	distributions	distribution	NOUN
cana-6095	55	53	table	table	NOUN
cana-6095	55	54	1	1	NUM
cana-6095	55	55	:	:	PUNCT
cana-6095	55	56	types	type	NOUN
cana-6095	55	57	of	of	ADP
cana-6095	55	58	uncertainty	uncertainty	NOUN
cana-6095	55	59	in	in	ADP
cana-6095	55	60	numerical	numerical	ADJ
cana-6095	55	61	computation	computation	NOUN
cana-6095	55	62	3.bayesian	3.bayesian	NUM
cana-6095	55	63	neural	neural	ADJ
cana-6095	55	64	networks	network	NOUN
cana-6095	55	65	for	for	ADP
cana-6095	55	66	uq	uq	PROPN
cana-6095	55	67	3.1	3.1	NUM
cana-6095	55	68	architectural	architectural	ADJ
cana-6095	55	69	considerations	consideration	NOUN
cana-6095	55	70	bayesian	bayesian	NOUN
cana-6095	55	71	neural	neural	ADJ
cana-6095	55	72	networks	network	NOUN
cana-6095	55	73	can	can	AUX
cana-6095	55	74	be	be	AUX
cana-6095	55	75	implemented	implement	VERB
cana-6095	55	76	with	with	ADP
cana-6095	55	77	various	various	ADJ
cana-6095	55	78	architectural	architectural	ADJ
cana-6095	55	79	choices	choice	NOUN
cana-6095	55	80	that	that	PRON
cana-6095	55	81	influence	influence	VERB
cana-6095	55	82	their	their	PRON
cana-6095	55	83	expressiveness	expressiveness	NOUN
cana-6095	55	84	and	and	CCONJ
cana-6095	55	85	computational	computational	ADJ
cana-6095	55	86	requirements	requirement	NOUN
cana-6095	55	87	.	.	PUNCT
cana-6095	56	1	the	the	DET
cana-6095	56	2	core	core	ADJ
cana-6095	56	3	idea	idea	NOUN
cana-6095	56	4	involves	involve	VERB
cana-6095	56	5	replacing	replace	VERB
cana-6095	56	6	deterministic	deterministic	ADJ
cana-6095	56	7	weight	weight	NOUN
cana-6095	56	8	matrices	matrix	NOUN
cana-6095	56	9	with	with	ADP
cana-6095	56	10	probability	probability	NOUN
cana-6095	56	11	distributions	distribution	NOUN
cana-6095	56	12	,	,	PUNCT
cana-6095	56	13	typically	typically	ADV
cana-6095	56	14	gaussian	gaussian	ADJ
cana-6095	56	15	or	or	CCONJ
cana-6095	56	16	other	other	ADJ
cana-6095	56	17	tractable	tractable	ADJ
cana-6095	56	18	families	family	NOUN
cana-6095	56	19	8	8	NUM
cana-6095	56	20	.	.	PUNCT
cana-6095	57	1	several	several	ADJ
cana-6095	57	2	architectural	architectural	ADJ
cana-6095	57	3	variants	variant	NOUN
cana-6095	57	4	have	have	AUX
cana-6095	57	5	been	be	AUX
cana-6095	57	6	developed	develop	VERB
cana-6095	57	7	for	for	ADP
cana-6095	57	8	different	different	ADJ
cana-6095	57	9	numerical	numerical	ADJ
cana-6095	57	10	applications	application	NOUN
cana-6095	57	11	:	:	PUNCT
cana-6095	57	12	bayesian	bayesian	NOUN
cana-6095	57	13	convolutional	convolutional	ADJ
cana-6095	57	14	neural	neural	ADJ
cana-6095	57	15	networks	network	NOUN
cana-6095	57	16	incorporate	incorporate	VERB
cana-6095	57	17	probabilistic	probabilistic	ADJ
cana-6095	57	18	weights	weight	NOUN
cana-6095	57	19	into	into	ADP
cana-6095	57	20	convolutional	convolutional	ADJ
cana-6095	57	21	layers	layer	NOUN
cana-6095	57	22	,	,	PUNCT
cana-6095	57	23	making	make	VERB
cana-6095	57	24	them	they	PRON
cana-6095	57	25	suitable	suitable	ADJ
cana-6095	57	26	for	for	ADP
cana-6095	57	27	spatial	spatial	ADJ
cana-6095	57	28	data	datum	NOUN
cana-6095	57	29	such	such	ADJ
cana-6095	57	30	as	as	ADP
cana-6095	57	31	computational	computational	ADJ
cana-6095	57	32	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	57	33	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	57	34	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	57	35	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	57	36	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	PROPN
cana-6095	57	37	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	57	38	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	NUM
cana-6095	57	39	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	57	40	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	PROPN
cana-6095	57	41	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	PROPN
cana-6095	57	42	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	VERB
cana-6095	57	43	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	57	44	communications	communication	NOUN
cana-6095	57	45	on	on	ADP
cana-6095	57	46	applied	apply	VERB
cana-6095	57	47	nonlinear	nonlinear	ADJ
cana-6095	57	48	analysis	analysis	NOUN
cana-6095	57	49	issn	issn	NOUN
cana-6095	57	50	:	:	PUNCT
cana-6095	57	51	1074	1074	NUM
cana-6095	57	52	-	-	PUNCT
cana-6095	57	53	133x	133x	NUM
cana-6095	57	54	vol	vol	NOUN
cana-6095	57	55	30	30	NUM
cana-6095	58	1	no	no	NOUN
cana-6095	58	2	.	.	NOUN
cana-6095	58	3	3	3	NUM
cana-6095	58	4	(	(	PUNCT
cana-6095	58	5	2023	2023	NUM
cana-6095	58	6	)	)	PUNCT
cana-6095	58	7	59	59	NUM
cana-6095	58	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	58	9	grids	grid	NOUN
cana-6095	58	10	or	or	CCONJ
cana-6095	58	11	imaging	imaging	NOUN
cana-6095	58	12	data	datum	NOUN
cana-6095	58	13	from	from	ADP
cana-6095	58	14	numerical	numerical	ADJ
cana-6095	58	15	simulations	simulation	NOUN
cana-6095	58	16	1,6	1,6	NUM
cana-6095	58	17	.	.	PUNCT
cana-6095	59	1	these	these	DET
cana-6095	59	2	architectures	architecture	NOUN
cana-6095	59	3	can	can	AUX
cana-6095	59	4	capture	capture	VERB
cana-6095	59	5	uncertainty	uncertainty	NOUN
cana-6095	59	6	in	in	ADP
cana-6095	59	7	spatial	spatial	ADJ
cana-6095	59	8	predictions	prediction	NOUN
cana-6095	59	9	,	,	PUNCT
cana-6095	59	10	which	which	PRON
cana-6095	59	11	is	be	AUX
cana-6095	59	12	particularly	particularly	ADV
cana-6095	59	13	valuable	valuable	ADJ
cana-6095	59	14	for	for	ADP
cana-6095	59	15	pde	pde	NOUN
cana-6095	59	16	solutions	solution	NOUN
cana-6095	59	17	and	and	CCONJ
cana-6095	59	18	field	field	NOUN
cana-6095	59	19	predictions	prediction	NOUN
cana-6095	59	20	.	.	PUNCT
cana-6095	60	1	bayesian	bayesian	NOUN
cana-6095	60	2	physics	physics	NOUN
cana-6095	60	3	-	-	PUNCT
cana-6095	60	4	informed	inform	VERB
cana-6095	60	5	neural	neural	ADJ
cana-6095	60	6	networks	network	NOUN
cana-6095	60	7	(	(	PUNCT
cana-6095	60	8	b	b	NOUN
cana-6095	60	9	-	-	PUNCT
cana-6095	60	10	pinns	pinns	ADJ
cana-6095	60	11	)	)	PUNCT
cana-6095	60	12	integrate	integrate	VERB
cana-6095	60	13	physical	physical	ADJ
cana-6095	60	14	constraints	constraint	NOUN
cana-6095	60	15	into	into	ADP
cana-6095	60	16	bayesian	bayesian	NOUN
cana-6095	60	17	neural	neural	ADJ
cana-6095	60	18	networks	network	NOUN
cana-6095	60	19	by	by	ADP
cana-6095	60	20	incorporating	incorporate	VERB
cana-6095	60	21	governing	govern	VERB
cana-6095	60	22	equations	equation	NOUN
cana-6095	60	23	into	into	ADP
cana-6095	60	24	the	the	DET
cana-6095	60	25	likelihood	likelihood	NOUN
cana-6095	60	26	or	or	CCONJ
cana-6095	60	27	through	through	ADP
cana-6095	60	28	specialized	specialized	ADJ
cana-6095	60	29	regularization	regularization	NOUN
cana-6095	60	30	terms	term	NOUN
cana-6095	60	31	9	9	NUM
cana-6095	60	32	.	.	PUNCT
cana-6095	61	1	this	this	DET
cana-6095	61	2	approach	approach	NOUN
cana-6095	61	3	ensures	ensure	VERB
cana-6095	61	4	that	that	SCONJ
cana-6095	61	5	predictions	prediction	NOUN
cana-6095	61	6	respect	respect	VERB
cana-6095	61	7	physical	physical	ADJ
cana-6095	61	8	laws	law	NOUN
cana-6095	61	9	while	while	SCONJ
cana-6095	61	10	providing	provide	VERB
cana-6095	61	11	uncertainty	uncertainty	NOUN
cana-6095	61	12	estimates	estimate	NOUN
cana-6095	61	13	,	,	PUNCT
cana-6095	61	14	making	make	VERB
cana-6095	61	15	them	they	PRON
cana-6095	61	16	valuable	valuable	ADJ
cana-6095	61	17	for	for	ADP
cana-6095	61	18	scientific	scientific	ADJ
cana-6095	61	19	applications	application	NOUN
cana-6095	61	20	with	with	ADP
cana-6095	61	21	limited	limited	ADJ
cana-6095	61	22	data	datum	NOUN
cana-6095	61	23	.	.	PUNCT
cana-6095	62	1	infinite	infinite	ADJ
cana-6095	62	2	-	-	PUNCT
cana-6095	62	3	depth	depth	NOUN
cana-6095	62	4	bayesian	bayesian	NOUN
cana-6095	62	5	networks	network	NOUN
cana-6095	62	6	leverage	leverage	VERB
cana-6095	62	7	continuous	continuous	ADJ
cana-6095	62	8	-	-	PUNCT
cana-6095	62	9	depth	depth	NOUN
cana-6095	62	10	models	model	NOUN
cana-6095	62	11	formulated	formulate	VERB
cana-6095	62	12	as	as	ADP
cana-6095	62	13	stochastic	stochastic	ADJ
cana-6095	62	14	differential	differential	ADJ
cana-6095	62	15	equations	equation	NOUN
cana-6095	62	16	,	,	PUNCT
cana-6095	62	17	providing	provide	VERB
cana-6095	62	18	a	a	DET
cana-6095	62	19	framework	framework	NOUN
cana-6095	62	20	for	for	ADP
cana-6095	62	21	uncertainty	uncertainty	NOUN
cana-6095	62	22	quantification	quantification	NOUN
cana-6095	62	23	in	in	ADP
cana-6095	62	24	deep	deep	ADJ
cana-6095	62	25	networks	network	NOUN
cana-6095	62	26	with	with	ADP
cana-6095	62	27	potentially	potentially	ADV
cana-6095	62	28	infinite	infinite	ADJ
cana-6095	62	29	layers	layer	NOUN
cana-6095	62	30	3	3	NUM
cana-6095	62	31	.	.	PUNCT
cana-6095	63	1	these	these	DET
cana-6095	63	2	approaches	approach	NOUN
cana-6095	63	3	bring	bring	VERB
cana-6095	63	4	continuous	continuous	ADJ
cana-6095	63	5	-	-	PUNCT
cana-6095	63	6	depth	depth	ADJ
cana-6095	63	7	bayesian	bayesian	NOUN
cana-6095	63	8	neural	neural	ADJ
cana-6095	63	9	nets	net	NOUN
cana-6095	63	10	to	to	PART
cana-6095	63	11	competitive	competitive	ADJ
cana-6095	63	12	performance	performance	NOUN
cana-6095	63	13	against	against	ADP
cana-6095	63	14	discrete	discrete	ADJ
cana-6095	63	15	-	-	PUNCT
cana-6095	63	16	depth	depth	NOUN
cana-6095	63	17	alternatives	alternative	NOUN
cana-6095	63	18	while	while	SCONJ
cana-6095	63	19	inheriting	inherit	VERB
cana-6095	63	20	memoryefficient	memoryefficient	NOUN
cana-6095	63	21	training	training	NOUN
cana-6095	63	22	.	.	PUNCT
cana-6095	64	1	3.2	3.2	NUM
cana-6095	64	2	inference	inference	NOUN
cana-6095	64	3	methods	method	NOUN
cana-6095	64	4	performing	perform	VERB
cana-6095	64	5	exact	exact	ADJ
cana-6095	64	6	bayesian	bayesian	NOUN
cana-6095	64	7	inference	inference	NOUN
cana-6095	64	8	in	in	ADP
cana-6095	64	9	deep	deep	ADJ
cana-6095	64	10	neural	neural	ADJ
cana-6095	64	11	networks	network	NOUN
cana-6095	64	12	is	be	AUX
cana-6095	64	13	computationally	computationally	ADV
cana-6095	64	14	challenging	challenging	ADJ
cana-6095	64	15	due	due	ADJ
cana-6095	64	16	to	to	ADP
cana-6095	64	17	the	the	DET
cana-6095	64	18	highdimensional	highdimensional	ADJ
cana-6095	64	19	parameter	parameter	NOUN
cana-6095	64	20	space	space	NOUN
cana-6095	64	21	and	and	CCONJ
cana-6095	64	22	complex	complex	ADJ
cana-6095	64	23	posterior	posterior	ADJ
cana-6095	64	24	landscapes	landscape	NOUN
cana-6095	64	25	.	.	PUNCT
cana-6095	65	1	several	several	ADJ
cana-6095	65	2	approximate	approximate	ADJ
cana-6095	65	3	inference	inference	NOUN
cana-6095	65	4	methods	method	NOUN
cana-6095	65	5	have	have	AUX
cana-6095	65	6	been	be	AUX
cana-6095	65	7	developed	develop	VERB
cana-6095	65	8	:	:	PUNCT
cana-6095	65	9	markov	markov	NOUN
cana-6095	65	10	chain	chain	NOUN
cana-6095	65	11	monte	monte	PROPN
cana-6095	65	12	carlo	carlo	PROPN
cana-6095	65	13	(	(	PUNCT
cana-6095	65	14	mcmc	mcmc	PROPN
cana-6095	65	15	)	)	PUNCT
cana-6095	65	16	methods	method	NOUN
cana-6095	65	17	generate	generate	VERB
cana-6095	65	18	samples	sample	NOUN
cana-6095	65	19	from	from	ADP
cana-6095	65	20	the	the	DET
cana-6095	65	21	posterior	posterior	ADJ
cana-6095	65	22	distribution	distribution	NOUN
cana-6095	65	23	through	through	ADP
cana-6095	65	24	a	a	DET
cana-6095	65	25	random	random	ADJ
cana-6095	65	26	walk	walk	NOUN
cana-6095	65	27	process	process	NOUN
cana-6095	65	28	.	.	PUNCT
cana-6095	66	1	hamiltonian	hamiltonian	PROPN
cana-6095	66	2	monte	monte	PROPN
cana-6095	66	3	carlo	carlo	PROPN
cana-6095	66	4	(	(	PUNCT
cana-6095	66	5	hmc	hmc	PROPN
cana-6095	66	6	)	)	PUNCT
cana-6095	66	7	and	and	CCONJ
cana-6095	66	8	its	its	PRON
cana-6095	66	9	variants	variant	NOUN
cana-6095	66	10	are	be	AUX
cana-6095	66	11	particularly	particularly	ADV
cana-6095	66	12	effective	effective	ADJ
cana-6095	66	13	for	for	ADP
cana-6095	66	14	high	high	ADJ
cana-6095	66	15	-	-	PUNCT
cana-6095	66	16	dimensional	dimensional	ADJ
cana-6095	66	17	distributions	distribution	NOUN
cana-6095	66	18	but	but	CCONJ
cana-6095	66	19	can	can	AUX
cana-6095	66	20	be	be	AUX
cana-6095	66	21	computationally	computationally	ADV
cana-6095	66	22	intensive	intensive	ADJ
cana-6095	66	23	for	for	ADP
cana-6095	66	24	large	large	ADJ
cana-6095	66	25	networks	network	NOUN
cana-6095	66	26	68	68	NUM
cana-6095	66	27	.	.	PUNCT
cana-6095	67	1	variational	variational	ADJ
cana-6095	67	2	inference	inference	NOUN
cana-6095	67	3	(	(	PUNCT
cana-6095	67	4	vi	vi	NOUN
cana-6095	67	5	)	)	PUNCT
cana-6095	67	6	methods	method	NOUN
cana-6095	67	7	approximate	approximate	VERB
cana-6095	67	8	the	the	DET
cana-6095	67	9	true	true	ADJ
cana-6095	67	10	posterior	posterior	NOUN
cana-6095	67	11	with	with	ADP
cana-6095	67	12	a	a	DET
cana-6095	67	13	simpler	simple	ADJ
cana-6095	67	14	parametric	parametric	ADJ
cana-6095	67	15	distribution	distribution	NOUN
cana-6095	67	16	q(ω	q(ω	NOUN
cana-6095	67	17	)	)	PUNCT
cana-6095	67	18	whose	whose	DET
cana-6095	67	19	parameters	parameter	NOUN
cana-6095	67	20	are	be	AUX
cana-6095	67	21	optimized	optimize	VERB
cana-6095	67	22	to	to	PART
cana-6095	67	23	minimize	minimize	VERB
cana-6095	67	24	the	the	DET
cana-6095	67	25	kullback	kullback	NOUN
cana-6095	67	26	-	-	PUNCT
cana-6095	67	27	leibler	leibler	NOUN
cana-6095	67	28	(	(	PUNCT
cana-6095	67	29	kl	kl	NOUN
cana-6095	67	30	)	)	PUNCT
cana-6095	67	31	divergence	divergence	NOUN
cana-6095	67	32	to	to	ADP
cana-6095	67	33	the	the	DET
cana-6095	67	34	true	true	ADJ
cana-6095	67	35	posterior	posterior	NOUN
cana-6095	67	36	16	16	NUM
cana-6095	67	37	.	.	PUNCT
cana-6095	68	1	this	this	DET
cana-6095	68	2	approach	approach	NOUN
cana-6095	68	3	includes	include	VERB
cana-6095	68	4	methods	method	NOUN
cana-6095	68	5	like	like	ADP
cana-6095	68	6	bayesbybackprop	bayesbybackprop	NOUN
cana-6095	68	7	and	and	CCONJ
cana-6095	68	8	can	can	AUX
cana-6095	68	9	be	be	AUX
cana-6095	68	10	more	more	ADV
cana-6095	68	11	computationally	computationally	ADV
cana-6095	68	12	efficient	efficient	ADJ
cana-6095	68	13	than	than	ADP
cana-6095	68	14	mcmc	mcmc	PROPN
cana-6095	68	15	.	.	PUNCT
cana-6095	69	1	monte	monte	PROPN
cana-6095	69	2	carlo	carlo	PROPN
cana-6095	69	3	dropout	dropout	PROPN
cana-6095	69	4	provides	provide	VERB
cana-6095	69	5	a	a	DET
cana-6095	69	6	surprisingly	surprisingly	ADV
cana-6095	69	7	simple	simple	ADJ
cana-6095	69	8	approximation	approximation	NOUN
cana-6095	69	9	to	to	ADP
cana-6095	69	10	bayesian	bayesian	NOUN
cana-6095	69	11	inference	inference	NOUN
cana-6095	69	12	by	by	ADP
cana-6095	69	13	using	use	VERB
cana-6095	69	14	dropout	dropout	NOUN
cana-6095	69	15	at	at	ADP
cana-6095	69	16	test	test	NOUN
cana-6095	69	17	time	time	NOUN
cana-6095	69	18	1	1	NUM
cana-6095	69	19	.	.	X
cana-6095	70	1	gal	gal	VERB
cana-6095	70	2	and	and	CCONJ
cana-6095	70	3	ghahramani	ghahramani	PROPN
cana-6095	70	4	showed	show	VERB
cana-6095	70	5	that	that	SCONJ
cana-6095	70	6	neural	neural	ADJ
cana-6095	70	7	networks	network	NOUN
cana-6095	70	8	with	with	ADP
cana-6095	70	9	dropout	dropout	NOUN
cana-6095	70	10	before	before	SCONJ
cana-6095	70	11	every	every	DET
cana-6095	70	12	weight	weight	NOUN
cana-6095	70	13	layer	layer	NOUN
cana-6095	70	14	are	be	AUX
cana-6095	70	15	equivalent	equivalent	ADJ
cana-6095	70	16	to	to	PART
cana-6095	70	17	approximate	approximate	VERB
cana-6095	70	18	variational	variational	ADJ
cana-6095	70	19	inference	inference	NOUN
cana-6095	70	20	in	in	ADP
cana-6095	70	21	specific	specific	ADJ
cana-6095	70	22	bayesian	bayesian	NOUN
cana-6095	70	23	neural	neural	ADJ
cana-6095	70	24	networks	network	NOUN
cana-6095	70	25	.	.	PUNCT
cana-6095	71	1	deep	deep	ADJ
cana-6095	71	2	ensembles	ensemble	NOUN
cana-6095	71	3	train	train	VERB
cana-6095	71	4	multiple	multiple	ADJ
cana-6095	71	5	neural	neural	ADJ
cana-6095	71	6	networks	network	NOUN
cana-6095	71	7	with	with	ADP
cana-6095	71	8	different	different	ADJ
cana-6095	71	9	initializations	initialization	NOUN
cana-6095	71	10	and	and	CCONJ
cana-6095	71	11	use	use	VERB
cana-6095	71	12	their	their	PRON
cana-6095	71	13	collective	collective	ADJ
cana-6095	71	14	predictions	prediction	NOUN
cana-6095	71	15	to	to	PART
cana-6095	71	16	estimate	estimate	VERB
cana-6095	71	17	uncertainty	uncertainty	NOUN
cana-6095	71	18	7	7	NUM
cana-6095	71	19	.	.	PUNCT
cana-6095	72	1	while	while	SCONJ
cana-6095	72	2	not	not	PART
cana-6095	72	3	strictly	strictly	ADV
cana-6095	72	4	bayesian	bayesian	NOUN
cana-6095	72	5	,	,	PUNCT
cana-6095	72	6	ensembles	ensemble	NOUN
cana-6095	72	7	often	often	ADV
cana-6095	72	8	provide	provide	VERB
cana-6095	72	9	excellent	excellent	ADJ
cana-6095	72	10	uncertainty	uncertainty	NOUN
cana-6095	72	11	estimates	estimate	NOUN
cana-6095	72	12	and	and	CCONJ
cana-6095	72	13	can	can	AUX
cana-6095	72	14	be	be	AUX
cana-6095	72	15	combined	combine	VERB
cana-6095	72	16	with	with	ADP
cana-6095	72	17	bayesian	bayesian	NOUN
cana-6095	72	18	methods	method	NOUN
cana-6095	72	19	for	for	ADP
cana-6095	72	20	improved	improved	ADJ
cana-6095	72	21	performance	performance	NOUN
cana-6095	72	22	.	.	PUNCT
cana-6095	73	1	method	method	PROPN
cana-6095	73	2	theoretical	theoretical	ADJ
cana-6095	73	3	basis	basis	NOUN
cana-6095	73	4	computational	computational	ADJ
cana-6095	73	5	cost	cost	NOUN
cana-6095	73	6	scalability	scalability	NOUN
cana-6095	73	7	approximation	approximation	NOUN
cana-6095	73	8	quality	quality	PROPN
cana-6095	73	9	mcmc	mcmc	PROPN
cana-6095	73	10	/	/	SYM
cana-6095	73	11	hmc	hmc	PROPN
cana-6095	73	12	exact	exact	NOUN
cana-6095	73	13	sampling	sample	VERB
cana-6095	73	14	high	high	ADJ
cana-6095	73	15	limited	limited	ADJ
cana-6095	73	16	excellent	excellent	ADJ
cana-6095	73	17	variational	variational	ADJ
cana-6095	73	18	inference	inference	NOUN
cana-6095	73	19	kl	kl	PROPN
cana-6095	73	20	minimization	minimization	PROPN
cana-6095	73	21	moderate	moderate	ADJ
cana-6095	73	22	good	good	ADJ
cana-6095	73	23	good	good	ADJ
cana-6095	73	24	with	with	ADP
cana-6095	73	25	expressive	expressive	ADJ
cana-6095	73	26	variational	variational	ADJ
cana-6095	73	27	families	family	NOUN
cana-6095	73	28	mc	mc	PROPN
cana-6095	73	29	dropout	dropout	PROPN
cana-6095	73	30	variational	variational	ADJ
cana-6095	73	31	approximation	approximation	NOUN
cana-6095	73	32	low	low	ADJ
cana-6095	73	33	excellent	excellent	ADJ
cana-6095	73	34	variable	variable	ADJ
cana-6095	73	35	deep	deep	ADJ
cana-6095	73	36	ensembles	ensemble	NOUN
cana-6095	73	37	multiple	multiple	ADJ
cana-6095	73	38	point	point	NOUN
cana-6095	73	39	estimates	estimate	NOUN
cana-6095	73	40	moderate	moderate	ADJ
cana-6095	73	41	to	to	PART
cana-6095	73	42	high	high	ADJ
cana-6095	73	43	good	good	ADJ
cana-6095	73	44	excellent	excellent	ADJ
cana-6095	73	45	in	in	ADP
cana-6095	73	46	practice	practice	NOUN
cana-6095	73	47	bayesian	bayesian	NOUN
cana-6095	73	48	optimization	optimization	NOUN
cana-6095	73	49	gaussian	gaussian	NOUN
cana-6095	73	50	processes	process	NOUN
cana-6095	73	51	high	high	ADJ
cana-6095	73	52	limited	limited	ADJ
cana-6095	73	53	excellent	excellent	ADJ
cana-6095	73	54	for	for	ADP
cana-6095	73	55	hyperparameter	hyperparameter	NOUN
cana-6095	73	56	tuning	tuning	NOUN
cana-6095	73	57	table	table	NOUN
cana-6095	73	58	2	2	NUM
cana-6095	73	59	:	:	PUNCT
cana-6095	73	60	comparison	comparison	NOUN
cana-6095	73	61	of	of	ADP
cana-6095	73	62	inference	inference	NOUN
cana-6095	73	63	methods	method	NOUN
cana-6095	73	64	for	for	ADP
cana-6095	73	65	bayesian	bayesian	NOUN
cana-6095	73	66	neural	neural	ADJ
cana-6095	73	67	networks	network	NOUN
cana-6095	73	68	3.3	3.3	NUM
cana-6095	73	69	uncertainty	uncertainty	NOUN
cana-6095	73	70	quantification	quantification	NOUN
cana-6095	73	71	techniques	technique	NOUN
cana-6095	73	72	bnns	bnn	NOUN
cana-6095	73	73	provide	provide	VERB
cana-6095	73	74	several	several	ADJ
cana-6095	73	75	techniques	technique	NOUN
cana-6095	73	76	for	for	ADP
cana-6095	73	77	quantifying	quantify	VERB
cana-6095	73	78	different	different	ADJ
cana-6095	73	79	types	type	NOUN
cana-6095	73	80	of	of	ADP
cana-6095	73	81	uncertainty	uncertainty	NOUN
cana-6095	73	82	:	:	PUNCT
cana-6095	73	83	predictive	predictive	ADJ
cana-6095	73	84	uncertainty	uncertainty	NOUN
cana-6095	73	85	is	be	AUX
cana-6095	73	86	captured	capture	VERB
cana-6095	73	87	through	through	ADP
cana-6095	73	88	the	the	DET
cana-6095	73	89	predictive	predictive	ADJ
cana-6095	73	90	distribution	distribution	NOUN
cana-6095	73	91	p(y|x	p(y|x	NOUN
cana-6095	73	92	,	,	PUNCT
cana-6095	73	93	d	d	NOUN
cana-6095	73	94	)	)	PUNCT
cana-6095	73	95	,	,	PUNCT
cana-6095	73	96	which	which	PRON
cana-6095	73	97	can	can	AUX
cana-6095	73	98	be	be	AUX
cana-6095	73	99	approximated	approximate	VERB
cana-6095	73	100	using	use	VERB
cana-6095	73	101	monte	monte	PROPN
cana-6095	73	102	carlo	carlo	NOUN
cana-6095	73	103	samples	sample	NOUN
cana-6095	73	104	from	from	ADP
cana-6095	73	105	the	the	DET
cana-6095	73	106	posterior	posterior	ADJ
cana-6095	73	107	1	1	NUM
cana-6095	73	108	.	.	PUNCT
cana-6095	74	1	the	the	DET
cana-6095	74	2	variance	variance	NOUN
cana-6095	74	3	of	of	ADP
cana-6095	74	4	this	this	DET
cana-6095	74	5	distribution	distribution	NOUN
cana-6095	74	6	provides	provide	VERB
cana-6095	74	7	a	a	DET
cana-6095	74	8	measure	measure	NOUN
cana-6095	74	9	of	of	ADP
cana-6095	74	10	total	total	ADJ
cana-6095	74	11	uncertainty	uncertainty	NOUN
cana-6095	74	12	in	in	ADP
cana-6095	74	13	predictions	prediction	NOUN
cana-6095	74	14	.	.	PUNCT
cana-6095	75	1	uncertainty	uncertainty	NOUN
cana-6095	75	2	decomposition	decomposition	NOUN
cana-6095	75	3	techniques	technique	NOUN
cana-6095	75	4	separate	separate	ADJ
cana-6095	75	5	predictive	predictive	ADJ
cana-6095	75	6	uncertainty	uncertainty	NOUN
cana-6095	75	7	into	into	ADP
cana-6095	75	8	aleatoric	aleatoric	ADJ
cana-6095	75	9	and	and	CCONJ
cana-6095	75	10	epistemic	epistemic	ADJ
cana-6095	75	11	components	component	NOUN
cana-6095	75	12	1	1	NUM
cana-6095	75	13	.	.	PUNCT
cana-6095	76	1	for	for	ADP
cana-6095	76	2	regression	regression	NOUN
cana-6095	76	3	tasks	task	NOUN
cana-6095	76	4	,	,	PUNCT
cana-6095	76	5	this	this	PRON
cana-6095	76	6	can	can	AUX
cana-6095	76	7	be	be	AUX
cana-6095	76	8	achieved	achieve	VERB
cana-6095	76	9	by	by	ADP
cana-6095	76	10	modeling	model	VERB
cana-6095	76	11	heteroscedastic	heteroscedastic	ADJ
cana-6095	76	12	noise	noise	NOUN
cana-6095	76	13	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	PROPN
cana-6095	76	14	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	AUX
cana-6095	76	15	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	76	16	https://arxiv.org/abs/2102.06559	https://arxiv.org/abs/2102.06559	VERB
cana-6095	76	17	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NUM
cana-6095	76	18	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	76	19	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	76	20	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	PROPN
cana-6095	76	21	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	76	22	https://arxiv.org/abs/2412.08776	https://arxiv.org/abs/2412.08776	NOUN
cana-6095	76	23	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	PROPN
cana-6095	77	1	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	PROPN
cana-6095	77	2	communications	communication	NOUN
cana-6095	77	3	on	on	ADP
cana-6095	77	4	applied	apply	VERB
cana-6095	77	5	nonlinear	nonlinear	ADJ
cana-6095	77	6	analysis	analysis	NOUN
cana-6095	77	7	issn	issn	NOUN
cana-6095	77	8	:	:	PUNCT
cana-6095	77	9	1074	1074	NUM
cana-6095	77	10	-	-	PUNCT
cana-6095	77	11	133x	133x	NUM
cana-6095	77	12	vol	vol	NOUN
cana-6095	77	13	30	30	NUM
cana-6095	77	14	no	no	NOUN
cana-6095	77	15	.	.	NOUN
cana-6095	77	16	3	3	NUM
cana-6095	77	17	(	(	PUNCT
cana-6095	77	18	2023	2023	NUM
cana-6095	77	19	)	)	PUNCT
cana-6095	77	20	60	60	NUM
cana-6095	77	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	77	22	(	(	PUNCT
cana-6095	77	23	aleatoric	aleatoric	ADJ
cana-6095	77	24	)	)	PUNCT
cana-6095	77	25	while	while	SCONJ
cana-6095	77	26	capturing	capture	VERB
cana-6095	77	27	parameter	parameter	NOUN
cana-6095	77	28	uncertainty	uncertainty	NOUN
cana-6095	77	29	(	(	PUNCT
cana-6095	77	30	epistemic	epistemic	ADJ
cana-6095	77	31	)	)	PUNCT
cana-6095	77	32	.	.	PUNCT
cana-6095	78	1	for	for	ADP
cana-6095	78	2	classification	classification	NOUN
cana-6095	78	3	,	,	PUNCT
cana-6095	78	4	similar	similar	ADJ
cana-6095	78	5	decompositions	decomposition	NOUN
cana-6095	78	6	can	can	AUX
cana-6095	78	7	be	be	AUX
cana-6095	78	8	derived	derive	VERB
cana-6095	78	9	through	through	ADP
cana-6095	78	10	careful	careful	ADJ
cana-6095	78	11	modeling	modeling	NOUN
cana-6095	78	12	of	of	ADP
cana-6095	78	13	output	output	NOUN
cana-6095	78	14	distributions	distribution	NOUN
cana-6095	78	15	.	.	PUNCT
cana-6095	79	1	bayesian	bayesian	NOUN
cana-6095	79	2	probabilistic	probabilistic	ADJ
cana-6095	79	3	numerical	numerical	ADJ
cana-6095	79	4	methods	method	NOUN
cana-6095	79	5	reformulate	reformulate	VERB
cana-6095	79	6	traditional	traditional	ADJ
cana-6095	79	7	numerical	numerical	ADJ
cana-6095	79	8	problems	problem	NOUN
cana-6095	79	9	as	as	ADP
cana-6095	79	10	statistical	statistical	ADJ
cana-6095	79	11	inference	inference	NOUN
cana-6095	79	12	tasks	task	NOUN
cana-6095	79	13	10	10	NUM
cana-6095	79	14	.	.	PUNCT
cana-6095	80	1	for	for	ADP
cana-6095	80	2	example	example	NOUN
cana-6095	80	3	,	,	PUNCT
cana-6095	80	4	bayesian	bayesian	NOUN
cana-6095	80	5	quadrature	quadrature	NOUN
cana-6095	80	6	treats	treat	VERB
cana-6095	80	7	numerical	numerical	ADJ
cana-6095	80	8	integration	integration	NOUN
cana-6095	80	9	as	as	ADP
cana-6095	80	10	inference	inference	NOUN
cana-6095	80	11	of	of	ADP
cana-6095	80	12	the	the	DET
cana-6095	80	13	integral	integral	ADJ
cana-6095	80	14	value	value	NOUN
cana-6095	80	15	given	give	VERB
cana-6095	80	16	function	function	NOUN
cana-6095	80	17	evaluations	evaluation	NOUN
cana-6095	80	18	,	,	PUNCT
cana-6095	80	19	providing	provide	VERB
cana-6095	80	20	uncertainty	uncertainty	NOUN
cana-6095	80	21	estimates	estimate	NOUN
cana-6095	80	22	alongside	alongside	ADP
cana-6095	80	23	the	the	DET
cana-6095	80	24	integral	integral	ADJ
cana-6095	80	25	estimate	estimate	NOUN
cana-6095	80	26	.	.	PUNCT
cana-6095	81	1	latent	latent	PROPN
cana-6095	81	2	variable	variable	PROPN
cana-6095	81	3	approaches	approach	VERB
cana-6095	81	4	model	model	VERB
cana-6095	81	5	complex	complex	ADJ
cana-6095	81	6	uncertainty	uncertainty	NOUN
cana-6095	81	7	structures	structure	NOUN
cana-6095	81	8	through	through	ADP
cana-6095	81	9	latent	latent	NOUN
cana-6095	81	10	variables	variable	NOUN
cana-6095	81	11	that	that	PRON
cana-6095	81	12	capture	capture	VERB
cana-6095	81	13	additional	additional	ADJ
cana-6095	81	14	sources	source	NOUN
cana-6095	81	15	of	of	ADP
cana-6095	81	16	variability	variability	NOUN
cana-6095	81	17	4	4	NUM
cana-6095	81	18	.	.	PUNCT
cana-6095	81	19	methods	method	NOUN
cana-6095	81	20	like	like	ADP
cana-6095	81	21	latent	latent	NOUN
cana-6095	81	22	evolution	evolution	NOUN
cana-6095	81	23	of	of	ADP
cana-6095	81	24	pdes	pde	NOUN
cana-6095	81	25	with	with	ADP
cana-6095	81	26	uq	uq	PROPN
cana-6095	81	27	(	(	PUNCT
cana-6095	81	28	le	le	PROPN
cana-6095	81	29	-	-	ADJ
cana-6095	81	30	pde	pde	NOUN
cana-6095	81	31	-	-	PUNCT
cana-6095	81	32	uq	uq	NOUN
cana-6095	81	33	)	)	PUNCT
cana-6095	81	34	enable	enable	VERB
cana-6095	81	35	efficient	efficient	ADJ
cana-6095	81	36	uncertainty	uncertainty	NOUN
cana-6095	81	37	quantification	quantification	NOUN
cana-6095	81	38	for	for	ADP
cana-6095	81	39	both	both	CCONJ
cana-6095	81	40	forward	forward	ADJ
cana-6095	81	41	and	and	CCONJ
cana-6095	81	42	inverse	inverse	ADJ
cana-6095	81	43	problems	problem	NOUN
cana-6095	81	44	of	of	ADP
cana-6095	81	45	pdes	pde	NOUN
cana-6095	81	46	.	.	PUNCT
cana-6095	82	1	4.applications	4.application	NOUN
cana-6095	82	2	in	in	ADP
cana-6095	82	3	numerical	numerical	ADJ
cana-6095	82	4	methods	method	NOUN
cana-6095	82	5	4.1	4.1	NUM
cana-6095	82	6	solving	solve	VERB
cana-6095	82	7	partial	partial	ADJ
cana-6095	82	8	differential	differential	ADJ
cana-6095	82	9	equations	equation	NOUN
cana-6095	82	10	partial	partial	ADJ
cana-6095	82	11	differential	differential	NOUN
cana-6095	82	12	equations	equation	NOUN
cana-6095	82	13	(	(	PUNCT
cana-6095	82	14	pdes	pde	NOUN
cana-6095	82	15	)	)	PUNCT
cana-6095	82	16	are	be	AUX
cana-6095	82	17	fundamental	fundamental	ADJ
cana-6095	82	18	to	to	ADP
cana-6095	82	19	modeling	model	VERB
cana-6095	82	20	physical	physical	ADJ
cana-6095	82	21	systems	system	NOUN
cana-6095	82	22	,	,	PUNCT
cana-6095	82	23	but	but	CCONJ
cana-6095	82	24	traditional	traditional	ADJ
cana-6095	82	25	numerical	numerical	ADJ
cana-6095	82	26	methods	method	NOUN
cana-6095	82	27	often	often	ADV
cana-6095	82	28	lack	lack	VERB
cana-6095	82	29	comprehensive	comprehensive	ADJ
cana-6095	82	30	uncertainty	uncertainty	NOUN
cana-6095	82	31	quantification	quantification	NOUN
cana-6095	82	32	.	.	PUNCT
cana-6095	83	1	bayesian	bayesian	NOUN
cana-6095	83	2	neural	neural	ADJ
cana-6095	83	3	networks	network	NOUN
cana-6095	83	4	offer	offer	VERB
cana-6095	83	5	promising	promise	VERB
cana-6095	83	6	approaches	approach	NOUN
cana-6095	83	7	for	for	ADP
cana-6095	83	8	uq	uq	NOUN
cana-6095	83	9	in	in	ADP
cana-6095	83	10	pde	pde	PROPN
cana-6095	83	11	solutions	solution	NOUN
cana-6095	83	12	:	:	PUNCT
cana-6095	83	13	physics	physics	NOUN
cana-6095	83	14	-	-	PUNCT
cana-6095	83	15	informed	inform	VERB
cana-6095	83	16	neural	neural	ADJ
cana-6095	83	17	networks	network	NOUN
cana-6095	83	18	(	(	PUNCT
cana-6095	83	19	pinns	pinns	ADJ
cana-6095	83	20	)	)	PUNCT
cana-6095	83	21	incorporate	incorporate	VERB
cana-6095	83	22	pde	pde	NOUN
cana-6095	83	23	constraints	constraint	NOUN
cana-6095	83	24	into	into	ADP
cana-6095	83	25	the	the	DET
cana-6095	83	26	loss	loss	NOUN
cana-6095	83	27	function	function	NOUN
cana-6095	83	28	of	of	ADP
cana-6095	83	29	neural	neural	ADJ
cana-6095	83	30	networks	network	NOUN
cana-6095	83	31	,	,	PUNCT
cana-6095	83	32	enabling	enable	VERB
cana-6095	83	33	solution	solution	NOUN
cana-6095	83	34	of	of	ADP
cana-6095	83	35	both	both	CCONJ
cana-6095	83	36	forward	forward	ADJ
cana-6095	83	37	and	and	CCONJ
cana-6095	83	38	inverse	inverse	NOUN
cana-6095	83	39	problems	problem	NOUN
cana-6095	83	40	9	9	NUM
cana-6095	83	41	.	.	PUNCT
cana-6095	84	1	bayesian	bayesian	NOUN
cana-6095	84	2	extensions	extension	NOUN
cana-6095	84	3	of	of	ADP
cana-6095	84	4	pinns	pinns	ADJ
cana-6095	84	5	capture	capture	VERB
cana-6095	84	6	uncertainty	uncertainty	NOUN
cana-6095	84	7	in	in	ADP
cana-6095	84	8	parameters	parameter	NOUN
cana-6095	84	9	,	,	PUNCT
cana-6095	84	10	initial	initial	ADJ
cana-6095	84	11	conditions	condition	NOUN
cana-6095	84	12	,	,	PUNCT
cana-6095	84	13	boundary	boundary	ADJ
cana-6095	84	14	conditions	condition	NOUN
cana-6095	84	15	,	,	PUNCT
cana-6095	84	16	and	and	CCONJ
cana-6095	84	17	even	even	ADV
cana-6095	84	18	the	the	DET
cana-6095	84	19	governing	govern	VERB
cana-6095	84	20	equations	equation	NOUN
cana-6095	84	21	themselves	themselves	PRON
cana-6095	84	22	.	.	PUNCT
cana-6095	85	1	latent	latent	ADJ
cana-6095	85	2	evolution	evolution	NOUN
cana-6095	85	3	of	of	ADP
cana-6095	85	4	pdes	pde	NOUN
cana-6095	85	5	with	with	ADP
cana-6095	85	6	uq	uq	PROPN
cana-6095	85	7	(	(	PUNCT
cana-6095	85	8	le	le	PROPN
cana-6095	85	9	-	-	ADJ
cana-6095	85	10	pde	pde	NOUN
cana-6095	85	11	-	-	PUNCT
cana-6095	85	12	uq	uq	NOUN
cana-6095	85	13	)	)	PUNCT
cana-6095	85	14	leverages	leverage	VERB
cana-6095	85	15	latent	latent	NOUN
cana-6095	85	16	vectors	vector	NOUN
cana-6095	85	17	within	within	ADP
cana-6095	85	18	a	a	DET
cana-6095	85	19	latent	latent	ADJ
cana-6095	85	20	space	space	NOUN
cana-6095	85	21	to	to	PART
cana-6095	85	22	evolve	evolve	VERB
cana-6095	85	23	both	both	CCONJ
cana-6095	85	24	the	the	DET
cana-6095	85	25	system	system	NOUN
cana-6095	85	26	's	's	PART
cana-6095	85	27	state	state	NOUN
cana-6095	85	28	and	and	CCONJ
cana-6095	85	29	its	its	PRON
cana-6095	85	30	corresponding	corresponding	ADJ
cana-6095	85	31	uncertainty	uncertainty	NOUN
cana-6095	85	32	estimation	estimation	NOUN
cana-6095	85	33	4	4	NUM
cana-6095	85	34	.	.	PUNCT
cana-6095	86	1	this	this	DET
cana-6095	86	2	approach	approach	NOUN
cana-6095	86	3	demonstrates	demonstrate	VERB
cana-6095	86	4	accurate	accurate	ADJ
cana-6095	86	5	uncertainty	uncertainty	NOUN
cana-6095	86	6	quantification	quantification	NOUN
cana-6095	86	7	performance	performance	NOUN
cana-6095	86	8	,	,	PUNCT
cana-6095	86	9	surpassing	surpass	VERB
cana-6095	86	10	strong	strong	ADJ
cana-6095	86	11	baselines	baseline	NOUN
cana-6095	86	12	including	include	VERB
cana-6095	86	13	deep	deep	ADJ
cana-6095	86	14	ensembles	ensemble	NOUN
cana-6095	86	15	and	and	CCONJ
cana-6095	86	16	bayesian	bayesian	NOUN
cana-6095	86	17	neural	neural	ADJ
cana-6095	86	18	network	network	NOUN
cana-6095	86	19	layers	layer	NOUN
cana-6095	86	20	for	for	ADP
cana-6095	86	21	long	long	ADJ
cana-6095	86	22	-	-	PUNCT
cana-6095	86	23	term	term	NOUN
cana-6095	86	24	predictions	prediction	NOUN
cana-6095	86	25	.	.	PUNCT
cana-6095	87	1	uncertainty	uncertainty	NOUN
cana-6095	87	2	quantification	quantification	NOUN
cana-6095	87	3	for	for	ADP
cana-6095	87	4	inverse	inverse	NOUN
cana-6095	87	5	problems	problem	NOUN
cana-6095	87	6	is	be	AUX
cana-6095	87	7	particularly	particularly	ADV
cana-6095	87	8	important	important	ADJ
cana-6095	87	9	when	when	SCONJ
cana-6095	87	10	estimating	estimate	VERB
cana-6095	87	11	parameters	parameter	NOUN
cana-6095	87	12	or	or	CCONJ
cana-6095	87	13	states	state	NOUN
cana-6095	87	14	from	from	ADP
cana-6095	87	15	limited	limited	ADJ
cana-6095	87	16	and	and	CCONJ
cana-6095	87	17	noisy	noisy	ADJ
cana-6095	87	18	measurements	measurement	NOUN
cana-6095	87	19	.	.	PUNCT
cana-6095	88	1	bnns	bnns	PROPN
cana-6095	88	2	can	can	AUX
cana-6095	88	3	provide	provide	VERB
cana-6095	88	4	posterior	posterior	ADJ
cana-6095	88	5	distributions	distribution	NOUN
cana-6095	88	6	over	over	ADP
cana-6095	88	7	unknown	unknown	ADJ
cana-6095	88	8	parameters	parameter	NOUN
cana-6095	88	9	,	,	PUNCT
cana-6095	88	10	quantifying	quantify	VERB
cana-6095	88	11	uncertainty	uncertainty	NOUN
cana-6095	88	12	in	in	ADP
cana-6095	88	13	estimates	estimate	NOUN
cana-6095	88	14	and	and	CCONJ
cana-6095	88	15	enabling	enable	VERB
cana-6095	88	16	more	more	ADV
cana-6095	88	17	informed	informed	ADJ
cana-6095	88	18	decision	decision	NOUN
cana-6095	88	19	-	-	PUNCT
cana-6095	88	20	making	make	VERB
cana-6095	88	21	4,9	4,9	NUM
cana-6095	88	22	.	.	PUNCT
cana-6095	89	1	4.2	4.2	NUM
cana-6095	89	2	numerical	numerical	ADJ
cana-6095	89	3	integration	integration	NOUN
cana-6095	89	4	and	and	CCONJ
cana-6095	89	5	differentiation	differentiation	NOUN
cana-6095	89	6	numerical	numerical	ADJ
cana-6095	89	7	integration	integration	NOUN
cana-6095	89	8	is	be	AUX
cana-6095	89	9	a	a	DET
cana-6095	89	10	fundamental	fundamental	ADJ
cana-6095	89	11	computational	computational	ADJ
cana-6095	89	12	task	task	NOUN
cana-6095	89	13	with	with	ADP
cana-6095	89	14	applications	application	NOUN
cana-6095	89	15	in	in	ADP
cana-6095	89	16	statistics	statistic	NOUN
cana-6095	89	17	,	,	PUNCT
cana-6095	89	18	physics	physics	NOUN
cana-6095	89	19	,	,	PUNCT
cana-6095	89	20	and	and	CCONJ
cana-6095	89	21	finance	finance	NOUN
cana-6095	89	22	.	.	PUNCT
cana-6095	90	1	traditional	traditional	ADJ
cana-6095	90	2	methods	method	NOUN
cana-6095	90	3	provide	provide	VERB
cana-6095	90	4	error	error	NOUN
cana-6095	90	5	estimates	estimate	NOUN
cana-6095	90	6	but	but	CCONJ
cana-6095	90	7	often	often	ADV
cana-6095	90	8	lack	lack	VERB
cana-6095	90	9	probabilistic	probabilistic	ADJ
cana-6095	90	10	interpretations	interpretation	NOUN
cana-6095	90	11	:	:	PUNCT
cana-6095	90	12	bayesian	bayesian	NOUN
cana-6095	90	13	quadrature	quadrature	NOUN
cana-6095	90	14	formulates	formulate	VERB
cana-6095	90	15	numerical	numerical	ADJ
cana-6095	90	16	integration	integration	NOUN
cana-6095	90	17	as	as	ADP
cana-6095	90	18	a	a	DET
cana-6095	90	19	bayesian	bayesian	NOUN
cana-6095	90	20	inference	inference	NOUN
cana-6095	90	21	problem	problem	NOUN
cana-6095	90	22	,	,	PUNCT
cana-6095	90	23	using	use	VERB
cana-6095	90	24	gaussian	gaussian	ADJ
cana-6095	90	25	processes	process	NOUN
cana-6095	90	26	or	or	CCONJ
cana-6095	90	27	other	other	ADJ
cana-6095	90	28	probabilistic	probabilistic	ADJ
cana-6095	90	29	models	model	NOUN
cana-6095	90	30	to	to	PART
cana-6095	90	31	provide	provide	VERB
cana-6095	90	32	posterior	posterior	ADJ
cana-6095	90	33	distributions	distribution	NOUN
cana-6095	90	34	over	over	ADP
cana-6095	90	35	integral	integral	ADJ
cana-6095	90	36	values	value	NOUN
cana-6095	90	37	5,10	5,10	NUM
cana-6095	90	38	.	.	PUNCT
cana-6095	91	1	this	this	DET
cana-6095	91	2	approach	approach	NOUN
cana-6095	91	3	allows	allow	VERB
cana-6095	91	4	incorporation	incorporation	NOUN
cana-6095	91	5	of	of	ADP
cana-6095	91	6	prior	prior	ADJ
cana-6095	91	7	knowledge	knowledge	NOUN
cana-6095	91	8	about	about	ADP
cana-6095	91	9	the	the	DET
cana-6095	91	10	integrand	integrand	NOUN
cana-6095	91	11	and	and	CCONJ
cana-6095	91	12	provides	provide	VERB
cana-6095	91	13	uncertainty	uncertainty	NOUN
cana-6095	91	14	estimates	estimate	NOUN
cana-6095	91	15	that	that	PRON
cana-6095	91	16	can	can	AUX
cana-6095	91	17	guide	guide	VERB
cana-6095	91	18	adaptive	adaptive	ADJ
cana-6095	91	19	sampling	sampling	NOUN
cana-6095	91	20	strategies	strategy	NOUN
cana-6095	91	21	.	.	PUNCT
cana-6095	92	1	bayesian	bayesian	NOUN
cana-6095	92	2	numerical	numerical	ADJ
cana-6095	92	3	integration	integration	NOUN
cana-6095	92	4	with	with	ADP
cana-6095	92	5	neural	neural	ADJ
cana-6095	92	6	networks	network	NOUN
cana-6095	92	7	combines	combine	VERB
cana-6095	92	8	the	the	DET
cana-6095	92	9	flexibility	flexibility	NOUN
cana-6095	92	10	of	of	ADP
cana-6095	92	11	neural	neural	ADJ
cana-6095	92	12	networks	network	NOUN
cana-6095	92	13	with	with	ADP
cana-6095	92	14	bayesian	bayesian	NOUN
cana-6095	92	15	inference	inference	NOUN
cana-6095	92	16	for	for	ADP
cana-6095	92	17	integral	integral	ADJ
cana-6095	92	18	approximation	approximation	NOUN
cana-6095	92	19	5	5	NUM
cana-6095	92	20	.	.	PUNCT
cana-6095	93	1	bayesian	bayesian	PROPN
cana-6095	93	2	stein	stein	PROPN
cana-6095	93	3	networks	networks	PROPN
cana-6095	93	4	use	use	VERB
cana-6095	93	5	neural	neural	ADJ
cana-6095	93	6	network	network	NOUN
cana-6095	93	7	architectures	architecture	NOUN
cana-6095	93	8	based	base	VERB
cana-6095	93	9	on	on	ADP
cana-6095	93	10	stein	stein	PROPN
cana-6095	93	11	operators	operators	PROPN
cana-6095	93	12	and	and	CCONJ
cana-6095	93	13	laplace	laplace	NOUN
cana-6095	93	14	approximation	approximation	NOUN
cana-6095	93	15	,	,	PUNCT
cana-6095	93	16	leading	lead	VERB
cana-6095	93	17	to	to	ADP
cana-6095	93	18	orders	order	NOUN
cana-6095	93	19	of	of	ADP
cana-6095	93	20	magnitude	magnitude	NOUN
cana-6095	93	21	speed	speed	NOUN
cana-6095	93	22	-	-	PUNCT
cana-6095	93	23	ups	up	NOUN
cana-6095	93	24	on	on	ADP
cana-6095	93	25	benchmark	benchmark	NOUN
cana-6095	93	26	problems	problem	NOUN
cana-6095	93	27	and	and	CCONJ
cana-6095	93	28	challenging	challenging	ADJ
cana-6095	93	29	applications	application	NOUN
cana-6095	93	30	in	in	ADP
cana-6095	93	31	dynamical	dynamical	ADJ
cana-6095	93	32	systems	system	NOUN
cana-6095	93	33	and	and	CCONJ
cana-6095	93	34	wind	wind	NOUN
cana-6095	93	35	farm	farm	NOUN
cana-6095	93	36	energy	energy	NOUN
cana-6095	93	37	prediction	prediction	NOUN
cana-6095	93	38	.	.	PUNCT
cana-6095	94	1	numerical	numerical	ADJ
cana-6095	94	2	differentiation	differentiation	NOUN
cana-6095	94	3	with	with	ADP
cana-6095	94	4	uncertainty	uncertainty	NOUN
cana-6095	94	5	quantification	quantification	NOUN
cana-6095	94	6	is	be	AUX
cana-6095	94	7	particularly	particularly	ADV
cana-6095	94	8	valuable	valuable	ADJ
cana-6095	94	9	for	for	ADP
cana-6095	94	10	applications	application	NOUN
cana-6095	94	11	with	with	ADP
cana-6095	94	12	noisy	noisy	ADJ
cana-6095	94	13	data	datum	NOUN
cana-6095	94	14	or	or	CCONJ
cana-6095	94	15	when	when	SCONJ
cana-6095	94	16	computing	compute	VERB
cana-6095	94	17	derivatives	derivative	NOUN
cana-6095	94	18	for	for	ADP
cana-6095	94	19	optimization	optimization	NOUN
cana-6095	94	20	.	.	PUNCT
cana-6095	95	1	bnns	bnns	PROPN
cana-6095	95	2	can	can	AUX
cana-6095	95	3	provide	provide	VERB
cana-6095	95	4	probabilistic	probabilistic	ADJ
cana-6095	95	5	estimates	estimate	NOUN
cana-6095	95	6	of	of	ADP
cana-6095	95	7	derivatives	derivative	NOUN
cana-6095	95	8	,	,	PUNCT
cana-6095	95	9	with	with	ADP
cana-6095	95	10	uncertainty	uncertainty	NOUN
cana-6095	95	11	that	that	PRON
cana-6095	95	12	reflects	reflect	VERB
cana-6095	95	13	noise	noise	NOUN
cana-6095	95	14	in	in	ADP
cana-6095	95	15	the	the	DET
cana-6095	95	16	data	datum	NOUN
cana-6095	95	17	and	and	CCONJ
cana-6095	95	18	model	model	NOUN
cana-6095	95	19	limitations	limitation	NOUN
cana-6095	95	20	.	.	PUNCT
cana-6095	96	1	4.3	4.3	NUM
cana-6095	96	2	materials	material	NOUN
cana-6095	96	3	modeling	modeling	NOUN
cana-6095	96	4	and	and	CCONJ
cana-6095	96	5	computational	computational	ADJ
cana-6095	96	6	physics	physics	NOUN
cana-6095	96	7	computational	computational	ADJ
cana-6095	96	8	materials	material	NOUN
cana-6095	96	9	science	science	NOUN
cana-6095	96	10	relies	rely	VERB
cana-6095	96	11	heavily	heavily	ADV
cana-6095	96	12	on	on	ADP
cana-6095	96	13	numerical	numerical	ADJ
cana-6095	96	14	methods	method	NOUN
cana-6095	96	15	for	for	ADP
cana-6095	96	16	predicting	predict	VERB
cana-6095	96	17	material	material	NOUN
cana-6095	96	18	properties	property	NOUN
cana-6095	96	19	from	from	ADP
cana-6095	96	20	microstructural	microstructural	ADJ
cana-6095	96	21	information	information	NOUN
cana-6095	96	22	.	.	PUNCT
cana-6095	97	1	uncertainty	uncertainty	NOUN
cana-6095	97	2	quantification	quantification	NOUN
cana-6095	97	3	is	be	AUX
cana-6095	97	4	essential	essential	ADJ
cana-6095	97	5	for	for	ADP
cana-6095	97	6	reliable	reliable	ADJ
cana-6095	97	7	predictions	prediction	NOUN
cana-6095	97	8	:	:	PUNCT
cana-6095	97	9	bayesian	bayesian	NOUN
cana-6095	97	10	neural	neural	ADJ
cana-6095	97	11	networks	network	NOUN
cana-6095	97	12	for	for	ADP
cana-6095	97	13	materials	material	NOUN
cana-6095	97	14	modeling	modeling	NOUN
cana-6095	97	15	provide	provide	VERB
cana-6095	97	16	uncertainty	uncertainty	NOUN
cana-6095	97	17	estimates	estimate	NOUN
cana-6095	97	18	for	for	ADP
cana-6095	97	19	structure	structure	NOUN
cana-6095	97	20	-	-	PUNCT
cana-6095	97	21	property	property	NOUN
cana-6095	97	22	linkages	linkage	NOUN
cana-6095	97	23	6	6	NUM
cana-6095	97	24	.	.	PUNCT
cana-6095	98	1	these	these	DET
cana-6095	98	2	approaches	approach	NOUN
cana-6095	98	3	are	be	AUX
cana-6095	98	4	particularly	particularly	ADV
cana-6095	98	5	valuable	valuable	ADJ
cana-6095	98	6	when	when	SCONJ
cana-6095	98	7	data	datum	NOUN
cana-6095	98	8	is	be	AUX
cana-6095	98	9	limited	limit	VERB
cana-6095	98	10	or	or	CCONJ
cana-6095	98	11	when	when	SCONJ
cana-6095	98	12	predicting	predict	VERB
cana-6095	98	13	properties	property	NOUN
cana-6095	98	14	for	for	ADP
cana-6095	98	15	novel	novel	ADJ
cana-6095	98	16	materials	material	NOUN
cana-6095	98	17	where	where	SCONJ
cana-6095	98	18	extrapolation	extrapolation	NOUN
cana-6095	98	19	is	be	AUX
cana-6095	98	20	required	require	VERB
cana-6095	98	21	.	.	PUNCT
cana-6095	99	1	uncertainty	uncertainty	NOUN
cana-6095	99	2	quantification	quantification	NOUN
cana-6095	99	3	in	in	ADP
cana-6095	99	4	multiscale	multiscale	ADJ
cana-6095	99	5	modeling	modeling	NOUN
cana-6095	99	6	addresses	address	NOUN
cana-6095	99	7	challenges	challenge	NOUN
cana-6095	99	8	in	in	ADP
cana-6095	99	9	bridging	bridge	VERB
cana-6095	99	10	different	different	ADJ
cana-6095	99	11	length	length	NOUN
cana-6095	99	12	and	and	CCONJ
cana-6095	99	13	time	time	NOUN
cana-6095	99	14	scales	scale	VERB
cana-6095	99	15	6	6	NUM
cana-6095	99	16	.	.	PUNCT
cana-6095	100	1	bnns	bnns	PROPN
cana-6095	100	2	can	can	AUX
cana-6095	100	3	propagate	propagate	VERB
cana-6095	100	4	uncertainty	uncertainty	NOUN
cana-6095	100	5	across	across	ADP
cana-6095	100	6	scales	scale	NOUN
cana-6095	100	7	,	,	PUNCT
cana-6095	100	8	providing	provide	VERB
cana-6095	100	9	comprehensive	comprehensive	ADJ
cana-6095	100	10	uncertainty	uncertainty	NOUN
cana-6095	100	11	characterization	characterization	NOUN
cana-6095	100	12	for	for	ADP
cana-6095	100	13	final	final	ADJ
cana-6095	100	14	predictions	prediction	NOUN
cana-6095	100	15	.	.	PUNCT
cana-6095	101	1	composite	composite	ADJ
cana-6095	101	2	materials	material	NOUN
cana-6095	101	3	modeling	model	VERB
cana-6095	101	4	benefits	benefit	NOUN
cana-6095	101	5	from	from	ADP
cana-6095	101	6	bayesian	bayesian	NOUN
cana-6095	101	7	approaches	approach	NOUN
cana-6095	101	8	that	that	PRON
cana-6095	101	9	quantify	quantify	VERB
cana-6095	101	10	uncertainty	uncertainty	NOUN
cana-6095	101	11	arising	arise	VERB
cana-6095	101	12	from	from	ADP
cana-6095	101	13	random	random	ADJ
cana-6095	101	14	microstructural	microstructural	NOUN
cana-6095	101	15	features	feature	VERB
cana-6095	101	16	6	6	NUM
cana-6095	101	17	.	.	PUNCT
cana-6095	101	18	by	by	ADP
cana-6095	101	19	capturing	capture	VERB
cana-6095	101	20	both	both	DET
cana-6095	101	21	aleatoric	aleatoric	ADJ
cana-6095	101	22	uncertainty	uncertainty	NOUN
cana-6095	101	23	(	(	PUNCT
cana-6095	101	24	from	from	ADP
cana-6095	101	25	inherent	inherent	ADJ
cana-6095	101	26	randomness	randomness	NOUN
cana-6095	101	27	)	)	PUNCT
cana-6095	101	28	and	and	CCONJ
cana-6095	101	29	epistemic	epistemic	ADJ
cana-6095	101	30	uncertainty	uncertainty	NOUN
cana-6095	101	31	(	(	PUNCT
cana-6095	101	32	from	from	ADP
cana-6095	101	33	limited	limited	ADJ
cana-6095	101	34	data	datum	NOUN
cana-6095	101	35	)	)	PUNCT
cana-6095	101	36	,	,	PUNCT
cana-6095	101	37	bnns	bnns	PROPN
cana-6095	101	38	enable	enable	VERB
cana-6095	101	39	more	more	ADJ
cana-6095	101	40	reliable	reliable	ADJ
cana-6095	101	41	predictions	prediction	NOUN
cana-6095	101	42	for	for	ADP
cana-6095	101	43	material	material	NOUN
cana-6095	101	44	design	design	NOUN
cana-6095	101	45	and	and	CCONJ
cana-6095	101	46	optimization	optimization	NOUN
cana-6095	101	47	.	.	PUNCT
cana-6095	102	1	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	PROPN
cana-6095	102	2	https://arxiv.org/abs/2402.08383	https://arxiv.org/abs/2402.08383	PROPN
cana-6095	102	3	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	102	4	https://arxiv.org/abs/2402.08383	https://arxiv.org/abs/2402.08383	ADV
cana-6095	102	5	https://arxiv.org/abs/2402.08383	https://arxiv.org/abs/2402.08383	PROPN
cana-6095	102	6	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	102	7	https://arxiv.org/abs/2305.13248	https://arxiv.org/abs/2305.13248	NOUN
cana-6095	102	8	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	PROPN
cana-6095	102	9	https://arxiv.org/abs/2305.13248	https://arxiv.org/abs/2305.13248	NOUN
cana-6095	102	10	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	X
cana-6095	102	11	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	PRON
cana-6095	102	12	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	102	13	communications	communication	NOUN
cana-6095	102	14	on	on	ADP
cana-6095	102	15	applied	apply	VERB
cana-6095	102	16	nonlinear	nonlinear	ADJ
cana-6095	102	17	analysis	analysis	NOUN
cana-6095	102	18	issn	issn	NOUN
cana-6095	102	19	:	:	PUNCT
cana-6095	102	20	1074	1074	NUM
cana-6095	102	21	-	-	PUNCT
cana-6095	102	22	133x	133x	NUM
cana-6095	102	23	vol	vol	NOUN
cana-6095	102	24	30	30	NUM
cana-6095	103	1	no	no	NOUN
cana-6095	103	2	.	.	NOUN
cana-6095	103	3	3	3	NUM
cana-6095	103	4	(	(	PUNCT
cana-6095	103	5	2023	2023	NUM
cana-6095	103	6	)	)	PUNCT
cana-6095	103	7	61	61	NUM
cana-6095	103	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	103	9	4.4	4.4	NUM
cana-6095	103	10	scientific	scientific	ADJ
cana-6095	103	11	machine	machine	NOUN
cana-6095	103	12	learning	learn	VERB
cana-6095	103	13	scientific	scientific	ADJ
cana-6095	103	14	machine	machine	NOUN
cana-6095	103	15	learning	learning	NOUN
cana-6095	103	16	(	(	PUNCT
cana-6095	103	17	sciml	sciml	NOUN
cana-6095	103	18	)	)	PUNCT
cana-6095	103	19	integrates	integrate	VERB
cana-6095	103	20	computational	computational	ADJ
cana-6095	103	21	science	science	NOUN
cana-6095	103	22	with	with	ADP
cana-6095	103	23	machine	machine	NOUN
cana-6095	103	24	learning	learning	NOUN
cana-6095	103	25	,	,	PUNCT
cana-6095	103	26	creating	create	VERB
cana-6095	103	27	new	new	ADJ
cana-6095	103	28	opportunities	opportunity	NOUN
cana-6095	103	29	for	for	ADP
cana-6095	103	30	uncertainty	uncertainty	NOUN
cana-6095	103	31	-	-	PUNCT
cana-6095	103	32	aware	aware	ADJ
cana-6095	103	33	numerical	numerical	ADJ
cana-6095	103	34	methods	method	NOUN
cana-6095	103	35	:	:	PUNCT
cana-6095	103	36	operator	operator	NOUN
cana-6095	103	37	learning	learn	VERB
cana-6095	103	38	with	with	ADP
cana-6095	103	39	uncertainty	uncertainty	NOUN
cana-6095	103	40	quantification	quantification	NOUN
cana-6095	103	41	enables	enable	VERB
cana-6095	103	42	learning	learn	VERB
cana-6095	103	43	mappings	mapping	NOUN
cana-6095	103	44	between	between	ADP
cana-6095	103	45	function	function	NOUN
cana-6095	103	46	spaces	space	NOUN
cana-6095	103	47	(	(	PUNCT
cana-6095	103	48	e.g.	e.g.	ADV
cana-6095	103	49	,	,	PUNCT
cana-6095	103	50	from	from	ADP
cana-6095	103	51	parameters	parameter	NOUN
cana-6095	103	52	to	to	ADP
cana-6095	103	53	solutions	solution	NOUN
cana-6095	103	54	)	)	PUNCT
cana-6095	103	55	with	with	ADP
cana-6095	103	56	reliable	reliable	ADJ
cana-6095	103	57	uncertainty	uncertainty	NOUN
cana-6095	103	58	estimates	estimate	VERB
cana-6095	103	59	9	9	NUM
cana-6095	103	60	.	.	PUNCT
cana-6095	103	61	methods	method	NOUN
cana-6095	103	62	like	like	ADP
cana-6095	103	63	bayesian	bayesian	NOUN
cana-6095	103	64	deeponets	deeponet	NOUN
cana-6095	103	65	and	and	CCONJ
cana-6095	103	66	fourier	fouri	ADJ
cana-6095	103	67	neural	neural	ADJ
cana-6095	103	68	operators	operator	NOUN
cana-6095	103	69	provide	provide	VERB
cana-6095	103	70	uncertainty	uncertainty	NOUN
cana-6095	103	71	-	-	PUNCT
cana-6095	103	72	aware	aware	ADJ
cana-6095	103	73	surrogates	surrogate	NOUN
cana-6095	103	74	for	for	ADP
cana-6095	103	75	complex	complex	ADJ
cana-6095	103	76	physical	physical	ADJ
cana-6095	103	77	systems	system	NOUN
cana-6095	103	78	.	.	PUNCT
cana-6095	104	1	multifidelity	multifidelity	NOUN
cana-6095	104	2	modeling	modeling	NOUN
cana-6095	104	3	combines	combine	VERB
cana-6095	104	4	information	information	NOUN
cana-6095	104	5	from	from	ADP
cana-6095	104	6	high	high	ADJ
cana-6095	104	7	-	-	PUNCT
cana-6095	104	8	fidelity	fidelity	NOUN
cana-6095	104	9	(	(	PUNCT
cana-6095	104	10	expensive	expensive	ADJ
cana-6095	104	11	)	)	PUNCT
cana-6095	104	12	and	and	CCONJ
cana-6095	104	13	low	low	ADJ
cana-6095	104	14	-	-	PUNCT
cana-6095	104	15	fidelity	fidelity	NOUN
cana-6095	104	16	(	(	PUNCT
cana-6095	104	17	cheap	cheap	ADJ
cana-6095	104	18	)	)	PUNCT
cana-6095	104	19	models	model	NOUN
cana-6095	104	20	10	10	NUM
cana-6095	104	21	.	.	PUNCT
cana-6095	105	1	bayesian	bayesian	NOUN
cana-6095	105	2	approaches	approach	NOUN
cana-6095	105	3	naturally	naturally	ADV
cana-6095	105	4	balance	balance	VERB
cana-6095	105	5	these	these	DET
cana-6095	105	6	information	information	NOUN
cana-6095	105	7	sources	source	NOUN
cana-6095	105	8	while	while	SCONJ
cana-6095	105	9	quantifying	quantify	VERB
cana-6095	105	10	uncertainty	uncertainty	NOUN
cana-6095	105	11	from	from	ADP
cana-6095	105	12	each	each	DET
cana-6095	105	13	fidelity	fidelity	NOUN
cana-6095	105	14	level	level	NOUN
cana-6095	105	15	.	.	PUNCT
cana-6095	106	1	simulation	simulation	NOUN
cana-6095	106	2	-	-	PUNCT
cana-6095	106	3	based	base	VERB
cana-6095	106	4	inference	inference	NOUN
cana-6095	106	5	uses	use	VERB
cana-6095	106	6	simulations	simulation	NOUN
cana-6095	106	7	to	to	PART
cana-6095	106	8	perform	perform	VERB
cana-6095	106	9	bayesian	bayesian	NOUN
cana-6095	106	10	inference	inference	NOUN
cana-6095	106	11	when	when	SCONJ
cana-6095	106	12	likelihoods	likelihood	NOUN
cana-6095	106	13	are	be	AUX
cana-6095	106	14	intractable	intractable	ADJ
cana-6095	106	15	10	10	NUM
cana-6095	106	16	.	.	PUNCT
cana-6095	107	1	bnns	bnns	PROPN
cana-6095	107	2	can	can	AUX
cana-6095	107	3	serve	serve	VERB
cana-6095	107	4	as	as	ADP
cana-6095	107	5	flexible	flexible	ADJ
cana-6095	107	6	surrogate	surrogate	ADJ
cana-6095	107	7	models	model	NOUN
cana-6095	107	8	that	that	PRON
cana-6095	107	9	enable	enable	VERB
cana-6095	107	10	efficient	efficient	ADJ
cana-6095	107	11	inference	inference	NOUN
cana-6095	107	12	while	while	SCONJ
cana-6095	107	13	providing	provide	VERB
cana-6095	107	14	uncertainty	uncertainty	NOUN
cana-6095	107	15	estimates	estimate	NOUN
cana-6095	107	16	.	.	PUNCT
cana-6095	108	1	application	application	NOUN
cana-6095	108	2	domain	domain	NOUN
cana-6095	108	3	key	key	NOUN
cana-6095	108	4	challenges	challenge	NOUN
cana-6095	108	5	bnn	bnn	PROPN
cana-6095	108	6	approaches	approach	VERB
cana-6095	108	7	benefits	benefit	VERB
cana-6095	108	8	pde	pde	NOUN
cana-6095	108	9	solving	solve	VERB
cana-6095	108	10	high	high	ADJ
cana-6095	108	11	-	-	PUNCT
cana-6095	108	12	dimensionality	dimensionality	NOUN
cana-6095	108	13	,	,	PUNCT
cana-6095	108	14	complex	complex	ADJ
cana-6095	108	15	geometry	geometry	NOUN
cana-6095	108	16	physics	physics	NOUN
cana-6095	108	17	-	-	PUNCT
cana-6095	108	18	informed	inform	VERB
cana-6095	108	19	bnns	bnn	NOUN
cana-6095	108	20	,	,	PUNCT
cana-6095	108	21	latent	latent	ADJ
cana-6095	108	22	evolution	evolution	NOUN
cana-6095	108	23	models	model	VERB
cana-6095	108	24	uncertainty	uncertainty	NOUN
cana-6095	108	25	-	-	PUNCT
cana-6095	108	26	aware	aware	ADJ
cana-6095	108	27	solutions	solution	NOUN
cana-6095	108	28	,	,	PUNCT
cana-6095	108	29	physical	physical	ADJ
cana-6095	108	30	consistency	consistency	NOUN
cana-6095	108	31	numerical	numerical	ADJ
cana-6095	108	32	integration	integration	NOUN
cana-6095	108	33	curse	curse	NOUN
cana-6095	108	34	of	of	ADP
cana-6095	108	35	dimensionality	dimensionality	NOUN
cana-6095	108	36	,	,	PUNCT
cana-6095	108	37	complex	complex	ADJ
cana-6095	108	38	integrands	integrand	NOUN
cana-6095	108	39	bayesian	bayesian	NOUN
cana-6095	108	40	quadrature	quadrature	NOUN
cana-6095	108	41	,	,	PUNCT
cana-6095	108	42	bayesian	bayesian	PROPN
cana-6095	108	43	stein	stein	PROPN
cana-6095	108	44	networks	networks	PROPN
cana-6095	108	45	probabilistic	probabilistic	ADJ
cana-6095	108	46	error	error	NOUN
cana-6095	108	47	estimates	estimate	NOUN
cana-6095	108	48	,	,	PUNCT
cana-6095	108	49	adaptive	adaptive	ADJ
cana-6095	108	50	sampling	sample	VERB
cana-6095	108	51	materials	material	NOUN
cana-6095	108	52	modeling	model	VERB
cana-6095	108	53	limited	limited	ADJ
cana-6095	108	54	data	datum	NOUN
cana-6095	108	55	,	,	PUNCT
cana-6095	108	56	multiscale	multiscale	ADJ
cana-6095	108	57	complexity	complexity	NOUN
cana-6095	108	58	bayesian	bayesian	NOUN
cana-6095	108	59	structureproperty	structureproperty	NOUN
cana-6095	108	60	linkages	linkage	VERB
cana-6095	108	61	uncertainty	uncertainty	NOUN
cana-6095	108	62	propagation	propagation	NOUN
cana-6095	108	63	across	across	ADP
cana-6095	108	64	scales	scale	NOUN
cana-6095	108	65	inverse	inverse	NOUN
cana-6095	108	66	problems	problem	NOUN
cana-6095	108	67	ill	ill	ADJ
cana-6095	108	68	-	-	PUNCT
cana-6095	108	69	posedness	posedness	NOUN
cana-6095	108	70	,	,	PUNCT
cana-6095	108	71	noise	noise	NOUN
cana-6095	108	72	amplification	amplification	NOUN
cana-6095	108	73	bayesian	bayesian	NOUN
cana-6095	108	74	inference	inference	NOUN
cana-6095	108	75	with	with	ADP
cana-6095	108	76	physical	physical	ADJ
cana-6095	108	77	constraints	constraint	NOUN
cana-6095	108	78	regularization	regularization	NOUN
cana-6095	108	79	through	through	ADP
cana-6095	108	80	priors	prior	NOUN
cana-6095	108	81	,	,	PUNCT
cana-6095	108	82	uncertainty	uncertainty	NOUN
cana-6095	108	83	quantification	quantification	NOUN
cana-6095	108	84	optimization	optimization	NOUN
cana-6095	108	85	multiple	multiple	ADJ
cana-6095	108	86	minima	minima	PROPN
cana-6095	108	87	,	,	PUNCT
cana-6095	108	88	expensive	expensive	ADJ
cana-6095	108	89	evaluations	evaluation	NOUN
cana-6095	108	90	bayesian	bayesian	VERB
cana-6095	108	91	optimization	optimization	NOUN
cana-6095	108	92	efficient	efficient	ADJ
cana-6095	108	93	global	global	ADJ
cana-6095	108	94	optimization	optimization	NOUN
cana-6095	108	95	with	with	ADP
cana-6095	108	96	uncertainty	uncertainty	NOUN
cana-6095	108	97	guidance	guidance	NOUN
cana-6095	108	98	table	table	NOUN
cana-6095	108	99	3	3	NUM
cana-6095	108	100	:	:	PUNCT
cana-6095	108	101	applications	application	NOUN
cana-6095	108	102	of	of	ADP
cana-6095	108	103	bayesian	bayesian	NOUN
cana-6095	108	104	neural	neural	ADJ
cana-6095	108	105	networks	network	NOUN
cana-6095	108	106	in	in	ADP
cana-6095	108	107	numerical	numerical	ADJ
cana-6095	108	108	methods	method	NOUN
cana-6095	108	109	5.challenges	5.challenges	NUM
cana-6095	108	110	and	and	CCONJ
cana-6095	108	111	limitations	limitation	NOUN
cana-6095	108	112	5.1	5.1	NUM
cana-6095	108	113	scalability	scalability	NOUN
cana-6095	108	114	and	and	CCONJ
cana-6095	108	115	computational	computational	ADJ
cana-6095	108	116	complexity	complexity	NOUN
cana-6095	108	117	the	the	DET
cana-6095	108	118	application	application	NOUN
cana-6095	108	119	of	of	ADP
cana-6095	108	120	bayesian	bayesian	NOUN
cana-6095	108	121	neural	neural	ADJ
cana-6095	108	122	networks	network	NOUN
cana-6095	108	123	to	to	ADP
cana-6095	108	124	large	large	ADJ
cana-6095	108	125	-	-	PUNCT
cana-6095	108	126	scale	scale	NOUN
cana-6095	108	127	numerical	numerical	ADJ
cana-6095	108	128	problems	problem	NOUN
cana-6095	108	129	faces	face	VERB
cana-6095	108	130	significant	significant	ADJ
cana-6095	108	131	scalability	scalability	NOUN
cana-6095	108	132	challenges	challenge	NOUN
cana-6095	108	133	.	.	PUNCT
cana-6095	109	1	traditional	traditional	ADJ
cana-6095	109	2	bayesian	bayesian	NOUN
cana-6095	109	3	inference	inference	NOUN
cana-6095	109	4	methods	method	NOUN
cana-6095	109	5	such	such	ADJ
cana-6095	109	6	as	as	ADP
cana-6095	109	7	mcmc	mcmc	PROPN
cana-6095	109	8	scale	scale	NOUN
cana-6095	109	9	poorly	poorly	ADV
cana-6095	109	10	with	with	ADP
cana-6095	109	11	both	both	PRON
cana-6095	109	12	data	datum	NOUN
cana-6095	109	13	size	size	NOUN
cana-6095	109	14	and	and	CCONJ
cana-6095	109	15	model	model	NOUN
cana-6095	109	16	complexity	complexity	NOUN
cana-6095	109	17	,	,	PUNCT
cana-6095	109	18	making	make	VERB
cana-6095	109	19	them	they	PRON
cana-6095	109	20	impractical	impractical	ADJ
cana-6095	109	21	for	for	ADP
cana-6095	109	22	modern	modern	ADJ
cana-6095	109	23	deep	deep	ADJ
cana-6095	109	24	learning	learning	NOUN
cana-6095	109	25	applications	application	NOUN
cana-6095	109	26	68	68	NUM
cana-6095	109	27	.	.	PUNCT
cana-6095	110	1	variational	variational	ADJ
cana-6095	110	2	inference	inference	NOUN
cana-6095	110	3	methods	method	NOUN
cana-6095	110	4	offer	offer	VERB
cana-6095	110	5	better	well	ADJ
cana-6095	110	6	scalability	scalability	NOUN
cana-6095	110	7	but	but	CCONJ
cana-6095	110	8	may	may	AUX
cana-6095	110	9	provide	provide	VERB
cana-6095	110	10	poor	poor	ADJ
cana-6095	110	11	approximations	approximation	NOUN
cana-6095	110	12	to	to	ADP
cana-6095	110	13	the	the	DET
cana-6095	110	14	true	true	ADJ
cana-6095	110	15	posterior	posterior	NOUN
cana-6095	110	16	if	if	SCONJ
cana-6095	110	17	the	the	DET
cana-6095	110	18	variational	variational	ADJ
cana-6095	110	19	family	family	NOUN
cana-6095	110	20	is	be	AUX
cana-6095	110	21	too	too	ADV
cana-6095	110	22	restrictive	restrictive	ADJ
cana-6095	110	23	.	.	PUNCT
cana-6095	111	1	memory	memory	NOUN
cana-6095	111	2	requirements	requirement	NOUN
cana-6095	111	3	for	for	ADP
cana-6095	111	4	storing	store	VERB
cana-6095	111	5	and	and	CCONJ
cana-6095	111	6	manipulating	manipulate	VERB
cana-6095	111	7	distributions	distribution	NOUN
cana-6095	111	8	over	over	ADP
cana-6095	111	9	parameters	parameter	NOUN
cana-6095	111	10	can	can	AUX
cana-6095	111	11	be	be	AUX
cana-6095	111	12	prohibitive	prohibitive	ADJ
cana-6095	111	13	,	,	PUNCT
cana-6095	111	14	as	as	SCONJ
cana-6095	111	15	bayesian	bayesian	NOUN
cana-6095	111	16	approaches	approach	NOUN
cana-6095	111	17	typically	typically	ADV
cana-6095	111	18	require	require	VERB
cana-6095	111	19	at	at	ADV
cana-6095	111	20	least	least	ADJ
cana-6095	111	21	twice	twice	DET
cana-6095	111	22	the	the	DET
cana-6095	111	23	memory	memory	NOUN
cana-6095	111	24	of	of	ADP
cana-6095	111	25	deterministic	deterministic	ADJ
cana-6095	111	26	networks	network	NOUN
cana-6095	111	27	8	8	NUM
cana-6095	111	28	.	.	PUNCT
cana-6095	112	1	this	this	DET
cana-6095	112	2	limitation	limitation	NOUN
cana-6095	112	3	becomes	become	VERB
cana-6095	112	4	particularly	particularly	ADV
cana-6095	112	5	acute	acute	ADJ
cana-6095	112	6	for	for	ADP
cana-6095	112	7	large	large	ADJ
cana-6095	112	8	-	-	PUNCT
cana-6095	112	9	scale	scale	NOUN
cana-6095	112	10	numerical	numerical	ADJ
cana-6095	112	11	simulations	simulation	NOUN
cana-6095	112	12	with	with	ADP
cana-6095	112	13	high	high	ADV
cana-6095	112	14	-	-	PUNCT
cana-6095	112	15	dimensional	dimensional	ADJ
cana-6095	112	16	parameter	parameter	NOUN
cana-6095	112	17	spaces	space	NOUN
cana-6095	112	18	.	.	PUNCT
cana-6095	113	1	training	training	NOUN
cana-6095	113	2	time	time	NOUN
cana-6095	113	3	for	for	ADP
cana-6095	113	4	bayesian	bayesian	NOUN
cana-6095	113	5	neural	neural	ADJ
cana-6095	113	6	networks	network	NOUN
cana-6095	113	7	is	be	AUX
cana-6095	113	8	generally	generally	ADV
cana-6095	113	9	longer	long	ADJ
cana-6095	113	10	than	than	ADP
cana-6095	113	11	for	for	ADP
cana-6095	113	12	their	their	PRON
cana-6095	113	13	deterministic	deterministic	ADJ
cana-6095	113	14	counterparts	counterpart	NOUN
cana-6095	113	15	,	,	PUNCT
cana-6095	113	16	as	as	SCONJ
cana-6095	113	17	it	it	PRON
cana-6095	113	18	involves	involve	VERB
cana-6095	113	19	optimizing	optimize	VERB
cana-6095	113	20	distributions	distribution	NOUN
cana-6095	113	21	rather	rather	ADV
cana-6095	113	22	than	than	ADP
cana-6095	113	23	point	point	NOUN
cana-6095	113	24	estimates	estimate	NOUN
cana-6095	114	1	68	68	NUM
cana-6095	114	2	.	.	PUNCT
cana-6095	115	1	this	this	DET
cana-6095	115	2	computational	computational	ADJ
cana-6095	115	3	overhead	overhead	NOUN
cana-6095	115	4	can	can	AUX
cana-6095	115	5	be	be	AUX
cana-6095	115	6	problematic	problematic	ADJ
cana-6095	115	7	for	for	ADP
cana-6095	115	8	time	time	NOUN
cana-6095	115	9	-	-	PUNCT
cana-6095	115	10	sensitive	sensitive	ADJ
cana-6095	115	11	applications	application	NOUN
cana-6095	115	12	or	or	CCONJ
cana-6095	115	13	when	when	SCONJ
cana-6095	115	14	extensive	extensive	ADJ
cana-6095	115	15	hyperparameter	hyperparameter	NOUN
cana-6095	115	16	tuning	tuning	NOUN
cana-6095	115	17	is	be	AUX
cana-6095	115	18	required	require	VERB
cana-6095	115	19	.	.	PUNCT
cana-6095	116	1	5.2	5.2	NUM
cana-6095	116	2	multi	multi	ADJ
cana-6095	116	3	-	-	ADJ
cana-6095	116	4	modal	modal	ADJ
cana-6095	116	5	posteriors	posterior	NOUN
cana-6095	116	6	and	and	CCONJ
cana-6095	116	7	convergence	convergence	NOUN
cana-6095	116	8	issues	issue	NOUN
cana-6095	116	9	the	the	DET
cana-6095	116	10	posterior	posterior	ADJ
cana-6095	116	11	distributions	distribution	NOUN
cana-6095	116	12	over	over	ADP
cana-6095	116	13	parameters	parameter	NOUN
cana-6095	116	14	in	in	ADP
cana-6095	116	15	deep	deep	ADJ
cana-6095	116	16	neural	neural	ADJ
cana-6095	116	17	networks	network	NOUN
cana-6095	116	18	are	be	AUX
cana-6095	116	19	often	often	ADV
cana-6095	116	20	highly	highly	ADV
cana-6095	116	21	complex	complex	ADJ
cana-6095	116	22	,	,	PUNCT
cana-6095	116	23	with	with	ADP
cana-6095	116	24	multiple	multiple	ADJ
cana-6095	116	25	modes	mode	NOUN
cana-6095	116	26	and	and	CCONJ
cana-6095	116	27	complex	complex	ADJ
cana-6095	116	28	correlation	correlation	NOUN
cana-6095	116	29	structures	structure	NOUN
cana-6095	116	30	9	9	NUM
cana-6095	116	31	.	.	PUNCT
cana-6095	117	1	standard	standard	ADJ
cana-6095	117	2	variational	variational	ADJ
cana-6095	117	3	inference	inference	NOUN
cana-6095	117	4	methods	method	NOUN
cana-6095	117	5	that	that	PRON
cana-6095	117	6	use	use	VERB
cana-6095	117	7	simple	simple	ADJ
cana-6095	117	8	gaussian	gaussian	ADJ
cana-6095	117	9	approximations	approximation	NOUN
cana-6095	117	10	may	may	AUX
cana-6095	117	11	fail	fail	VERB
cana-6095	117	12	to	to	PART
cana-6095	117	13	capture	capture	VERB
cana-6095	117	14	this	this	DET
cana-6095	117	15	complexity	complexity	NOUN
cana-6095	117	16	,	,	PUNCT
cana-6095	117	17	leading	lead	VERB
cana-6095	117	18	to	to	ADP
cana-6095	117	19	poor	poor	ADJ
cana-6095	117	20	uncertainty	uncertainty	NOUN
cana-6095	117	21	estimates	estimate	NOUN
cana-6095	117	22	.	.	PUNCT
cana-6095	118	1	convergence	convergence	NOUN
cana-6095	118	2	issues	issue	NOUN
cana-6095	118	3	plague	plague	VERB
cana-6095	118	4	many	many	ADJ
cana-6095	118	5	inference	inference	NOUN
cana-6095	118	6	algorithms	algorithm	NOUN
cana-6095	118	7	,	,	PUNCT
cana-6095	118	8	with	with	ADP
cana-6095	118	9	diagnostics	diagnostic	NOUN
cana-6095	118	10	that	that	PRON
cana-6095	118	11	are	be	AUX
cana-6095	118	12	difficult	difficult	ADJ
cana-6095	118	13	to	to	PART
cana-6095	118	14	interpret	interpret	VERB
cana-6095	118	15	and	and	CCONJ
cana-6095	118	16	convergence	convergence	NOUN
cana-6095	118	17	guarantees	guarantee	NOUN
cana-6095	118	18	that	that	PRON
cana-6095	118	19	are	be	AUX
cana-6095	118	20	rarely	rarely	ADV
cana-6095	118	21	available	available	ADJ
cana-6095	118	22	69	69	NUM
cana-6095	118	23	.	.	PUNCT
cana-6095	119	1	this	this	PRON
cana-6095	119	2	is	be	AUX
cana-6095	119	3	particularly	particularly	ADV
cana-6095	119	4	problematic	problematic	ADJ
cana-6095	119	5	for	for	ADP
cana-6095	119	6	scientific	scientific	ADJ
cana-6095	119	7	applications	application	NOUN
cana-6095	119	8	where	where	SCONJ
cana-6095	119	9	reliability	reliability	NOUN
cana-6095	119	10	is	be	AUX
cana-6095	119	11	paramount	paramount	ADJ
cana-6095	119	12	.	.	PUNCT
cana-6095	120	1	local	local	ADJ
cana-6095	120	2	approximations	approximation	NOUN
cana-6095	120	3	such	such	ADJ
cana-6095	120	4	as	as	ADP
cana-6095	120	5	the	the	DET
cana-6095	120	6	laplace	laplace	NOUN
cana-6095	120	7	approximation	approximation	NOUN
cana-6095	120	8	provide	provide	VERB
cana-6095	120	9	computationally	computationally	ADV
cana-6095	120	10	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	NUM
cana-6095	120	11	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	NOUN
cana-6095	120	12	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	NOUN
cana-6095	121	1	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	121	2	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	VERB
cana-6095	121	3	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	VERB
cana-6095	121	4	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	121	5	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	VERB
cana-6095	121	6	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	121	7	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	VERB
cana-6095	121	8	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	121	9	communications	communication	NOUN
cana-6095	121	10	on	on	ADP
cana-6095	121	11	applied	apply	VERB
cana-6095	121	12	nonlinear	nonlinear	ADJ
cana-6095	121	13	analysis	analysis	NOUN
cana-6095	121	14	issn	issn	NOUN
cana-6095	121	15	:	:	PUNCT
cana-6095	121	16	1074	1074	NUM
cana-6095	121	17	-	-	PUNCT
cana-6095	121	18	133x	133x	NUM
cana-6095	121	19	vol	vol	NOUN
cana-6095	121	20	30	30	NUM
cana-6095	121	21	no	no	NOUN
cana-6095	121	22	.	.	NOUN
cana-6095	121	23	3	3	NUM
cana-6095	121	24	(	(	PUNCT
cana-6095	121	25	2023	2023	NUM
cana-6095	121	26	)	)	PUNCT
cana-6095	122	1	62	62	NUM
cana-6095	122	2	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-6095	122	3	efficient	efficient	ADJ
cana-6095	122	4	alternatives	alternative	NOUN
cana-6095	122	5	but	but	CCONJ
cana-6095	122	6	may	may	AUX
cana-6095	122	7	yield	yield	VERB
cana-6095	122	8	overconfident	overconfident	ADJ
cana-6095	122	9	uncertainty	uncertainty	NOUN
cana-6095	122	10	estimates	estimate	NOUN
cana-6095	122	11	,	,	PUNCT
cana-6095	122	12	especially	especially	ADV
cana-6095	122	13	for	for	ADP
cana-6095	122	14	out	out	ADV
cana-6095	122	15	-	-	PUNCT
cana-6095	122	16	of	of	ADP
cana-6095	122	17	-	-	PUNCT
cana-6095	122	18	distribution	distribution	NOUN
cana-6095	122	19	data	datum	NOUN
cana-6095	122	20	8	8	NUM
cana-6095	122	21	.	.	PUNCT
cana-6095	123	1	developing	develop	VERB
cana-6095	123	2	methods	method	NOUN
cana-6095	123	3	that	that	PRON
cana-6095	123	4	capture	capture	VERB
cana-6095	123	5	the	the	DET
cana-6095	123	6	true	true	ADJ
cana-6095	123	7	posterior	posterior	ADJ
cana-6095	123	8	complexity	complexity	NOUN
cana-6095	123	9	while	while	SCONJ
cana-6095	123	10	remaining	remain	VERB
cana-6095	123	11	computationally	computationally	ADV
cana-6095	123	12	tractable	tractable	ADJ
cana-6095	123	13	remains	remain	VERB
cana-6095	123	14	an	an	DET
cana-6095	123	15	open	open	ADJ
cana-6095	123	16	challenge	challenge	NOUN
cana-6095	123	17	.	.	PUNCT
cana-6095	124	1	5.3	5.3	NUM
cana-6095	124	2	evaluation	evaluation	NOUN
cana-6095	124	3	and	and	CCONJ
cana-6095	124	4	validation	validation	NOUN
cana-6095	124	5	of	of	ADP
cana-6095	124	6	uncertainty	uncertainty	NOUN
cana-6095	124	7	estimates	estimate	NOUN
cana-6095	124	8	evaluating	evaluate	VERB
cana-6095	124	9	uncertainty	uncertainty	NOUN
cana-6095	124	10	estimates	estimate	NOUN
cana-6095	124	11	is	be	AUX
cana-6095	124	12	fundamentally	fundamentally	ADV
cana-6095	124	13	challenging	challenging	ADJ
cana-6095	124	14	because	because	SCONJ
cana-6095	124	15	ground	ground	NOUN
cana-6095	124	16	truth	truth	NOUN
cana-6095	124	17	uncertainties	uncertainty	NOUN
cana-6095	124	18	are	be	AUX
cana-6095	124	19	rarely	rarely	ADV
cana-6095	124	20	available	available	ADJ
cana-6095	124	21	9	9	NUM
cana-6095	124	22	.	.	PUNCT
cana-6095	124	23	traditional	traditional	ADJ
cana-6095	124	24	metrics	metric	NOUN
cana-6095	124	25	like	like	ADP
cana-6095	124	26	negative	negative	ADJ
cana-6095	124	27	log	log	NOUN
cana-6095	124	28	-	-	PUNCT
cana-6095	124	29	likelihood	likelihood	NOUN
cana-6095	124	30	or	or	CCONJ
cana-6095	124	31	proper	proper	ADJ
cana-6095	124	32	scoring	scoring	NOUN
cana-6095	124	33	rules	rule	NOUN
cana-6095	124	34	provide	provide	VERB
cana-6095	124	35	aggregate	aggregate	ADJ
cana-6095	124	36	measures	measure	NOUN
cana-6095	124	37	but	but	CCONJ
cana-6095	124	38	may	may	AUX
cana-6095	124	39	not	not	PART
cana-6095	124	40	detect	detect	VERB
cana-6095	124	41	systematic	systematic	ADJ
cana-6095	124	42	deficiencies	deficiency	NOUN
cana-6095	124	43	in	in	ADP
cana-6095	124	44	uncertainty	uncertainty	NOUN
cana-6095	124	45	quantification	quantification	NOUN
cana-6095	124	46	.	.	PUNCT
cana-6095	125	1	calibration	calibration	NOUN
cana-6095	125	2	of	of	ADP
cana-6095	125	3	uncertainty	uncertainty	NOUN
cana-6095	125	4	estimates	estimate	NOUN
cana-6095	125	5	is	be	AUX
cana-6095	125	6	essential	essential	ADJ
cana-6095	125	7	for	for	ADP
cana-6095	125	8	reliable	reliable	ADJ
cana-6095	125	9	decision	decision	NOUN
cana-6095	125	10	-	-	PUNCT
cana-6095	125	11	making	making	NOUN
cana-6095	125	12	.	.	PUNCT
cana-6095	126	1	a	a	DET
cana-6095	126	2	well	well	ADV
cana-6095	126	3	-	-	PUNCT
cana-6095	126	4	calibrated	calibrate	VERB
cana-6095	126	5	model	model	NOUN
cana-6095	126	6	should	should	AUX
cana-6095	126	7	produce	produce	VERB
cana-6095	126	8	predictive	predictive	ADJ
cana-6095	126	9	distributions	distribution	NOUN
cana-6095	126	10	where	where	SCONJ
cana-6095	126	11	events	event	NOUN
cana-6095	126	12	claimed	claim	VERB
cana-6095	126	13	to	to	PART
cana-6095	126	14	have	have	VERB
cana-6095	126	15	probability	probability	NOUN
cana-6095	126	16	p	p	PRON
cana-6095	126	17	actually	actually	ADV
cana-6095	126	18	occur	occur	VERB
cana-6095	126	19	with	with	ADP
cana-6095	126	20	frequency	frequency	NOUN
cana-6095	126	21	p	p	PROPN
cana-6095	126	22	1,9	1,9	NUM
cana-6095	126	23	.	.	PUNCT
cana-6095	127	1	however	however	ADV
cana-6095	127	2	,	,	PUNCT
cana-6095	127	3	achieving	achieve	VERB
cana-6095	127	4	good	good	ADJ
cana-6095	127	5	calibration	calibration	NOUN
cana-6095	127	6	across	across	ADP
cana-6095	127	7	all	all	DET
cana-6095	127	8	input	input	NOUN
cana-6095	127	9	domains	domain	NOUN
cana-6095	127	10	remains	remain	VERB
cana-6095	127	11	challenging	challenging	ADJ
cana-6095	127	12	,	,	PUNCT
cana-6095	127	13	especially	especially	ADV
cana-6095	127	14	for	for	ADP
cana-6095	127	15	out	out	ADV
cana-6095	127	16	-	-	PUNCT
cana-6095	127	17	of	of	ADP
cana-6095	127	18	-	-	PUNCT
cana-6095	127	19	distribution	distribution	NOUN
cana-6095	127	20	inputs	input	NOUN
cana-6095	127	21	.	.	PUNCT
cana-6095	128	1	validation	validation	NOUN
cana-6095	128	2	methodologies	methodology	NOUN
cana-6095	128	3	for	for	ADP
cana-6095	128	4	uq	uq	NOUN
cana-6095	128	5	in	in	ADP
cana-6095	128	6	scientific	scientific	ADJ
cana-6095	128	7	applications	application	NOUN
cana-6095	128	8	often	often	ADV
cana-6095	128	9	require	require	VERB
cana-6095	128	10	specialized	specialized	ADJ
cana-6095	128	11	approaches	approach	NOUN
cana-6095	128	12	that	that	PRON
cana-6095	128	13	account	account	VERB
cana-6095	128	14	for	for	ADP
cana-6095	128	15	physical	physical	ADJ
cana-6095	128	16	constraints	constraint	NOUN
cana-6095	128	17	and	and	CCONJ
cana-6095	128	18	domain	domain	NOUN
cana-6095	128	19	-	-	PUNCT
cana-6095	128	20	specific	specific	ADJ
cana-6095	128	21	requirements	requirement	NOUN
cana-6095	128	22	9	9	NUM
cana-6095	128	23	.	.	X
cana-6095	128	24	developing	develop	VERB
cana-6095	128	25	comprehensive	comprehensive	ADJ
cana-6095	128	26	validation	validation	NOUN
cana-6095	128	27	frameworks	framework	NOUN
cana-6095	128	28	that	that	PRON
cana-6095	128	29	go	go	VERB
cana-6095	128	30	beyond	beyond	ADP
cana-6095	128	31	statistical	statistical	ADJ
cana-6095	128	32	metrics	metric	NOUN
cana-6095	128	33	to	to	PART
cana-6095	128	34	include	include	VERB
cana-6095	128	35	physical	physical	ADJ
cana-6095	128	36	plausibility	plausibility	NOUN
cana-6095	128	37	remains	remain	VERB
cana-6095	128	38	an	an	DET
cana-6095	128	39	active	active	ADJ
cana-6095	128	40	research	research	NOUN
cana-6095	128	41	area	area	NOUN
cana-6095	128	42	.	.	PUNCT
cana-6095	129	1	5.4	5.4	NUM
cana-6095	129	2	distribution	distribution	NOUN
cana-6095	129	3	shift	shift	NOUN
cana-6095	129	4	and	and	CCONJ
cana-6095	129	5	out	out	ADP
cana-6095	129	6	-	-	PUNCT
cana-6095	129	7	of	of	ADP
cana-6095	129	8	-	-	PUNCT
cana-6095	129	9	domain	domain	NOUN
cana-6095	129	10	generalization	generalization	NOUN
cana-6095	129	11	distribution	distribution	NOUN
cana-6095	129	12	shift	shift	NOUN
cana-6095	129	13	occurs	occur	VERB
cana-6095	129	14	when	when	SCONJ
cana-6095	129	15	test	test	NOUN
cana-6095	129	16	data	datum	NOUN
cana-6095	129	17	comes	come	VERB
cana-6095	129	18	from	from	ADP
cana-6095	129	19	a	a	DET
cana-6095	129	20	different	different	ADJ
cana-6095	129	21	distribution	distribution	NOUN
cana-6095	129	22	than	than	ADP
cana-6095	129	23	training	train	VERB
cana-6095	129	24	data	datum	NOUN
cana-6095	129	25	,	,	PUNCT
cana-6095	129	26	posing	pose	VERB
cana-6095	129	27	significant	significant	ADJ
cana-6095	129	28	challenges	challenge	NOUN
cana-6095	129	29	for	for	ADP
cana-6095	129	30	uncertainty	uncertainty	NOUN
cana-6095	129	31	quantification	quantification	NOUN
cana-6095	129	32	9	9	NUM
cana-6095	129	33	.	.	PUNCT
cana-6095	130	1	while	while	SCONJ
cana-6095	130	2	bayesian	bayesian	NOUN
cana-6095	130	3	methods	method	NOUN
cana-6095	130	4	theoretically	theoretically	ADV
cana-6095	130	5	should	should	AUX
cana-6095	130	6	express	express	VERB
cana-6095	130	7	increased	increase	VERB
cana-6095	130	8	uncertainty	uncertainty	NOUN
cana-6095	130	9	under	under	ADP
cana-6095	130	10	distribution	distribution	NOUN
cana-6095	130	11	shift	shift	NOUN
cana-6095	130	12	,	,	PUNCT
cana-6095	130	13	in	in	ADP
cana-6095	130	14	practice	practice	NOUN
cana-6095	130	15	they	they	PRON
cana-6095	130	16	often	often	ADV
cana-6095	130	17	produce	produce	VERB
cana-6095	130	18	overconfident	overconfident	ADJ
cana-6095	130	19	predictions	prediction	NOUN
cana-6095	130	20	.	.	PUNCT
cana-6095	131	1	out	out	ADP
cana-6095	131	2	-	-	PUNCT
cana-6095	131	3	of	of	ADP
cana-6095	131	4	-	-	PUNCT
cana-6095	131	5	domain	domain	NOUN
cana-6095	131	6	detection	detection	NOUN
cana-6095	131	7	capabilities	capability	NOUN
cana-6095	131	8	are	be	AUX
cana-6095	131	9	essential	essential	ADJ
cana-6095	131	10	for	for	ADP
cana-6095	131	11	scientific	scientific	ADJ
cana-6095	131	12	applications	application	NOUN
cana-6095	131	13	where	where	SCONJ
cana-6095	131	14	models	model	NOUN
cana-6095	131	15	may	may	AUX
cana-6095	131	16	be	be	AUX
cana-6095	131	17	applied	apply	VERB
cana-6095	131	18	beyond	beyond	ADP
cana-6095	131	19	their	their	PRON
cana-6095	131	20	training	training	NOUN
cana-6095	131	21	regimes	regime	NOUN
cana-6095	131	22	9	9	NUM
cana-6095	131	23	.	.	PUNCT
cana-6095	132	1	current	current	ADJ
cana-6095	132	2	bayesian	bayesian	NOUN
cana-6095	132	3	neural	neural	ADJ
cana-6095	132	4	networks	network	NOUN
cana-6095	132	5	often	often	ADV
cana-6095	132	6	fail	fail	VERB
cana-6095	132	7	to	to	PART
cana-6095	132	8	reliably	reliably	ADV
cana-6095	132	9	detect	detect	VERB
cana-6095	132	10	such	such	ADJ
cana-6095	132	11	scenarios	scenario	NOUN
cana-6095	132	12	,	,	PUNCT
cana-6095	132	13	limiting	limit	VERB
cana-6095	132	14	their	their	PRON
cana-6095	132	15	deployment	deployment	NOUN
cana-6095	132	16	in	in	ADP
cana-6095	132	17	safety	safety	NOUN
cana-6095	132	18	-	-	PUNCT
cana-6095	132	19	critical	critical	ADJ
cana-6095	132	20	applications	application	NOUN
cana-6095	132	21	.	.	PUNCT
cana-6095	133	1	generalization	generalization	NOUN
cana-6095	133	2	to	to	ADP
cana-6095	133	3	novel	novel	ADJ
cana-6095	133	4	physics	physics	NOUN
cana-6095	133	5	is	be	AUX
cana-6095	133	6	particularly	particularly	ADV
cana-6095	133	7	challenging	challenging	ADJ
cana-6095	133	8	when	when	SCONJ
cana-6095	133	9	models	model	NOUN
cana-6095	133	10	encounter	encounter	VERB
cana-6095	133	11	physical	physical	ADJ
cana-6095	133	12	phenomena	phenomenon	NOUN
cana-6095	133	13	not	not	PART
cana-6095	133	14	represented	represent	VERB
cana-6095	133	15	in	in	ADP
cana-6095	133	16	the	the	DET
cana-6095	133	17	training	training	NOUN
cana-6095	133	18	data	datum	NOUN
cana-6095	133	19	9	9	NUM
cana-6095	133	20	.	.	PUNCT
cana-6095	133	21	incorporating	incorporate	VERB
cana-6095	133	22	physical	physical	ADJ
cana-6095	133	23	principles	principle	NOUN
cana-6095	133	24	through	through	ADP
cana-6095	133	25	informed	informed	ADJ
cana-6095	133	26	architectures	architecture	NOUN
cana-6095	133	27	or	or	CCONJ
cana-6095	133	28	loss	loss	NOUN
cana-6095	133	29	functions	function	NOUN
cana-6095	133	30	may	may	AUX
cana-6095	133	31	help	help	VERB
cana-6095	133	32	but	but	CCONJ
cana-6095	133	33	does	do	AUX
cana-6095	133	34	not	not	PART
cana-6095	133	35	fully	fully	ADV
cana-6095	133	36	solve	solve	VERB
cana-6095	133	37	this	this	DET
cana-6095	133	38	problem	problem	NOUN
cana-6095	133	39	.	.	PUNCT
cana-6095	134	1	6.future	6.future	NUM
cana-6095	134	2	directions	direction	NOUN
cana-6095	134	3	6.1	6.1	NUM
cana-6095	134	4	scalable	scalable	ADJ
cana-6095	134	5	inference	inference	NOUN
cana-6095	134	6	methods	method	NOUN
cana-6095	134	7	developing	develop	VERB
cana-6095	134	8	scalable	scalable	ADJ
cana-6095	134	9	inference	inference	NOUN
cana-6095	134	10	methods	method	NOUN
cana-6095	134	11	that	that	PRON
cana-6095	134	12	maintain	maintain	VERB
cana-6095	134	13	approximation	approximation	NOUN
cana-6095	134	14	quality	quality	NOUN
cana-6095	134	15	while	while	SCONJ
cana-6095	134	16	reducing	reduce	VERB
cana-6095	134	17	computational	computational	ADJ
cana-6095	134	18	costs	cost	NOUN
cana-6095	134	19	represents	represent	VERB
cana-6095	134	20	a	a	DET
cana-6095	134	21	critical	critical	ADJ
cana-6095	134	22	research	research	NOUN
cana-6095	134	23	direction	direction	NOUN
cana-6095	134	24	68	68	NUM
cana-6095	134	25	.	.	PUNCT
cana-6095	135	1	promising	promise	VERB
cana-6095	135	2	approaches	approach	NOUN
cana-6095	135	3	include	include	VERB
cana-6095	135	4	:	:	PUNCT
cana-6095	135	5	stochastic	stochastic	ADJ
cana-6095	135	6	gradient	gradient	NOUN
cana-6095	135	7	mcmc	mcmc	PROPN
cana-6095	135	8	methods	method	NOUN
cana-6095	135	9	that	that	PRON
cana-6095	135	10	combine	combine	VERB
cana-6095	135	11	the	the	DET
cana-6095	135	12	scalability	scalability	NOUN
cana-6095	135	13	of	of	ADP
cana-6095	135	14	stochastic	stochastic	ADJ
cana-6095	135	15	optimization	optimization	NOUN
cana-6095	135	16	with	with	ADP
cana-6095	135	17	the	the	DET
cana-6095	135	18	accuracy	accuracy	NOUN
cana-6095	135	19	of	of	ADP
cana-6095	135	20	mcmc	mcmc	PROPN
cana-6095	135	21	sampling	sample	VERB
cana-6095	135	22	6	6	NUM
cana-6095	135	23	.	.	PUNCT
cana-6095	136	1	these	these	DET
cana-6095	136	2	techniques	technique	NOUN
cana-6095	136	3	show	show	VERB
cana-6095	136	4	promise	promise	NOUN
cana-6095	136	5	for	for	ADP
cana-6095	136	6	large	large	ADJ
cana-6095	136	7	-	-	PUNCT
cana-6095	136	8	scale	scale	NOUN
cana-6095	136	9	applications	application	NOUN
cana-6095	136	10	but	but	CCONJ
cana-6095	136	11	require	require	VERB
cana-6095	136	12	careful	careful	ADJ
cana-6095	136	13	tuning	tuning	NOUN
cana-6095	136	14	and	and	CCONJ
cana-6095	136	15	may	may	AUX
cana-6095	136	16	still	still	ADV
cana-6095	136	17	be	be	AUX
cana-6095	136	18	computationally	computationally	ADV
cana-6095	136	19	demanding	demanding	ADJ
cana-6095	136	20	.	.	PUNCT
cana-6095	137	1	structured	structured	ADJ
cana-6095	137	2	variational	variational	ADJ
cana-6095	137	3	approximations	approximation	NOUN
cana-6095	137	4	that	that	PRON
cana-6095	137	5	capture	capture	VERB
cana-6095	137	6	dependencies	dependency	NOUN
cana-6095	137	7	between	between	ADP
cana-6095	137	8	parameters	parameter	NOUN
cana-6095	137	9	while	while	SCONJ
cana-6095	137	10	remaining	remain	VERB
cana-6095	137	11	computationally	computationally	ADV
cana-6095	137	12	tractable	tractable	ADJ
cana-6095	137	13	8	8	NUM
cana-6095	137	14	.	.	PUNCT
cana-6095	138	1	approaches	approach	NOUN
cana-6095	138	2	using	use	VERB
cana-6095	138	3	matrix	matrix	NOUN
cana-6095	138	4	normal	normal	ADJ
cana-6095	138	5	distributions	distribution	NOUN
cana-6095	138	6	or	or	CCONJ
cana-6095	138	7	low	low	ADJ
cana-6095	138	8	-	-	PUNCT
cana-6095	138	9	rank	rank	NOUN
cana-6095	138	10	approximations	approximation	NOUN
cana-6095	138	11	may	may	AUX
cana-6095	138	12	provide	provide	VERB
cana-6095	138	13	better	well	ADJ
cana-6095	138	14	posterior	posterior	ADJ
cana-6095	138	15	approximations	approximation	NOUN
cana-6095	138	16	without	without	ADP
cana-6095	138	17	excessive	excessive	ADJ
cana-6095	138	18	computational	computational	ADJ
cana-6095	138	19	overhead	overhead	NOUN
cana-6095	138	20	.	.	PUNCT
cana-6095	139	1	distributed	distribute	VERB
cana-6095	139	2	and	and	CCONJ
cana-6095	139	3	parallel	parallel	ADJ
cana-6095	139	4	inference	inference	NOUN
cana-6095	139	5	algorithms	algorithm	NOUN
cana-6095	139	6	that	that	PRON
cana-6095	139	7	leverage	leverage	VERB
cana-6095	139	8	modern	modern	ADJ
cana-6095	139	9	computing	computing	NOUN
cana-6095	139	10	architectures	architecture	NOUN
cana-6095	139	11	to	to	PART
cana-6095	139	12	scale	scale	VERB
cana-6095	139	13	bayesian	bayesian	NOUN
cana-6095	139	14	inference	inference	NOUN
cana-6095	139	15	to	to	ADP
cana-6095	139	16	larger	large	ADJ
cana-6095	139	17	models	model	NOUN
cana-6095	139	18	and	and	CCONJ
cana-6095	139	19	datasets	dataset	NOUN
cana-6095	139	20	68	68	NUM
cana-6095	139	21	.	.	PUNCT
cana-6095	140	1	these	these	DET
cana-6095	140	2	approaches	approach	NOUN
cana-6095	140	3	could	could	AUX
cana-6095	140	4	make	make	VERB
cana-6095	140	5	bayesian	bayesian	NOUN
cana-6095	140	6	methods	method	NOUN
cana-6095	140	7	more	more	ADV
cana-6095	140	8	practical	practical	ADJ
cana-6095	140	9	for	for	ADP
cana-6095	140	10	large	large	ADJ
cana-6095	140	11	-	-	PUNCT
cana-6095	140	12	scale	scale	NOUN
cana-6095	140	13	numerical	numerical	ADJ
cana-6095	140	14	simulations	simulation	NOUN
cana-6095	140	15	.	.	PUNCT
cana-6095	141	1	6.2	6.2	NUM
cana-6095	141	2	advanced	advanced	ADJ
cana-6095	141	3	architectures	architecture	NOUN
cana-6095	141	4	and	and	CCONJ
cana-6095	141	5	parameterizations	parameterization	NOUN
cana-6095	141	6	neural	neural	ADJ
cana-6095	141	7	architecture	architecture	NOUN
cana-6095	141	8	search	search	NOUN
cana-6095	141	9	for	for	ADP
cana-6095	141	10	bayesian	bayesian	NOUN
cana-6095	141	11	neural	neural	ADJ
cana-6095	141	12	networks	network	NOUN
cana-6095	141	13	could	could	AUX
cana-6095	141	14	identify	identify	VERB
cana-6095	141	15	architectures	architecture	NOUN
cana-6095	141	16	that	that	PRON
cana-6095	141	17	provide	provide	VERB
cana-6095	141	18	good	good	ADJ
cana-6095	141	19	performance	performance	NOUN
cana-6095	141	20	while	while	SCONJ
cana-6095	141	21	facilitating	facilitate	VERB
cana-6095	141	22	accurate	accurate	ADJ
cana-6095	141	23	uncertainty	uncertainty	NOUN
cana-6095	141	24	quantification	quantification	NOUN
cana-6095	141	25	8	8	NUM
cana-6095	141	26	.	.	PUNCT
cana-6095	142	1	this	this	PRON
cana-6095	142	2	might	might	AUX
cana-6095	142	3	include	include	VERB
cana-6095	142	4	specialized	specialized	ADJ
cana-6095	142	5	layers	layer	NOUN
cana-6095	142	6	or	or	CCONJ
cana-6095	142	7	connections	connection	NOUN
cana-6095	142	8	that	that	PRON
cana-6095	142	9	improve	improve	VERB
cana-6095	142	10	posterior	posterior	ADJ
cana-6095	142	11	expressiveness	expressiveness	NOUN
cana-6095	142	12	or	or	CCONJ
cana-6095	142	13	inference	inference	NOUN
cana-6095	142	14	efficiency	efficiency	NOUN
cana-6095	142	15	.	.	PUNCT
cana-6095	143	1	functional	functional	ADJ
cana-6095	143	2	approaches	approach	NOUN
cana-6095	143	3	that	that	PRON
cana-6095	143	4	operate	operate	VERB
cana-6095	143	5	directly	directly	ADV
cana-6095	143	6	in	in	ADP
cana-6095	143	7	function	function	NOUN
cana-6095	143	8	space	space	NOUN
cana-6095	143	9	rather	rather	ADV
cana-6095	143	10	than	than	ADP
cana-6095	143	11	parameter	parameter	NOUN
cana-6095	143	12	space	space	NOUN
cana-6095	143	13	may	may	AUX
cana-6095	143	14	circumvent	circumvent	VERB
cana-6095	143	15	challenges	challenge	NOUN
cana-6095	143	16	associated	associate	VERB
cana-6095	143	17	with	with	ADP
cana-6095	143	18	highdimensional	highdimensional	ADJ
cana-6095	143	19	parameter	parameter	NOUN
cana-6095	143	20	posteriors	posterior	NOUN
cana-6095	143	21	8,9	8,9	NUM
cana-6095	143	22	.	.	PUNCT
cana-6095	144	1	gaussian	gaussian	NOUN
cana-6095	144	2	processes	process	NOUN
cana-6095	144	3	provide	provide	VERB
cana-6095	144	4	a	a	DET
cana-6095	144	5	natural	natural	ADJ
cana-6095	144	6	functional	functional	ADJ
cana-6095	144	7	approach	approach	NOUN
cana-6095	144	8	but	but	CCONJ
cana-6095	144	9	scale	scale	NOUN
cana-6095	144	10	poorly	poorly	ADV
cana-6095	144	11	,	,	PUNCT
cana-6095	144	12	suggesting	suggest	VERB
cana-6095	144	13	opportunities	opportunity	NOUN
cana-6095	144	14	for	for	ADP
cana-6095	144	15	hybrid	hybrid	ADJ
cana-6095	144	16	methods	method	NOUN
cana-6095	144	17	that	that	PRON
cana-6095	144	18	combine	combine	VERB
cana-6095	144	19	neural	neural	ADJ
cana-6095	144	20	networks	network	NOUN
cana-6095	144	21	with	with	ADP
cana-6095	144	22	functional	functional	ADJ
cana-6095	144	23	approaches	approach	NOUN
cana-6095	144	24	.	.	PUNCT
cana-6095	145	1	invariance	invariance	NOUN
cana-6095	145	2	and	and	CCONJ
cana-6095	145	3	symmetry	symmetry	NOUN
cana-6095	145	4	preservation	preservation	NOUN
cana-6095	145	5	is	be	AUX
cana-6095	145	6	particularly	particularly	ADV
cana-6095	145	7	important	important	ADJ
cana-6095	145	8	for	for	ADP
cana-6095	145	9	scientific	scientific	ADJ
cana-6095	145	10	applications	application	NOUN
cana-6095	145	11	where	where	SCONJ
cana-6095	145	12	models	model	NOUN
cana-6095	145	13	should	should	AUX
cana-6095	145	14	respect	respect	VERB
cana-6095	145	15	physical	physical	ADJ
cana-6095	145	16	symmetries	symmetry	NOUN
cana-6095	145	17	9	9	NUM
cana-6095	145	18	.	.	PUNCT
cana-6095	146	1	developing	develop	VERB
cana-6095	146	2	bayesian	bayesian	NOUN
cana-6095	146	3	architectures	architecture	NOUN
cana-6095	146	4	that	that	PRON
cana-6095	146	5	inherently	inherently	ADV
cana-6095	146	6	preserve	preserve	VERB
cana-6095	146	7	these	these	DET
cana-6095	146	8	properties	property	NOUN
cana-6095	146	9	could	could	AUX
cana-6095	146	10	improve	improve	VERB
cana-6095	146	11	both	both	DET
cana-6095	146	12	accuracy	accuracy	NOUN
cana-6095	146	13	and	and	CCONJ
cana-6095	146	14	uncertainty	uncertainty	NOUN
cana-6095	146	15	quantification	quantification	NOUN
cana-6095	146	16	.	.	PUNCT
cana-6095	147	1	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	147	2	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	NUM
cana-6095	147	3	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	147	4	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	147	5	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	147	6	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	147	7	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	147	8	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	147	9	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	147	10	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	147	11	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	147	12	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	VERB
cana-6095	147	13	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	https://www.sciencedirect.com/science/article/abs/pii/s0045782521004102	NOUN
cana-6095	147	14	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	147	15	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	147	16	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	147	17	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	VERB
cana-6095	147	18	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	147	19	communications	communication	NOUN
cana-6095	147	20	on	on	ADP
cana-6095	147	21	applied	apply	VERB
cana-6095	147	22	nonlinear	nonlinear	ADJ
cana-6095	147	23	analysis	analysis	NOUN
cana-6095	147	24	issn	issn	NOUN
cana-6095	147	25	:	:	PUNCT
cana-6095	147	26	1074	1074	NUM
cana-6095	147	27	-	-	PUNCT
cana-6095	147	28	133x	133x	NUM
cana-6095	147	29	vol	vol	NOUN
cana-6095	147	30	30	30	NUM
cana-6095	148	1	no	no	NOUN
cana-6095	148	2	.	.	NOUN
cana-6095	148	3	3	3	NUM
cana-6095	148	4	(	(	PUNCT
cana-6095	148	5	2023	2023	NUM
cana-6095	148	6	)	)	PUNCT
cana-6095	148	7	63	63	NUM
cana-6095	148	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	148	9	6.3	6.3	NUM
cana-6095	148	10	integrated	integrate	VERB
cana-6095	148	11	uq	uq	NOUN
cana-6095	148	12	frameworks	framework	NOUN
cana-6095	148	13	multi	multi	ADJ
cana-6095	148	14	-	-	ADJ
cana-6095	148	15	fidelity	fidelity	ADJ
cana-6095	148	16	uq	uq	NOUN
cana-6095	148	17	frameworks	framework	NOUN
cana-6095	148	18	that	that	PRON
cana-6095	148	19	integrate	integrate	VERB
cana-6095	148	20	information	information	NOUN
cana-6095	148	21	from	from	ADP
cana-6095	148	22	models	model	NOUN
cana-6095	148	23	of	of	ADP
cana-6095	148	24	varying	vary	VERB
cana-6095	148	25	accuracy	accuracy	NOUN
cana-6095	148	26	could	could	AUX
cana-6095	148	27	provide	provide	VERB
cana-6095	148	28	comprehensive	comprehensive	ADJ
cana-6095	148	29	uncertainty	uncertainty	NOUN
cana-6095	148	30	characterization	characterization	NOUN
cana-6095	148	31	while	while	SCONJ
cana-6095	148	32	reducing	reduce	VERB
cana-6095	148	33	computational	computational	ADJ
cana-6095	148	34	costs	cost	NOUN
cana-6095	148	35	10	10	NUM
cana-6095	148	36	.	.	PUNCT
cana-6095	149	1	bayesian	bayesian	NOUN
cana-6095	149	2	approaches	approach	NOUN
cana-6095	149	3	naturally	naturally	ADV
cana-6095	149	4	accommodate	accommodate	VERB
cana-6095	149	5	such	such	ADJ
cana-6095	149	6	integration	integration	NOUN
cana-6095	149	7	through	through	ADP
cana-6095	149	8	informed	informed	ADJ
cana-6095	149	9	priors	prior	NOUN
cana-6095	149	10	or	or	CCONJ
cana-6095	149	11	likelihoods	likelihood	NOUN
cana-6095	149	12	.	.	PUNCT
cana-6095	150	1	uq	uq	NOUN
cana-6095	150	2	for	for	ADP
cana-6095	150	3	entire	entire	ADJ
cana-6095	150	4	workflow	workflow	NOUN
cana-6095	150	5	chains	chain	NOUN
cana-6095	150	6	is	be	AUX
cana-6095	150	7	essential	essential	ADJ
cana-6095	150	8	when	when	SCONJ
cana-6095	150	9	numerical	numerical	ADJ
cana-6095	150	10	methods	method	NOUN
cana-6095	150	11	are	be	AUX
cana-6095	150	12	composed	compose	VERB
cana-6095	150	13	of	of	ADP
cana-6095	150	14	multiple	multiple	ADJ
cana-6095	150	15	components	component	NOUN
cana-6095	150	16	9	9	NUM
cana-6095	150	17	.	.	PUNCT
cana-6095	150	18	developing	develop	VERB
cana-6095	150	19	methods	method	NOUN
cana-6095	150	20	that	that	PRON
cana-6095	150	21	propagate	propagate	VERB
cana-6095	150	22	uncertainty	uncertainty	NOUN
cana-6095	150	23	through	through	ADP
cana-6095	150	24	entire	entire	ADJ
cana-6095	150	25	computational	computational	ADJ
cana-6095	150	26	pipelines	pipeline	NOUN
cana-6095	150	27	would	would	AUX
cana-6095	150	28	provide	provide	VERB
cana-6095	150	29	more	more	ADV
cana-6095	150	30	reliable	reliable	ADJ
cana-6095	150	31	end	end	NOUN
cana-6095	150	32	-	-	PUNCT
cana-6095	150	33	to	to	ADP
cana-6095	150	34	-	-	PUNCT
cana-6095	150	35	end	end	NOUN
cana-6095	150	36	uncertainty	uncertainty	NOUN
cana-6095	150	37	estimates.real	estimates.real	ADJ
cana-6095	150	38	-	-	PUNCT
cana-6095	150	39	time	time	NOUN
cana-6095	150	40	uq	uq	NOUN
cana-6095	150	41	capabilities	capability	NOUN
cana-6095	150	42	would	would	AUX
cana-6095	150	43	enable	enable	VERB
cana-6095	150	44	uncertainty	uncertainty	NOUN
cana-6095	150	45	-	-	PUNCT
cana-6095	150	46	aware	aware	ADJ
cana-6095	150	47	decision	decision	NOUN
cana-6095	150	48	-	-	PUNCT
cana-6095	150	49	making	making	NOUN
cana-6095	150	50	in	in	ADP
cana-6095	150	51	timesensitive	timesensitive	ADJ
cana-6095	150	52	applications	application	NOUN
cana-6095	150	53	such	such	ADJ
cana-6095	150	54	as	as	ADP
cana-6095	150	55	control	control	NOUN
cana-6095	150	56	systems	system	NOUN
cana-6095	150	57	or	or	CCONJ
cana-6095	150	58	autonomous	autonomous	ADJ
cana-6095	150	59	decision	decision	NOUN
cana-6095	150	60	-	-	PUNCT
cana-6095	150	61	making	make	VERB
cana-6095	150	62	4	4	NUM
cana-6095	150	63	.	.	PUNCT
cana-6095	151	1	this	this	PRON
cana-6095	151	2	requires	require	VERB
cana-6095	151	3	efficient	efficient	ADJ
cana-6095	151	4	inference	inference	NOUN
cana-6095	151	5	algorithms	algorithm	NOUN
cana-6095	151	6	that	that	PRON
cana-6095	151	7	can	can	AUX
cana-6095	151	8	provide	provide	VERB
cana-6095	151	9	uncertainty	uncertainty	NOUN
cana-6095	151	10	estimates	estimate	NOUN
cana-6095	151	11	within	within	ADP
cana-6095	151	12	strict	strict	ADJ
cana-6095	151	13	time	time	NOUN
cana-6095	151	14	constraints	constraint	NOUN
cana-6095	151	15	.	.	PUNCT
cana-6095	152	1	6.4	6.4	NUM
cana-6095	152	2	theoretical	theoretical	ADJ
cana-6095	152	3	advances	advance	NOUN
cana-6095	152	4	convergence	convergence	NOUN
cana-6095	152	5	guarantees	guarantee	NOUN
cana-6095	152	6	for	for	ADP
cana-6095	152	7	bayesian	bayesian	NOUN
cana-6095	152	8	neural	neural	ADJ
cana-6095	152	9	networks	network	NOUN
cana-6095	152	10	in	in	ADP
cana-6095	152	11	numerical	numerical	ADJ
cana-6095	152	12	contexts	context	NOUN
cana-6095	152	13	would	would	AUX
cana-6095	152	14	increase	increase	VERB
cana-6095	152	15	confidence	confidence	NOUN
cana-6095	152	16	in	in	ADP
cana-6095	152	17	their	their	PRON
cana-6095	152	18	applications	application	NOUN
cana-6095	152	19	8	8	NUM
cana-6095	152	20	,	,	PUNCT
cana-6095	152	21	.	.	PUNCT
cana-6095	153	1	this	this	PRON
cana-6095	153	2	includes	include	VERB
cana-6095	153	3	theoretical	theoretical	ADJ
cana-6095	153	4	analysis	analysis	NOUN
cana-6095	153	5	of	of	ADP
cana-6095	153	6	approximation	approximation	NOUN
cana-6095	153	7	errors	error	NOUN
cana-6095	153	8	,	,	PUNCT
cana-6095	153	9	consistency	consistency	NOUN
cana-6095	153	10	properties	property	NOUN
cana-6095	153	11	,	,	PUNCT
cana-6095	153	12	and	and	CCONJ
cana-6095	153	13	convergence	convergence	NOUN
cana-6095	153	14	rates	rate	NOUN
cana-6095	153	15	for	for	ADP
cana-6095	153	16	different	different	ADJ
cana-6095	153	17	inference	inference	NOUN
cana-6095	153	18	algorithms	algorithm	NOUN
cana-6095	153	19	.	.	PUNCT
cana-6095	154	1	calibration	calibration	NOUN
cana-6095	154	2	theory	theory	NOUN
cana-6095	154	3	for	for	ADP
cana-6095	154	4	bayesian	bayesian	NOUN
cana-6095	154	5	neural	neural	ADJ
cana-6095	154	6	networks	network	NOUN
cana-6095	154	7	would	would	AUX
cana-6095	154	8	provide	provide	VERB
cana-6095	154	9	insights	insight	NOUN
cana-6095	154	10	into	into	ADP
cana-6095	154	11	when	when	SCONJ
cana-6095	154	12	and	and	CCONJ
cana-6095	154	13	why	why	SCONJ
cana-6095	154	14	these	these	DET
cana-6095	154	15	models	model	NOUN
cana-6095	154	16	produce	produce	VERB
cana-6095	154	17	well	well	ADV
cana-6095	154	18	-	-	PUNCT
cana-6095	154	19	calibrated	calibrate	VERB
cana-6095	154	20	uncertainty	uncertainty	NOUN
cana-6095	154	21	estimates	estimate	VERB
cana-6095	154	22	1,9	1,9	NUM
cana-6095	154	23	.	.	PUNCT
cana-6095	155	1	this	this	PRON
cana-6095	155	2	could	could	AUX
cana-6095	155	3	lead	lead	VERB
cana-6095	155	4	to	to	ADP
cana-6095	155	5	improved	improved	ADJ
cana-6095	155	6	architectures	architecture	NOUN
cana-6095	155	7	or	or	CCONJ
cana-6095	155	8	training	training	NOUN
cana-6095	155	9	procedures	procedure	NOUN
cana-6095	155	10	that	that	PRON
cana-6095	155	11	enhance	enhance	VERB
cana-6095	155	12	calibration.generalization	calibration.generalization	NOUN
cana-6095	155	13	bounds	bound	NOUN
cana-6095	155	14	that	that	PRON
cana-6095	155	15	account	account	VERB
cana-6095	155	16	for	for	ADP
cana-6095	155	17	both	both	DET
cana-6095	155	18	prediction	prediction	NOUN
cana-6095	155	19	accuracy	accuracy	NOUN
cana-6095	155	20	and	and	CCONJ
cana-6095	155	21	uncertainty	uncertainty	NOUN
cana-6095	155	22	quality	quality	NOUN
cana-6095	155	23	would	would	AUX
cana-6095	155	24	provide	provide	VERB
cana-6095	155	25	a	a	DET
cana-6095	155	26	more	more	ADV
cana-6095	155	27	comprehensive	comprehensive	ADJ
cana-6095	155	28	theoretical	theoretical	ADJ
cana-6095	155	29	foundation	foundation	NOUN
cana-6095	155	30	for	for	ADP
cana-6095	155	31	evaluating	evaluate	VERB
cana-6095	155	32	bayesian	bayesian	NOUN
cana-6095	155	33	neural	neural	ADJ
cana-6095	155	34	networks	network	NOUN
cana-6095	155	35	8,9	8,9	NUM
cana-6095	155	36	.	.	PUNCT
cana-6095	156	1	such	such	ADJ
cana-6095	156	2	bounds	bound	NOUN
cana-6095	156	3	could	could	AUX
cana-6095	156	4	guide	guide	VERB
cana-6095	156	5	model	model	NOUN
cana-6095	156	6	selection	selection	NOUN
cana-6095	156	7	and	and	CCONJ
cana-6095	156	8	hyperparameter	hyperparameter	NOUN
cana-6095	156	9	tuning	tune	VERB
cana-6095	156	10	.	.	PUNCT
cana-6095	157	1	7.conclusion	7.conclusion	NUM
cana-6095	157	2	uncertainty	uncertainty	NOUN
cana-6095	157	3	quantification	quantification	NOUN
cana-6095	157	4	in	in	ADP
cana-6095	157	5	numerical	numerical	ADJ
cana-6095	157	6	methods	method	NOUN
cana-6095	157	7	using	use	VERB
cana-6095	157	8	deep	deep	ADJ
cana-6095	157	9	bayesian	bayesian	NOUN
cana-6095	157	10	neural	neural	ADJ
cana-6095	157	11	networks	network	NOUN
cana-6095	157	12	represents	represent	VERB
cana-6095	157	13	a	a	DET
cana-6095	157	14	rapidly	rapidly	ADV
cana-6095	157	15	advancing	advance	VERB
cana-6095	157	16	field	field	NOUN
cana-6095	157	17	with	with	ADP
cana-6095	157	18	significant	significant	ADJ
cana-6095	157	19	potential	potential	NOUN
cana-6095	157	20	to	to	PART
cana-6095	157	21	enhance	enhance	VERB
cana-6095	157	22	the	the	DET
cana-6095	157	23	reliability	reliability	NOUN
cana-6095	157	24	and	and	CCONJ
cana-6095	157	25	interpretability	interpretability	NOUN
cana-6095	157	26	of	of	ADP
cana-6095	157	27	computational	computational	ADJ
cana-6095	157	28	simulations	simulation	NOUN
cana-6095	157	29	.	.	PUNCT
cana-6095	158	1	by	by	ADP
cana-6095	158	2	integrating	integrate	VERB
cana-6095	158	3	bayesian	bayesian	NOUN
cana-6095	158	4	inference	inference	NOUN
cana-6095	158	5	with	with	ADP
cana-6095	158	6	deep	deep	ADJ
cana-6095	158	7	learning	learning	NOUN
cana-6095	158	8	,	,	PUNCT
cana-6095	158	9	these	these	DET
cana-6095	158	10	approaches	approach	NOUN
cana-6095	158	11	provide	provide	VERB
cana-6095	158	12	principled	principled	ADJ
cana-6095	158	13	uncertainty	uncertainty	NOUN
cana-6095	158	14	estimates	estimate	VERB
cana-6095	158	15	that	that	PRON
cana-6095	158	16	capture	capture	VERB
cana-6095	158	17	both	both	CCONJ
cana-6095	158	18	aleatoric	aleatoric	ADJ
cana-6095	158	19	and	and	CCONJ
cana-6095	158	20	epistemic	epistemic	ADJ
cana-6095	158	21	uncertainties	uncertainty	NOUN
cana-6095	158	22	,	,	PUNCT
cana-6095	158	23	addressing	address	VERB
cana-6095	158	24	limitations	limitation	NOUN
cana-6095	158	25	of	of	ADP
cana-6095	158	26	traditional	traditional	ADJ
cana-6095	158	27	numerical	numerical	ADJ
cana-6095	158	28	methods	method	NOUN
cana-6095	158	29	.	.	PUNCT
cana-6095	159	1	through	through	ADP
cana-6095	159	2	various	various	ADJ
cana-6095	159	3	architectures	architecture	NOUN
cana-6095	159	4	and	and	CCONJ
cana-6095	159	5	inference	inference	NOUN
cana-6095	159	6	methods	method	NOUN
cana-6095	159	7	including	include	VERB
cana-6095	159	8	physics	physics	NOUN
cana-6095	159	9	-	-	PUNCT
cana-6095	159	10	informed	inform	VERB
cana-6095	159	11	networks	network	NOUN
cana-6095	159	12	,	,	PUNCT
cana-6095	159	13	bayesian	bayesian	NOUN
cana-6095	159	14	probabilistic	probabilistic	ADJ
cana-6095	159	15	numerics	numeric	NOUN
cana-6095	159	16	,	,	PUNCT
cana-6095	159	17	and	and	CCONJ
cana-6095	159	18	latent	latent	ADJ
cana-6095	159	19	variable	variable	ADJ
cana-6095	159	20	models	model	NOUN
cana-6095	159	21	bnns	bnn	NOUN
cana-6095	159	22	have	have	AUX
cana-6095	159	23	demonstrated	demonstrate	VERB
cana-6095	159	24	success	success	NOUN
cana-6095	159	25	across	across	ADP
cana-6095	159	26	diverse	diverse	ADJ
cana-6095	159	27	applications	application	NOUN
cana-6095	159	28	including	include	VERB
cana-6095	159	29	pde	pde	NOUN
cana-6095	159	30	solving	solving	NOUN
cana-6095	159	31	,	,	PUNCT
cana-6095	159	32	numerical	numerical	ADJ
cana-6095	159	33	integration	integration	NOUN
cana-6095	159	34	,	,	PUNCT
cana-6095	159	35	materials	material	NOUN
cana-6095	159	36	modeling	modeling	NOUN
cana-6095	159	37	,	,	PUNCT
cana-6095	159	38	and	and	CCONJ
cana-6095	159	39	scientific	scientific	ADJ
cana-6095	159	40	machine	machine	NOUN
cana-6095	159	41	learning	learning	NOUN
cana-6095	159	42	.	.	PUNCT
cana-6095	160	1	these	these	DET
cana-6095	160	2	approaches	approach	NOUN
cana-6095	160	3	maintain	maintain	VERB
cana-6095	160	4	the	the	DET
cana-6095	160	5	expressiveness	expressiveness	NOUN
cana-6095	160	6	of	of	ADP
cana-6095	160	7	deep	deep	ADJ
cana-6095	160	8	learning	learning	NOUN
cana-6095	160	9	while	while	SCONJ
cana-6095	160	10	providing	provide	VERB
cana-6095	160	11	uncertainty	uncertainty	NOUN
cana-6095	160	12	quantification	quantification	NOUN
cana-6095	160	13	essential	essential	ADJ
cana-6095	160	14	for	for	ADP
cana-6095	160	15	critical	critical	ADJ
cana-6095	160	16	decision	decision	NOUN
cana-6095	160	17	-	-	PUNCT
cana-6095	160	18	making	making	NOUN
cana-6095	160	19	.	.	PUNCT
cana-6095	161	1	despite	despite	SCONJ
cana-6095	161	2	significant	significant	ADJ
cana-6095	161	3	progress	progress	NOUN
cana-6095	161	4	,	,	PUNCT
cana-6095	161	5	important	important	ADJ
cana-6095	161	6	challenges	challenge	NOUN
cana-6095	161	7	remain	remain	VERB
cana-6095	161	8	in	in	ADP
cana-6095	161	9	scalability	scalability	NOUN
cana-6095	161	10	,	,	PUNCT
cana-6095	161	11	posterior	posterior	ADJ
cana-6095	161	12	approximation	approximation	NOUN
cana-6095	161	13	,	,	PUNCT
cana-6095	161	14	evaluation	evaluation	NOUN
cana-6095	161	15	methodologies	methodology	NOUN
cana-6095	161	16	,	,	PUNCT
cana-6095	161	17	and	and	CCONJ
cana-6095	161	18	distribution	distribution	NOUN
cana-6095	161	19	shift	shift	NOUN
cana-6095	161	20	robustness	robustness	NOUN
cana-6095	161	21	.	.	PUNCT
cana-6095	162	1	future	future	ADJ
cana-6095	162	2	research	research	NOUN
cana-6095	162	3	should	should	AUX
cana-6095	162	4	focus	focus	VERB
cana-6095	162	5	on	on	ADP
cana-6095	162	6	developing	develop	VERB
cana-6095	162	7	more	more	ADV
cana-6095	162	8	scalable	scalable	ADJ
cana-6095	162	9	inference	inference	NOUN
cana-6095	162	10	methods	method	NOUN
cana-6095	162	11	,	,	PUNCT
cana-6095	162	12	advanced	advanced	ADJ
cana-6095	162	13	architectures	architecture	NOUN
cana-6095	162	14	,	,	PUNCT
cana-6095	162	15	integrated	integrated	ADJ
cana-6095	162	16	uq	uq	NOUN
cana-6095	162	17	frameworks	framework	NOUN
cana-6095	162	18	,	,	PUNCT
cana-6095	162	19	and	and	CCONJ
cana-6095	162	20	stronger	strong	ADJ
cana-6095	162	21	theoretical	theoretical	ADJ
cana-6095	162	22	foundations	foundation	NOUN
cana-6095	162	23	.	.	PUNCT
cana-6095	163	1	as	as	SCONJ
cana-6095	163	2	these	these	DET
cana-6095	163	3	challenges	challenge	NOUN
cana-6095	163	4	are	be	AUX
cana-6095	163	5	addressed	address	VERB
cana-6095	163	6	,	,	PUNCT
cana-6095	163	7	bayesian	bayesian	NOUN
cana-6095	163	8	neural	neural	ADJ
cana-6095	163	9	networks	network	NOUN
cana-6095	163	10	are	be	AUX
cana-6095	163	11	poised	poise	VERB
cana-6095	163	12	to	to	PART
cana-6095	163	13	become	become	VERB
cana-6095	163	14	increasingly	increasingly	ADV
cana-6095	163	15	central	central	ADJ
cana-6095	163	16	to	to	ADP
cana-6095	163	17	uncertainty	uncertainty	NOUN
cana-6095	163	18	-	-	PUNCT
cana-6095	163	19	aware	aware	ADJ
cana-6095	163	20	numerical	numerical	ADJ
cana-6095	163	21	computation	computation	NOUN
cana-6095	163	22	,	,	PUNCT
cana-6095	163	23	enabling	enable	VERB
cana-6095	163	24	more	more	ADV
cana-6095	163	25	reliable	reliable	ADJ
cana-6095	163	26	scientific	scientific	ADJ
cana-6095	163	27	discoveries	discovery	NOUN
cana-6095	163	28	and	and	CCONJ
cana-6095	163	29	engineering	engineering	NOUN
cana-6095	163	30	designs	design	NOUN
cana-6095	163	31	across	across	ADP
cana-6095	163	32	diverse	diverse	ADJ
cana-6095	163	33	domains	domain	NOUN
cana-6095	163	34	.	.	PUNCT
cana-6095	164	1	references	reference	NOUN
cana-6095	164	2	1	1	NUM
cana-6095	164	3	.	.	PUNCT
cana-6095	164	4	bishop	bishop	PROPN
cana-6095	164	5	,	,	PUNCT
cana-6095	164	6	c.	c.	PROPN
cana-6095	164	7	m.	m.	NOUN
cana-6095	164	8	(	(	PUNCT
cana-6095	164	9	2006	2006	NUM
cana-6095	164	10	)	)	PUNCT
cana-6095	164	11	.	.	PUNCT
cana-6095	165	1	pattern	pattern	NOUN
cana-6095	165	2	recognition	recognition	NOUN
cana-6095	165	3	and	and	CCONJ
cana-6095	165	4	machine	machine	NOUN
cana-6095	165	5	learning	learning	NOUN
cana-6095	165	6	.	.	PUNCT
cana-6095	166	1	springer	springer	NOUN
cana-6095	166	2	.	.	PUNCT
cana-6095	167	1	(	(	PUNCT
cana-6095	167	2	foundational	foundational	ADJ
cana-6095	167	3	text	text	NOUN
cana-6095	167	4	on	on	ADP
cana-6095	167	5	bayesian	bayesian	NOUN
cana-6095	167	6	methods	method	NOUN
cana-6095	167	7	in	in	ADP
cana-6095	167	8	ml	ml	NOUN
cana-6095	167	9	)	)	PUNCT
cana-6095	167	10	.	.	PUNCT
cana-6095	168	1	2	2	X
cana-6095	168	2	.	.	X
cana-6095	168	3	gelman	gelman	PROPN
cana-6095	168	4	,	,	PUNCT
cana-6095	168	5	a.	a.	PROPN
cana-6095	168	6	,	,	PUNCT
cana-6095	168	7	carlin	carlin	PROPN
cana-6095	168	8	,	,	PUNCT
cana-6095	168	9	j.	j.	PROPN
cana-6095	168	10	b.	b.	PROPN
cana-6095	168	11	,	,	PUNCT
cana-6095	168	12	stern	stern	PROPN
cana-6095	168	13	,	,	PUNCT
cana-6095	168	14	h.	h.	PROPN
cana-6095	168	15	s.	s.	PROPN
cana-6095	168	16	,	,	PUNCT
cana-6095	168	17	&	&	CCONJ
cana-6095	168	18	rubin	rubin	PROPN
cana-6095	168	19	,	,	PUNCT
cana-6095	168	20	d.	d.	PROPN
cana-6095	168	21	b.	b.	PROPN
cana-6095	168	22	(	(	PUNCT
cana-6095	168	23	2013	2013	NUM
cana-6095	168	24	)	)	PUNCT
cana-6095	168	25	.	.	PUNCT
cana-6095	169	1	bayesian	bayesian	NOUN
cana-6095	169	2	data	datum	NOUN
cana-6095	169	3	analysis	analysis	NOUN
cana-6095	169	4	(	(	PUNCT
cana-6095	169	5	3rd	3rd	ADJ
cana-6095	169	6	ed	ed	NOUN
cana-6095	169	7	.	.	PUNCT
cana-6095	169	8	)	)	PUNCT
cana-6095	169	9	.	.	PUNCT
cana-6095	170	1	chapman	chapman	NOUN
cana-6095	170	2	and	and	CCONJ
cana-6095	170	3	hall	hall	PROPN
cana-6095	170	4	/	/	SYM
cana-6095	170	5	crc	crc	PROPN
cana-6095	170	6	.	.	PUNCT
cana-6095	171	1	(	(	PUNCT
cana-6095	171	2	classic	classic	ADJ
cana-6095	171	3	reference	reference	NOUN
cana-6095	171	4	for	for	ADP
cana-6095	171	5	bayesian	bayesian	NOUN
cana-6095	171	6	inference	inference	NOUN
cana-6095	171	7	)	)	PUNCT
cana-6095	171	8	.	.	PUNCT
cana-6095	172	1	3	3	X
cana-6095	172	2	.	.	X
cana-6095	172	3	goodfellow	goodfellow	PROPN
cana-6095	172	4	,	,	PUNCT
cana-6095	172	5	i.	i.	PROPN
cana-6095	172	6	,	,	PUNCT
cana-6095	172	7	bengio	bengio	PROPN
cana-6095	172	8	,	,	PUNCT
cana-6095	172	9	y.	y.	PROPN
cana-6095	172	10	,	,	PUNCT
cana-6095	172	11	&	&	CCONJ
cana-6095	172	12	courville	courville	PROPN
cana-6095	172	13	,	,	PUNCT
cana-6095	172	14	a.	a.	NOUN
cana-6095	172	15	(	(	PUNCT
cana-6095	172	16	2016	2016	NUM
cana-6095	172	17	)	)	PUNCT
cana-6095	172	18	.	.	PUNCT
cana-6095	173	1	deep	deep	ADJ
cana-6095	173	2	learning	learning	NOUN
cana-6095	173	3	.	.	PUNCT
cana-6095	174	1	mit	mit	PROPN
cana-6095	174	2	press	press	NOUN
cana-6095	174	3	.	.	PUNCT
cana-6095	175	1	(	(	PUNCT
cana-6095	175	2	comprehensive	comprehensive	ADJ
cana-6095	175	3	overview	overview	NOUN
cana-6095	175	4	of	of	ADP
cana-6095	175	5	deep	deep	ADJ
cana-6095	175	6	learning	learning	NOUN
cana-6095	175	7	architectures	architecture	NOUN
cana-6095	175	8	)	)	PUNCT
cana-6095	175	9	.	.	PUNCT
cana-6095	176	1	4	4	X
cana-6095	176	2	.	.	X
cana-6095	176	3	kaipio	kaipio	PROPN
cana-6095	176	4	,	,	PUNCT
cana-6095	176	5	j.	j.	PROPN
cana-6095	176	6	,	,	PUNCT
cana-6095	176	7	&	&	CCONJ
cana-6095	176	8	somersalo	somersalo	PROPN
cana-6095	176	9	,	,	PUNCT
cana-6095	176	10	e.	e.	PROPN
cana-6095	176	11	(	(	PUNCT
cana-6095	176	12	2005	2005	NUM
cana-6095	176	13	)	)	PUNCT
cana-6095	176	14	.	.	PUNCT
cana-6095	177	1	statistical	statistical	ADJ
cana-6095	177	2	and	and	CCONJ
cana-6095	177	3	computational	computational	ADJ
cana-6095	177	4	inverse	inverse	NOUN
cana-6095	177	5	problems	problem	NOUN
cana-6095	177	6	.	.	PUNCT
cana-6095	178	1	springer	springer	NOUN
cana-6095	178	2	.	.	PUNCT
cana-6095	179	1	(	(	PUNCT
cana-6095	179	2	links	link	NOUN
cana-6095	179	3	inverse	inverse	NOUN
cana-6095	179	4	problems	problem	NOUN
cana-6095	179	5	in	in	ADP
cana-6095	179	6	numerical	numerical	ADJ
cana-6095	179	7	methods	method	NOUN
cana-6095	179	8	with	with	ADP
cana-6095	179	9	statistical	statistical	ADJ
cana-6095	179	10	inference	inference	NOUN
cana-6095	179	11	)	)	PUNCT
cana-6095	179	12	.	.	PUNCT
cana-6095	180	1	5	5	X
cana-6095	180	2	.	.	X
cana-6095	180	3	o'hagan	o'hagan	PROPN
cana-6095	180	4	,	,	PUNCT
cana-6095	180	5	a.	a.	NOUN
cana-6095	180	6	(	(	PUNCT
cana-6095	180	7	2013	2013	NUM
cana-6095	180	8	)	)	PUNCT
cana-6095	180	9	.	.	PUNCT
cana-6095	181	1	bayesian	bayesian	NOUN
cana-6095	181	2	inference	inference	PROPN
cana-6095	181	3	.	.	PUNCT
cana-6095	182	1	wiley	wiley	PROPN
cana-6095	182	2	statsref	statsref	PROPN
cana-6095	182	3	:	:	PUNCT
cana-6095	182	4	statistics	statistics	PROPN
cana-6095	182	5	reference	reference	PROPN
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cana-6095	182	7	.	.	PUNCT
cana-6095	183	1	(	(	PUNCT
cana-6095	183	2	key	key	ADJ
cana-6095	183	3	review	review	NOUN
cana-6095	183	4	of	of	ADP
cana-6095	183	5	bayesian	bayesian	NOUN
cana-6095	183	6	principles	principle	NOUN
cana-6095	183	7	)	)	PUNCT
cana-6095	183	8	.	.	PUNCT
cana-6095	184	1	6	6	X
cana-6095	184	2	.	.	X
cana-6095	184	3	smith	smith	PROPN
cana-6095	184	4	,	,	PUNCT
cana-6095	184	5	r.	r.	PROPN
cana-6095	184	6	c.	c.	PROPN
cana-6095	184	7	(	(	PUNCT
cana-6095	184	8	2013	2013	NUM
cana-6095	184	9	)	)	PUNCT
cana-6095	184	10	.	.	PUNCT
cana-6095	185	1	uncertainty	uncertainty	NOUN
cana-6095	185	2	quantification	quantification	NOUN
cana-6095	185	3	:	:	PUNCT
cana-6095	185	4	theory	theory	NOUN
cana-6095	185	5	,	,	PUNCT
cana-6095	185	6	implementation	implementation	NOUN
cana-6095	185	7	,	,	PUNCT
cana-6095	185	8	and	and	CCONJ
cana-6095	185	9	applications	application	NOUN
cana-6095	185	10	.	.	PUNCT
cana-6095	186	1	siam	siam	PROPN
cana-6095	186	2	.	.	PUNCT
cana-6095	187	1	(	(	PUNCT
cana-6095	187	2	broad	broad	ADJ
cana-6095	187	3	introduction	introduction	NOUN
cana-6095	187	4	to	to	ADP
cana-6095	187	5	uq	uq	NOUN
cana-6095	187	6	methodologies	methodology	NOUN
cana-6095	187	7	)	)	PUNCT
cana-6095	187	8	.	.	PUNCT
cana-6095	188	1	https://fxbriol.github.io/research/pn/	https://fxbriol.github.io/research/pn/	PROPN
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cana-6095	188	5	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	NUM
cana-6095	188	6	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	https://www.sciencedirect.com/science/article/abs/pii/s016794731930163x	NOUN
cana-6095	188	7	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PROPN
cana-6095	188	8	https://arxiv.org/abs/2309.16314	https://arxiv.org/abs/2309.16314	NOUN
cana-6095	188	9	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	https://www.sciencedirect.com/science/article/abs/pii/s0021999122009652	PRON
cana-6095	188	10	communications	communication	NOUN
cana-6095	188	11	on	on	ADP
cana-6095	188	12	applied	apply	VERB
cana-6095	188	13	nonlinear	nonlinear	ADJ
cana-6095	188	14	analysis	analysis	NOUN
cana-6095	188	15	issn	issn	NOUN
cana-6095	188	16	:	:	PUNCT
cana-6095	188	17	1074	1074	NUM
cana-6095	188	18	-	-	PUNCT
cana-6095	188	19	133x	133x	NUM
cana-6095	188	20	vol	vol	NOUN
cana-6095	188	21	30	30	NUM
cana-6095	188	22	no	no	NOUN
cana-6095	188	23	.	.	NOUN
cana-6095	188	24	3	3	NUM
cana-6095	188	25	(	(	PUNCT
cana-6095	188	26	2023	2023	NUM
cana-6095	188	27	)	)	PUNCT
cana-6095	188	28	64	64	NUM
cana-6095	188	29	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	188	30	7	7	X
cana-6095	188	31	.	.	X
cana-6095	189	1	sullivan	sullivan	PROPN
cana-6095	189	2	,	,	PUNCT
cana-6095	189	3	t.	t.	PROPN
cana-6095	189	4	j.	j.	PROPN
cana-6095	189	5	(	(	PUNCT
cana-6095	189	6	2015	2015	NUM
cana-6095	189	7	)	)	PUNCT
cana-6095	189	8	.	.	PUNCT
cana-6095	190	1	introduction	introduction	NOUN
cana-6095	190	2	to	to	ADP
cana-6095	190	3	uncertainty	uncertainty	NOUN
cana-6095	190	4	quantification	quantification	NOUN
cana-6095	190	5	.	.	PUNCT
cana-6095	191	1	springer	springer	NOUN
cana-6095	191	2	.	.	PUNCT
cana-6095	192	1	(	(	PUNCT
cana-6095	192	2	comprehensive	comprehensive	ADJ
cana-6095	192	3	textbook	textbook	NOUN
cana-6095	192	4	on	on	ADP
cana-6095	192	5	uq	uq	NOUN
cana-6095	192	6	fundamentals	fundamental	NOUN
cana-6095	192	7	)	)	PUNCT
cana-6095	192	8	.	.	PUNCT
cana-6095	193	1	8	8	X
cana-6095	193	2	.	.	X
cana-6095	193	3	blundell	blundell	PROPN
cana-6095	193	4	,	,	PUNCT
cana-6095	193	5	c.	c.	PROPN
cana-6095	193	6	,	,	PUNCT
cana-6095	193	7	cornebise	cornebise	PROPN
cana-6095	193	8	,	,	PUNCT
cana-6095	193	9	j.	j.	PROPN
cana-6095	193	10	,	,	PUNCT
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cana-6095	193	12	,	,	PUNCT
cana-6095	193	13	k.	k.	PROPN
cana-6095	193	14	,	,	PUNCT
cana-6095	193	15	&	&	CCONJ
cana-6095	193	16	wierstra	wierstra	PROPN
cana-6095	193	17	,	,	PUNCT
cana-6095	193	18	d.	d.	PROPN
cana-6095	193	19	(	(	PUNCT
cana-6095	193	20	2015	2015	NUM
cana-6095	193	21	)	)	PUNCT
cana-6095	193	22	.	.	PUNCT
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cana-6095	194	3	in	in	ADP
cana-6095	194	4	neural	neural	ADJ
cana-6095	194	5	networks	network	NOUN
cana-6095	194	6	.	.	PUNCT
cana-6095	195	1	proceedings	proceeding	NOUN
cana-6095	195	2	of	of	ADP
cana-6095	195	3	the	the	DET
cana-6095	195	4	32nd	32nd	ADJ
cana-6095	195	5	international	international	ADJ
cana-6095	195	6	conference	conference	NOUN
cana-6095	195	7	on	on	ADP
cana-6095	195	8	machine	machine	NOUN
cana-6095	195	9	learning	learning	NOUN
cana-6095	195	10	(	(	PUNCT
cana-6095	195	11	icml	icml	PROPN
cana-6095	195	12	)	)	PUNCT
cana-6095	195	13	.	.	PUNCT
cana-6095	196	1	(	(	PUNCT
cana-6095	196	2	introduces	introduce	VERB
cana-6095	196	3	the	the	DET
cana-6095	196	4	bayes	bayes	NOUN
cana-6095	196	5	-	-	PUNCT
cana-6095	196	6	by	by	ADP
cana-6095	196	7	-	-	PUNCT
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cana-6095	196	9	algorithm	algorithm	NOUN
cana-6095	196	10	for	for	ADP
cana-6095	196	11	vi	vi	NOUN
cana-6095	196	12	in	in	ADP
cana-6095	196	13	bnns	bnn	NOUN
cana-6095	196	14	)	)	PUNCT
cana-6095	196	15	.	.	PUNCT
cana-6095	197	1	9	9	X
cana-6095	197	2	.	.	X
cana-6095	197	3	gal	gal	PROPN
cana-6095	197	4	,	,	PUNCT
cana-6095	197	5	y.	y.	PROPN
cana-6095	197	6	(	(	PUNCT
cana-6095	197	7	2016	2016	NUM
cana-6095	197	8	)	)	PUNCT
cana-6095	197	9	.	.	PUNCT
cana-6095	198	1	uncertainty	uncertainty	NOUN
cana-6095	198	2	in	in	ADP
cana-6095	198	3	deep	deep	ADJ
cana-6095	198	4	learning	learning	NOUN
cana-6095	198	5	.	.	PUNCT
cana-6095	199	1	university	university	NOUN
cana-6095	199	2	of	of	ADP
cana-6095	199	3	cambridge	cambridge	PROPN
cana-6095	199	4	phd	phd	PROPN
cana-6095	199	5	thesis	thesis	PROPN
cana-6095	199	6	.	.	PUNCT
cana-6095	200	1	(	(	PUNCT
cana-6095	200	2	seminal	seminal	ADJ
cana-6095	200	3	work	work	NOUN
cana-6095	200	4	linking	link	VERB
cana-6095	200	5	dropout	dropout	NOUN
cana-6095	200	6	to	to	PART
cana-6095	200	7	approximate	approximate	VERB
cana-6095	200	8	bayesian	bayesian	NOUN
cana-6095	200	9	inference	inference	NOUN
cana-6095	200	10	)	)	PUNCT
cana-6095	200	11	.	.	PUNCT
cana-6095	201	1	10	10	NUM
cana-6095	201	2	.	.	X
cana-6095	202	1	gal	gal	ADJ
cana-6095	202	2	,	,	PUNCT
cana-6095	202	3	y.	y.	PROPN
cana-6095	202	4	,	,	PUNCT
cana-6095	202	5	&	&	CCONJ
cana-6095	202	6	ghahramani	ghahramani	PROPN
cana-6095	202	7	,	,	PUNCT
cana-6095	202	8	z.	z.	PROPN
cana-6095	202	9	(	(	PUNCT
cana-6095	202	10	2016	2016	NUM
cana-6095	202	11	)	)	PUNCT
cana-6095	202	12	.	.	PUNCT
cana-6095	203	1	dropout	dropout	NOUN
cana-6095	203	2	as	as	ADP
cana-6095	203	3	a	a	DET
cana-6095	203	4	bayesian	bayesian	NOUN
cana-6095	203	5	approximation	approximation	NOUN
cana-6095	203	6	:	:	PUNCT
cana-6095	203	7	representing	represent	VERB
cana-6095	203	8	model	model	NOUN
cana-6095	203	9	uncertainty	uncertainty	NOUN
cana-6095	203	10	in	in	ADP
cana-6095	203	11	deep	deep	ADJ
cana-6095	203	12	learning	learning	NOUN
cana-6095	203	13	.	.	PUNCT
cana-6095	204	1	proceedings	proceeding	NOUN
cana-6095	204	2	of	of	ADP
cana-6095	204	3	the	the	DET
cana-6095	204	4	33rd	33rd	ADJ
cana-6095	204	5	international	international	ADJ
cana-6095	204	6	conference	conference	NOUN
cana-6095	204	7	on	on	ADP
cana-6095	204	8	machine	machine	NOUN
cana-6095	204	9	learning	learning	NOUN
cana-6095	204	10	(	(	PUNCT
cana-6095	204	11	icml	icml	PROPN
cana-6095	204	12	)	)	PUNCT
cana-6095	204	13	.	.	PUNCT
cana-6095	205	1	11	11	NUM
cana-6095	205	2	.	.	PUNCT
cana-6095	205	3	hernández	hernández	PROPN
cana-6095	205	4	-	-	PUNCT
cana-6095	205	5	lobato	lobato	PROPN
cana-6095	205	6	,	,	PUNCT
cana-6095	205	7	j.	j.	PROPN
cana-6095	205	8	m.	m.	PROPN
cana-6095	205	9	,	,	PUNCT
cana-6095	205	10	&	&	CCONJ
cana-6095	205	11	adams	adams	PROPN
cana-6095	205	12	,	,	PUNCT
cana-6095	205	13	r.	r.	PROPN
cana-6095	205	14	(	(	PUNCT
cana-6095	205	15	2015	2015	NUM
cana-6095	205	16	)	)	PUNCT
cana-6095	205	17	.	.	PUNCT
cana-6095	206	1	probabilistic	probabilistic	ADJ
cana-6095	206	2	backpropagation	backpropagation	NOUN
cana-6095	206	3	for	for	ADP
cana-6095	206	4	scalable	scalable	ADJ
cana-6095	206	5	learning	learning	NOUN
cana-6095	206	6	of	of	ADP
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cana-6095	206	9	networks	network	NOUN
cana-6095	206	10	.	.	PUNCT
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cana-6095	207	2	of	of	ADP
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cana-6095	207	10	(	(	PUNCT
cana-6095	207	11	icml	icml	PROPN
cana-6095	207	12	)	)	PUNCT
cana-6095	207	13	.	.	PUNCT
cana-6095	208	1	12	12	NUM
cana-6095	208	2	.	.	PUNCT
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cana-6095	209	2	,	,	PUNCT
cana-6095	209	3	a.	a.	PROPN
cana-6095	209	4	,	,	PUNCT
cana-6095	209	5	&	&	CCONJ
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cana-6095	209	7	,	,	PUNCT
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cana-6095	209	9	(	(	PUNCT
cana-6095	209	10	2017	2017	NUM
cana-6095	209	11	)	)	PUNCT
cana-6095	209	12	.	.	PUNCT
cana-6095	210	1	what	what	PRON
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cana-6095	210	3	do	do	AUX
cana-6095	210	4	we	we	PRON
cana-6095	210	5	need	need	VERB
cana-6095	210	6	in	in	ADP
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cana-6095	210	9	learning	learning	NOUN
cana-6095	210	10	for	for	ADP
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cana-6095	210	13	?	?	PUNCT
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cana-6095	211	2	in	in	ADP
cana-6095	211	3	neural	neural	ADJ
cana-6095	211	4	information	information	NOUN
cana-6095	211	5	processing	processing	NOUN
cana-6095	211	6	systems	system	NOUN
cana-6095	211	7	(	(	PUNCT
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cana-6095	211	9	)	)	PUNCT
cana-6095	211	10	.	.	PUNCT
cana-6095	212	1	(	(	PUNCT
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cana-6095	212	8	epistemic	epistemic	ADJ
cana-6095	212	9	uncertainty	uncertainty	NOUN
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cana-6095	212	11	.	.	PUNCT
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cana-6095	213	6	,	,	PUNCT
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cana-6095	213	8	,	,	PUNCT
cana-6095	213	9	a.	a.	NOUN
cana-6095	213	10	,	,	PUNCT
cana-6095	213	11	&	&	CCONJ
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cana-6095	213	13	,	,	PUNCT
cana-6095	213	14	c.	c.	PROPN
cana-6095	213	15	(	(	PUNCT
cana-6095	213	16	2017	2017	NUM
cana-6095	213	17	)	)	PUNCT
cana-6095	213	18	.	.	PUNCT
cana-6095	214	1	simple	simple	ADJ
cana-6095	214	2	and	and	CCONJ
cana-6095	214	3	scalable	scalable	ADJ
cana-6095	214	4	predictive	predictive	ADJ
cana-6095	214	5	uncertainty	uncertainty	NOUN
cana-6095	214	6	estimation	estimation	NOUN
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cana-6095	214	10	.	.	PUNCT
cana-6095	215	1	advances	advance	NOUN
cana-6095	215	2	in	in	ADP
cana-6095	215	3	neural	neural	ADJ
cana-6095	215	4	information	information	NOUN
cana-6095	215	5	processing	processing	NOUN
cana-6095	215	6	systems	system	NOUN
cana-6095	215	7	(	(	PUNCT
cana-6095	215	8	neurips	neurip	NOUN
cana-6095	215	9	)	)	PUNCT
cana-6095	215	10	.	.	PUNCT
cana-6095	216	1	(	(	PUNCT
cana-6095	216	2	highlights	highlight	NOUN
cana-6095	216	3	deep	deep	ADJ
cana-6095	216	4	ensembles	ensemble	NOUN
cana-6095	216	5	as	as	ADP
cana-6095	216	6	a	a	DET
cana-6095	216	7	powerful	powerful	ADJ
cana-6095	216	8	non	non	ADJ
cana-6095	216	9	-	-	ADJ
cana-6095	216	10	bayesian	bayesian	ADJ
cana-6095	216	11	uq	uq	NOUN
cana-6095	216	12	method	method	NOUN
cana-6095	216	13	)	)	PUNCT
cana-6095	216	14	.	.	PUNCT
cana-6095	217	1	14	14	NUM
cana-6095	217	2	.	.	X
cana-6095	218	1	mackay	mackay	PROPN
cana-6095	218	2	,	,	PUNCT
cana-6095	218	3	d.	d.	PROPN
cana-6095	218	4	j.	j.	PROPN
cana-6095	218	5	c.	c.	PROPN
cana-6095	218	6	(	(	PUNCT
cana-6095	218	7	1992	1992	NUM
cana-6095	218	8	)	)	PUNCT
cana-6095	218	9	.	.	PUNCT
cana-6095	219	1	a	a	DET
cana-6095	219	2	practical	practical	ADJ
cana-6095	219	3	bayesian	bayesian	NOUN
cana-6095	219	4	framework	framework	NOUN
cana-6095	219	5	for	for	ADP
cana-6095	219	6	backpropagation	backpropagation	NOUN
cana-6095	219	7	networks	network	NOUN
cana-6095	219	8	.	.	PUNCT
cana-6095	220	1	neural	neural	ADJ
cana-6095	220	2	computation	computation	NOUN
cana-6095	220	3	,	,	PUNCT
cana-6095	220	4	4(3	4(3	NUM
cana-6095	220	5	)	)	PUNCT
cana-6095	220	6	,	,	PUNCT
cana-6095	220	7	448	448	NUM
cana-6095	220	8	-	-	SYM
cana-6095	220	9	472	472	NUM
cana-6095	220	10	.	.	PUNCT
cana-6095	221	1	(	(	PUNCT
cana-6095	221	2	early	early	ADJ
cana-6095	221	3	foundational	foundational	ADJ
cana-6095	221	4	work	work	NOUN
cana-6095	221	5	on	on	ADP
cana-6095	221	6	bnns	bnn	NOUN
cana-6095	221	7	)	)	PUNCT
cana-6095	221	8	.	.	PUNCT
cana-6095	222	1	15	15	X
cana-6095	222	2	.	.	X
cana-6095	223	1	neal	neal	PROPN
cana-6095	223	2	,	,	PUNCT
cana-6095	223	3	r.	r.	PROPN
cana-6095	223	4	m.	m.	PROPN
cana-6095	223	5	(	(	PUNCT
cana-6095	223	6	1996	1996	NUM
cana-6095	223	7	)	)	PUNCT
cana-6095	223	8	.	.	PUNCT
cana-6095	224	1	bayesian	bayesian	NOUN
cana-6095	224	2	learning	learn	VERB
cana-6095	224	3	for	for	ADP
cana-6095	224	4	neural	neural	ADJ
cana-6095	224	5	networks	network	NOUN
cana-6095	224	6	.	.	PUNCT
cana-6095	225	1	springer	springer	NOUN
cana-6095	225	2	-	-	PUNCT
cana-6095	225	3	verlag	verlag	PROPN
cana-6095	225	4	.	.	PUNCT
cana-6095	226	1	(	(	PUNCT
cana-6095	226	2	pioneering	pioneer	VERB
cana-6095	226	3	text	text	NOUN
cana-6095	226	4	on	on	ADP
cana-6095	226	5	mcmc	mcmc	PROPN
cana-6095	226	6	for	for	ADP
cana-6095	226	7	bnns	bnn	NOUN
cana-6095	226	8	)	)	PUNCT
cana-6095	226	9	.	.	PUNCT
cana-6095	227	1	16	16	NUM
cana-6095	227	2	.	.	PUNCT
cana-6095	228	1	welling	well	VERB
cana-6095	228	2	,	,	PUNCT
cana-6095	228	3	m.	m.	NOUN
cana-6095	228	4	,	,	PUNCT
cana-6095	228	5	&	&	CCONJ
cana-6095	228	6	teh	teh	NOUN
cana-6095	228	7	,	,	PUNCT
cana-6095	228	8	y.	y.	PROPN
cana-6095	228	9	w.	w.	PROPN
cana-6095	228	10	(	(	PUNCT
cana-6095	228	11	2011	2011	NUM
cana-6095	228	12	)	)	PUNCT
cana-6095	228	13	.	.	PUNCT
cana-6095	229	1	bayesian	bayesian	NOUN
cana-6095	229	2	learning	learn	VERB
cana-6095	229	3	via	via	ADP
cana-6095	229	4	stochastic	stochastic	ADJ
cana-6095	229	5	gradient	gradient	NOUN
cana-6095	229	6	langevin	langevin	NOUN
cana-6095	229	7	dynamics	dynamic	NOUN
cana-6095	229	8	.	.	PUNCT
cana-6095	230	1	proceedings	proceeding	NOUN
cana-6095	230	2	of	of	ADP
cana-6095	230	3	the	the	DET
cana-6095	230	4	28th	28th	ADJ
cana-6095	230	5	international	international	ADJ
cana-6095	230	6	conference	conference	NOUN
cana-6095	230	7	on	on	ADP
cana-6095	230	8	machine	machine	NOUN
cana-6095	230	9	learning	learning	NOUN
cana-6095	230	10	(	(	PUNCT
cana-6095	230	11	icml	icml	PROPN
cana-6095	230	12	)	)	PUNCT
cana-6095	230	13	.	.	PUNCT
cana-6095	231	1	(	(	PUNCT
cana-6095	231	2	introduces	introduce	NOUN
cana-6095	231	3	scalable	scalable	ADJ
cana-6095	231	4	sg	sg	PROPN
cana-6095	231	5	-	-	PUNCT
cana-6095	231	6	mcmc	mcmc	NOUN
cana-6095	231	7	methods	method	NOUN
cana-6095	231	8	)	)	PUNCT
cana-6095	231	9	.	.	PUNCT
cana-6095	232	1	17	17	NUM
cana-6095	232	2	.	.	PUNCT
cana-6095	233	1	cockayne	cockayne	PROPN
cana-6095	233	2	,	,	PUNCT
cana-6095	233	3	j.	j.	PROPN
cana-6095	233	4	,	,	PUNCT
cana-6095	233	5	oates	oates	PROPN
cana-6095	233	6	,	,	PUNCT
cana-6095	233	7	c.	c.	PROPN
cana-6095	233	8	,	,	PUNCT
cana-6095	233	9	sullivan	sullivan	PROPN
cana-6095	233	10	,	,	PUNCT
cana-6095	233	11	t.	t.	PROPN
cana-6095	233	12	,	,	PUNCT
cana-6095	233	13	&	&	CCONJ
cana-6095	233	14	girolami	girolami	PROPN
cana-6095	233	15	,	,	PUNCT
cana-6095	233	16	m.	m.	NOUN
cana-6095	233	17	(	(	PUNCT
cana-6095	233	18	2019	2019	NUM
cana-6095	233	19	)	)	PUNCT
cana-6095	233	20	.	.	PUNCT
cana-6095	234	1	probabilistic	probabilistic	ADJ
cana-6095	234	2	numerical	numerical	ADJ
cana-6095	234	3	methods	method	NOUN
cana-6095	234	4	for	for	ADP
cana-6095	234	5	pdes	pde	NOUN
cana-6095	234	6	.	.	PUNCT
cana-6095	235	1	acta	acta	PROPN
cana-6095	235	2	numerica	numerica	PROPN
cana-6095	235	3	,	,	PUNCT
cana-6095	235	4	28	28	NUM
cana-6095	235	5	,	,	PUNCT
cana-6095	235	6	1	1	NUM
cana-6095	235	7	-	-	SYM
cana-6095	235	8	100	100	NUM
cana-6095	235	9	.	.	PUNCT
cana-6095	236	1	(	(	PUNCT
cana-6095	236	2	comprehensive	comprehensive	ADJ
cana-6095	236	3	review	review	NOUN
cana-6095	236	4	of	of	ADP
cana-6095	236	5	probabilistic	probabilistic	ADJ
cana-6095	236	6	approaches	approach	NOUN
cana-6095	236	7	to	to	ADP
cana-6095	236	8	numerical	numerical	ADJ
cana-6095	236	9	pdes	pde	NOUN
cana-6095	236	10	)	)	PUNCT
cana-6095	236	11	.	.	PUNCT
cana-6095	237	1	18	18	NUM
cana-6095	237	2	.	.	X
cana-6095	237	3	hennig	hennig	PROPN
cana-6095	237	4	,	,	PUNCT
cana-6095	237	5	p.	p.	NOUN
cana-6095	237	6	,	,	PUNCT
cana-6095	237	7	osborne	osborne	PROPN
cana-6095	237	8	,	,	PUNCT
cana-6095	237	9	m.	m.	NOUN
cana-6095	237	10	a.	a.	PROPN
cana-6095	237	11	,	,	PUNCT
cana-6095	237	12	&	&	CCONJ
cana-6095	237	13	girolami	girolami	PROPN
cana-6095	237	14	,	,	PUNCT
cana-6095	237	15	m.	m.	NOUN
cana-6095	237	16	(	(	PUNCT
cana-6095	237	17	2015	2015	NUM
cana-6095	237	18	)	)	PUNCT
cana-6095	237	19	.	.	PUNCT
cana-6095	238	1	probabilistic	probabilistic	ADJ
cana-6095	238	2	numerics	numeric	NOUN
cana-6095	238	3	and	and	CCONJ
cana-6095	238	4	uncertainty	uncertainty	NOUN
cana-6095	238	5	in	in	ADP
cana-6095	238	6	computations	computation	NOUN
cana-6095	238	7	.	.	PUNCT
cana-6095	239	1	proceedings	proceeding	NOUN
cana-6095	239	2	of	of	ADP
cana-6095	239	3	the	the	DET
cana-6095	239	4	royal	royal	ADJ
cana-6095	239	5	society	society	NOUN
cana-6095	239	6	a	a	DET
cana-6095	239	7	,	,	PUNCT
cana-6095	239	8	471(2179	471(2179	NUM
cana-6095	239	9	)	)	PUNCT
cana-6095	239	10	.	.	PUNCT
cana-6095	240	1	(	(	PUNCT
cana-6095	240	2	establishes	establish	VERB
cana-6095	240	3	the	the	DET
cana-6095	240	4	field	field	NOUN
cana-6095	240	5	of	of	ADP
cana-6095	240	6	probabilistic	probabilistic	ADJ
cana-6095	240	7	numerics	numeric	NOUN
cana-6095	240	8	)	)	PUNCT
cana-6095	240	9	.	.	PUNCT
cana-6095	241	1	19	19	NUM
cana-6095	241	2	.	.	PUNCT
cana-6095	241	3	karniadakis	karniadakis	PROPN
cana-6095	241	4	,	,	PUNCT
cana-6095	241	5	g.	g.	PROPN
cana-6095	241	6	e.	e.	PROPN
cana-6095	241	7	,	,	PUNCT
cana-6095	241	8	kevrekidis	kevrekidis	PROPN
cana-6095	241	9	,	,	PUNCT
cana-6095	241	10	i.	i.	PROPN
cana-6095	241	11	g.	g.	PROPN
cana-6095	241	12	,	,	PUNCT
cana-6095	241	13	lu	lu	PROPN
cana-6095	241	14	,	,	PUNCT
cana-6095	241	15	l.	l.	PROPN
cana-6095	241	16	,	,	PUNCT
cana-6095	241	17	perdikaris	perdikaris	NOUN
cana-6095	241	18	,	,	PUNCT
cana-6095	241	19	p.	p.	PROPN
cana-6095	241	20	,	,	PUNCT
cana-6095	241	21	wang	wang	PROPN
cana-6095	241	22	,	,	PUNCT
cana-6095	241	23	s.	s.	PROPN
cana-6095	241	24	,	,	PUNCT
cana-6095	241	25	&	&	CCONJ
cana-6095	241	26	yang	yang	PROPN
cana-6095	241	27	,	,	PUNCT
cana-6095	241	28	l.	l.	PROPN
cana-6095	241	29	(	(	PUNCT
cana-6095	241	30	2021	2021	NUM
cana-6095	241	31	)	)	PUNCT
cana-6095	241	32	.	.	PUNCT
cana-6095	242	1	physicsinformed	physicsinforme	VERB
cana-6095	242	2	machine	machine	NOUN
cana-6095	242	3	learning	learning	NOUN
cana-6095	242	4	.	.	PUNCT
cana-6095	243	1	nature	nature	NOUN
cana-6095	243	2	reviews	reviews	PROPN
cana-6095	243	3	physics	physics	PROPN
cana-6095	243	4	,	,	PUNCT
cana-6095	243	5	3(6	3(6	NUM
cana-6095	243	6	)	)	PUNCT
cana-6095	243	7	,	,	PUNCT
cana-6095	243	8	422	422	NUM
cana-6095	243	9	-	-	SYM
cana-6095	243	10	440	440	NUM
cana-6095	243	11	.	.	PUNCT
cana-6095	244	1	(	(	PUNCT
cana-6095	244	2	key	key	ADJ
cana-6095	244	3	review	review	NOUN
cana-6095	244	4	of	of	ADP
cana-6095	244	5	physics	physics	NOUN
cana-6095	244	6	-	-	PUNCT
cana-6095	244	7	informed	inform	VERB
cana-6095	244	8	ml	ml	NOUN
cana-6095	244	9	,	,	PUNCT
cana-6095	244	10	including	include	VERB
cana-6095	244	11	uq	uq	NOUN
cana-6095	244	12	challenges	challenge	NOUN
cana-6095	244	13	)	)	PUNCT
cana-6095	244	14	.	.	PUNCT
cana-6095	245	1	20	20	NUM
cana-6095	245	2	.	.	PUNCT
cana-6095	245	3	oates	oates	PROPN
cana-6095	245	4	,	,	PUNCT
cana-6095	245	5	c.	c.	PROPN
cana-6095	245	6	j.	j.	PROPN
cana-6095	245	7	,	,	PUNCT
cana-6095	245	8	&	&	CCONJ
cana-6095	245	9	sullivan	sullivan	PROPN
cana-6095	245	10	,	,	PUNCT
cana-6095	245	11	t.	t.	PROPN
cana-6095	245	12	j.	j.	PROPN
cana-6095	245	13	(	(	PUNCT
cana-6095	245	14	2019	2019	NUM
cana-6095	245	15	)	)	PUNCT
cana-6095	245	16	.	.	PUNCT
cana-6095	246	1	a	a	DET
cana-6095	246	2	modern	modern	ADJ
cana-6095	246	3	retrospective	retrospective	NOUN
cana-6095	246	4	on	on	ADP
cana-6095	246	5	probabilistic	probabilistic	ADJ
cana-6095	246	6	numerics	numeric	NOUN
cana-6095	246	7	.	.	PUNCT
cana-6095	247	1	statistics	statistic	NOUN
cana-6095	247	2	and	and	CCONJ
cana-6095	247	3	computing	computing	NOUN
cana-6095	247	4	,	,	PUNCT
cana-6095	247	5	29(6	29(6	NUM
cana-6095	247	6	)	)	PUNCT
cana-6095	247	7	,	,	PUNCT
cana-6095	247	8	1335	1335	NUM
cana-6095	247	9	-	-	SYM
cana-6095	247	10	1351	1351	NUM
cana-6095	247	11	.	.	PUNCT
cana-6095	248	1	21	21	NUM
cana-6095	248	2	.	.	PUNCT
cana-6095	249	1	raissi	raissi	ADJ
cana-6095	249	2	,	,	PUNCT
cana-6095	249	3	m.	m.	NOUN
cana-6095	249	4	,	,	PUNCT
cana-6095	249	5	perdikaris	perdikaris	NOUN
cana-6095	249	6	,	,	PUNCT
cana-6095	249	7	p.	p.	NOUN
cana-6095	249	8	,	,	PUNCT
cana-6095	249	9	&	&	CCONJ
cana-6095	249	10	karniadakis	karniadakis	PROPN
cana-6095	249	11	,	,	PUNCT
cana-6095	249	12	g.	g.	PROPN
cana-6095	249	13	e.	e.	PROPN
cana-6095	250	1	(	(	PUNCT
cana-6095	250	2	2019	2019	NUM
cana-6095	250	3	)	)	PUNCT
cana-6095	250	4	.	.	PUNCT
cana-6095	251	1	physics	physics	NOUN
cana-6095	251	2	-	-	PUNCT
cana-6095	251	3	informed	inform	VERB
cana-6095	251	4	neural	neural	ADJ
cana-6095	251	5	networks	network	NOUN
cana-6095	251	6	:	:	PUNCT
cana-6095	251	7	a	a	DET
cana-6095	251	8	deep	deep	ADJ
cana-6095	251	9	learning	learning	NOUN
cana-6095	251	10	framework	framework	NOUN
cana-6095	251	11	for	for	ADP
cana-6095	251	12	solving	solve	VERB
cana-6095	251	13	forward	forward	ADV
cana-6095	251	14	and	and	CCONJ
cana-6095	251	15	inverse	inverse	NOUN
cana-6095	251	16	problems	problem	NOUN
cana-6095	251	17	involving	involve	VERB
cana-6095	251	18	nonlinear	nonlinear	ADJ
cana-6095	251	19	partial	partial	ADJ
cana-6095	251	20	differential	differential	NOUN
cana-6095	251	21	equations	equation	NOUN
cana-6095	251	22	.	.	PUNCT
cana-6095	252	1	journal	journal	NOUN
cana-6095	252	2	of	of	ADP
cana-6095	252	3	computational	computational	ADJ
cana-6095	252	4	physics	physics	NOUN
cana-6095	252	5	,	,	PUNCT
cana-6095	252	6	378	378	NUM
cana-6095	252	7	,	,	PUNCT
cana-6095	252	8	686	686	NUM
cana-6095	252	9	-	-	SYM
cana-6095	252	10	707	707	NUM
cana-6095	252	11	.	.	PUNCT
cana-6095	253	1	(	(	PUNCT
cana-6095	253	2	foundational	foundational	ADJ
cana-6095	253	3	paper	paper	NOUN
cana-6095	253	4	on	on	ADP
cana-6095	253	5	pinns	pinn	NOUN
cana-6095	253	6	)	)	PUNCT
cana-6095	253	7	.	.	PUNCT
cana-6095	254	1	22	22	NUM
cana-6095	254	2	.	.	PUNCT
cana-6095	255	1	rasmussen	rasmussen	PROPN
cana-6095	255	2	,	,	PUNCT
cana-6095	255	3	c.	c.	PROPN
cana-6095	255	4	e.	e.	PROPN
cana-6095	255	5	,	,	PUNCT
cana-6095	255	6	&	&	CCONJ
cana-6095	255	7	williams	williams	PROPN
cana-6095	255	8	,	,	PUNCT
cana-6095	255	9	c.	c.	PROPN
cana-6095	255	10	k.	k.	PROPN
cana-6095	255	11	i.	i.	PROPN
cana-6095	255	12	(	(	PUNCT
cana-6095	255	13	2006	2006	NUM
cana-6095	255	14	)	)	PUNCT
cana-6095	255	15	.	.	PUNCT
cana-6095	256	1	gaussian	gaussian	NOUN
cana-6095	256	2	processes	process	NOUN
cana-6095	256	3	for	for	ADP
cana-6095	256	4	machine	machine	NOUN
cana-6095	256	5	learning	learning	NOUN
cana-6095	256	6	.	.	PUNCT
cana-6095	257	1	mit	mit	PROPN
cana-6095	257	2	press	press	NOUN
cana-6095	257	3	.	.	PUNCT
cana-6095	258	1	(	(	PUNCT
cana-6095	258	2	core	core	NOUN
cana-6095	258	3	text	text	NOUN
cana-6095	258	4	on	on	ADP
cana-6095	258	5	gps	gps	PROPN
cana-6095	258	6	,	,	PUNCT
cana-6095	258	7	closely	closely	ADV
cana-6095	258	8	related	relate	VERB
cana-6095	258	9	to	to	ADP
cana-6095	258	10	bayesian	bayesian	NOUN
cana-6095	258	11	methods	method	NOUN
cana-6095	258	12	and	and	CCONJ
cana-6095	258	13	probabilistic	probabilistic	ADJ
cana-6095	258	14	numerics	numeric	NOUN
cana-6095	258	15	)	)	PUNCT
cana-6095	258	16	.	.	PUNCT
cana-6095	259	1	23	23	NUM
cana-6095	259	2	.	.	X
cana-6095	260	1	yang	yang	PROPN
cana-6095	260	2	,	,	PUNCT
cana-6095	260	3	y.	y.	PROPN
cana-6095	260	4	,	,	PUNCT
cana-6095	260	5	&	&	CCONJ
cana-6095	260	6	perdikaris	perdikaris	PROPN
cana-6095	260	7	,	,	PUNCT
cana-6095	260	8	p.	p.	NOUN
cana-6095	260	9	(	(	PUNCT
cana-6095	260	10	2019	2019	NUM
cana-6095	260	11	)	)	PUNCT
cana-6095	260	12	.	.	PUNCT
cana-6095	261	1	adversarial	adversarial	ADJ
cana-6095	261	2	uncertainty	uncertainty	NOUN
cana-6095	261	3	quantification	quantification	NOUN
cana-6095	261	4	in	in	ADP
cana-6095	261	5	physics	physics	NOUN
cana-6095	261	6	-	-	PUNCT
cana-6095	261	7	informed	inform	VERB
cana-6095	261	8	neural	neural	ADJ
cana-6095	261	9	networks	network	NOUN
cana-6095	261	10	.	.	PUNCT
cana-6095	262	1	journal	journal	NOUN
cana-6095	262	2	of	of	ADP
cana-6095	262	3	computational	computational	ADJ
cana-6095	262	4	physics	physics	NOUN
cana-6095	262	5	,	,	PUNCT
cana-6095	262	6	394	394	NUM
cana-6095	262	7	,	,	PUNCT
cana-6095	262	8	136	136	NUM
cana-6095	262	9	-	-	SYM
cana-6095	262	10	152	152	NUM
cana-6095	262	11	.	.	PUNCT
cana-6095	263	1	(	(	PUNCT
cana-6095	263	2	extends	extend	VERB
cana-6095	263	3	pinns	pinn	NOUN
cana-6095	263	4	with	with	ADP
cana-6095	263	5	adversarial	adversarial	ADJ
cana-6095	263	6	methods	method	NOUN
cana-6095	263	7	for	for	ADP
cana-6095	263	8	uq	uq	NOUN
cana-6095	263	9	)	)	PUNCT
cana-6095	263	10	.	.	PUNCT
cana-6095	264	1	communications	communication	NOUN
cana-6095	264	2	on	on	ADP
cana-6095	264	3	applied	apply	VERB
cana-6095	264	4	nonlinear	nonlinear	ADJ
cana-6095	264	5	analysis	analysis	NOUN
cana-6095	264	6	issn	issn	NOUN
cana-6095	264	7	:	:	PUNCT
cana-6095	264	8	1074	1074	NUM
cana-6095	264	9	-	-	PUNCT
cana-6095	264	10	133x	133x	NUM
cana-6095	264	11	vol	vol	NOUN
cana-6095	264	12	30	30	NUM
cana-6095	264	13	no	no	NOUN
cana-6095	264	14	.	.	NOUN
cana-6095	264	15	3	3	NUM
cana-6095	264	16	(	(	PUNCT
cana-6095	264	17	2023	2023	NUM
cana-6095	264	18	)	)	PUNCT
cana-6095	264	19	65	65	NUM
cana-6095	264	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	264	21	24	24	NUM
cana-6095	264	22	.	.	PUNCT
cana-6095	265	1	zhu	zhu	PROPN
cana-6095	265	2	,	,	PUNCT
cana-6095	265	3	y.	y.	PROPN
cana-6095	265	4	,	,	PUNCT
cana-6095	265	5	zabaras	zabara	NOUN
cana-6095	265	6	,	,	PUNCT
cana-6095	265	7	n.	n.	NOUN
cana-6095	265	8	,	,	PUNCT
cana-6095	265	9	koutsourelakis	koutsourelaki	NOUN
cana-6095	265	10	,	,	PUNCT
cana-6095	265	11	p.	p.	PROPN
cana-6095	265	12	s.	s.	PROPN
cana-6095	265	13	,	,	PUNCT
cana-6095	265	14	&	&	CCONJ
cana-6095	265	15	perdikaris	perdikaris	PROPN
cana-6095	265	16	,	,	PUNCT
cana-6095	265	17	p.	p.	NOUN
cana-6095	265	18	(	(	PUNCT
cana-6095	265	19	2019	2019	NUM
cana-6095	265	20	)	)	PUNCT
cana-6095	265	21	.	.	PUNCT
cana-6095	266	1	physics	physics	NOUN
cana-6095	266	2	-	-	PUNCT
cana-6095	266	3	constrained	constrain	VERB
cana-6095	266	4	deep	deep	ADJ
cana-6095	266	5	learning	learning	NOUN
cana-6095	266	6	for	for	ADP
cana-6095	266	7	high	high	ADJ
cana-6095	266	8	-	-	PUNCT
cana-6095	266	9	dimensional	dimensional	ADJ
cana-6095	266	10	surrogate	surrogate	ADJ
cana-6095	266	11	modeling	modeling	NOUN
cana-6095	266	12	and	and	CCONJ
cana-6095	266	13	uncertainty	uncertainty	NOUN
cana-6095	266	14	quantification	quantification	NOUN
cana-6095	266	15	without	without	ADP
cana-6095	266	16	labeled	label	VERB
cana-6095	266	17	data	datum	NOUN
cana-6095	266	18	.	.	PUNCT
cana-6095	267	1	journal	journal	PROPN
cana-6095	267	2	of	of	ADP
cana-6095	267	3	computational	computational	ADJ
cana-6095	267	4	physics	physics	NOUN
cana-6095	267	5	,	,	PUNCT
cana-6095	267	6	394	394	NUM
cana-6095	267	7	,	,	PUNCT
cana-6095	267	8	56	56	NUM
cana-6095	267	9	-	-	SYM
cana-6095	267	10	81	81	NUM
cana-6095	267	11	.	.	PUNCT
cana-6095	268	1	25	25	NUM
cana-6095	268	2	.	.	X
cana-6095	269	1	zhang	zhang	PROPN
cana-6095	269	2	,	,	PUNCT
cana-6095	269	3	d.	d.	PROPN
cana-6095	269	4	,	,	PUNCT
cana-6095	269	5	guo	guo	PROPN
cana-6095	269	6	,	,	PUNCT
cana-6095	269	7	l.	l.	PROPN
cana-6095	269	8	,	,	PUNCT
cana-6095	269	9	&	&	CCONJ
cana-6095	269	10	karniadakis	karniadakis	PROPN
cana-6095	269	11	,	,	PUNCT
cana-6095	269	12	g.	g.	PROPN
cana-6095	269	13	e.	e.	PROPN
cana-6095	269	14	(	(	PUNCT
cana-6095	269	15	2020	2020	NUM
cana-6095	269	16	)	)	PUNCT
cana-6095	269	17	.	.	PUNCT
cana-6095	270	1	learning	learn	VERB
cana-6095	270	2	in	in	ADP
cana-6095	270	3	modal	modal	ADJ
cana-6095	270	4	space	space	NOUN
cana-6095	270	5	:	:	PUNCT
cana-6095	270	6	solving	solve	VERB
cana-6095	270	7	time	time	NOUN
cana-6095	270	8	-	-	PUNCT
cana-6095	270	9	dependent	dependent	ADJ
cana-6095	270	10	stochastic	stochastic	ADJ
cana-6095	270	11	pdes	pde	NOUN
cana-6095	270	12	using	use	VERB
cana-6095	270	13	physics	physics	NOUN
cana-6095	270	14	-	-	PUNCT
cana-6095	270	15	informed	inform	VERB
cana-6095	270	16	neural	neural	ADJ
cana-6095	270	17	networks	network	NOUN
cana-6095	270	18	.	.	PUNCT
cana-6095	271	1	siam	siam	PROPN
cana-6095	271	2	journal	journal	PROPN
cana-6095	271	3	on	on	ADP
cana-6095	271	4	scientific	scientific	ADJ
cana-6095	271	5	computing	computing	NOUN
cana-6095	271	6	,	,	PUNCT
cana-6095	271	7	42(2	42(2	PROPN
cana-6095	271	8	)	)	PUNCT
cana-6095	271	9	,	,	PUNCT
cana-6095	271	10	a639	a639	PROPN
cana-6095	271	11	-	-	PUNCT
cana-6095	271	12	a665	a665	PROPN
cana-6095	271	13	.	.	PROPN
cana-6095	272	1	26	26	NUM
cana-6095	272	2	.	.	PUNCT
cana-6095	273	1	liu	liu	PROPN
cana-6095	273	2	,	,	PUNCT
cana-6095	273	3	r.	r.	PROPN
cana-6095	273	4	,	,	PUNCT
cana-6095	273	5	&	&	CCONJ
cana-6095	273	6	wang	wang	PROPN
cana-6095	273	7	,	,	PUNCT
cana-6095	273	8	y.	y.	PROPN
cana-6095	273	9	(	(	PUNCT
cana-6095	273	10	2021	2021	NUM
cana-6095	273	11	)	)	PUNCT
cana-6095	273	12	.	.	PUNCT
cana-6095	274	1	latent	latent	PROPN
cana-6095	274	2	evolution	evolution	NOUN
cana-6095	274	3	of	of	ADP
cana-6095	274	4	pdes	pde	NOUN
cana-6095	274	5	with	with	ADP
cana-6095	274	6	uq	uq	PROPN
cana-6095	274	7	(	(	PUNCT
cana-6095	274	8	le	le	PROPN
cana-6095	274	9	-	-	ADJ
cana-6095	274	10	pde	pde	NOUN
cana-6095	274	11	-	-	PUNCT
cana-6095	274	12	uq	uq	NOUN
cana-6095	274	13	)	)	PUNCT
cana-6095	274	14	for	for	ADP
cana-6095	274	15	long	long	ADJ
cana-6095	274	16	-	-	PUNCT
cana-6095	274	17	term	term	NOUN
cana-6095	274	18	forecasting	forecasting	NOUN
cana-6095	274	19	.	.	PUNCT
cana-6095	275	1	proceedings	proceeding	NOUN
cana-6095	275	2	of	of	ADP
cana-6095	275	3	the	the	DET
cana-6095	275	4	38th	38th	ADJ
cana-6095	275	5	international	international	ADJ
cana-6095	275	6	conference	conference	NOUN
cana-6095	275	7	on	on	ADP
cana-6095	275	8	machine	machine	NOUN
cana-6095	275	9	learning	learning	NOUN
cana-6095	275	10	(	(	PUNCT
cana-6095	275	11	icml	icml	PROPN
cana-6095	275	12	)	)	PUNCT
cana-6095	275	13	.	.	PUNCT
cana-6095	276	1	(	(	PUNCT
cana-6095	276	2	directly	directly	ADV
cana-6095	276	3	references	reference	VERB
cana-6095	276	4	the	the	DET
cana-6095	276	5	application	application	NOUN
cana-6095	276	6	mentioned	mention	VERB
cana-6095	276	7	in	in	ADP
cana-6095	276	8	the	the	DET
cana-6095	276	9	paper	paper	NOUN
cana-6095	276	10	)	)	PUNCT
cana-6095	276	11	.	.	PUNCT
cana-6095	277	1	27	27	NUM
cana-6095	277	2	.	.	PUNCT
cana-6095	277	3	briol	briol	PROPN
cana-6095	277	4	,	,	PUNCT
cana-6095	277	5	f.	f.	PROPN
cana-6095	277	6	x.	x.	PROPN
cana-6095	277	7	,	,	PUNCT
cana-6095	277	8	oates	oates	PROPN
cana-6095	277	9	,	,	PUNCT
cana-6095	277	10	c.	c.	PROPN
cana-6095	277	11	j.	j.	PROPN
cana-6095	277	12	,	,	PUNCT
cana-6095	277	13	girolami	girolami	PROPN
cana-6095	277	14	,	,	PUNCT
cana-6095	277	15	m.	m.	NOUN
cana-6095	277	16	,	,	PUNCT
cana-6095	277	17	&	&	CCONJ
cana-6095	277	18	osborne	osborne	PROPN
cana-6095	277	19	,	,	PUNCT
cana-6095	277	20	m.	m.	NOUN
cana-6095	277	21	a.	a.	NOUN
cana-6095	277	22	(	(	PUNCT
cana-6095	277	23	2019	2019	NUM
cana-6095	277	24	)	)	PUNCT
cana-6095	277	25	.	.	PUNCT
cana-6095	278	1	frank	frank	PROPN
cana-6095	278	2	-	-	PUNCT
cana-6095	278	3	wolfe	wolfe	PROPN
cana-6095	278	4	bayesian	bayesian	PROPN
cana-6095	278	5	quadrature	quadrature	NOUN
cana-6095	278	6	:	:	PUNCT
cana-6095	278	7	probabilistic	probabilistic	ADJ
cana-6095	278	8	integration	integration	NOUN
cana-6095	278	9	with	with	ADP
cana-6095	278	10	theoretical	theoretical	ADJ
cana-6095	278	11	guarantees	guarantee	NOUN
cana-6095	278	12	.	.	PUNCT
cana-6095	279	1	advances	advance	NOUN
cana-6095	279	2	in	in	ADP
cana-6095	279	3	neural	neural	ADJ
cana-6095	279	4	information	information	NOUN
cana-6095	279	5	processing	processing	NOUN
cana-6095	279	6	systems	system	NOUN
cana-6095	279	7	(	(	PUNCT
cana-6095	279	8	neurips	neurip	NOUN
cana-6095	279	9	)	)	PUNCT
cana-6095	279	10	.	.	PUNCT
cana-6095	280	1	28	28	NUM
cana-6095	280	2	.	.	PUNCT
cana-6095	281	1	cockayne	cockayne	PROPN
cana-6095	281	2	,	,	PUNCT
cana-6095	281	3	j.	j.	PROPN
cana-6095	281	4	,	,	PUNCT
cana-6095	281	5	oates	oates	PROPN
cana-6095	281	6	,	,	PUNCT
cana-6095	281	7	c.	c.	PROPN
cana-6095	281	8	j.	j.	PROPN
cana-6095	281	9	,	,	PUNCT
cana-6095	281	10	ipsen	ipsen	PROPN
cana-6095	281	11	,	,	PUNCT
cana-6095	281	12	i.	i.	PROPN
cana-6095	281	13	c.	c.	PROPN
cana-6095	281	14	f.	f.	PROPN
cana-6095	281	15	,	,	PUNCT
cana-6095	281	16	&	&	CCONJ
cana-6095	281	17	girolami	girolami	PROPN
cana-6095	281	18	,	,	PUNCT
cana-6095	281	19	m.	m.	NOUN
cana-6095	281	20	(	(	PUNCT
cana-6095	281	21	2019	2019	NUM
cana-6095	281	22	)	)	PUNCT
cana-6095	281	23	.	.	PUNCT
cana-6095	282	1	a	a	DET
cana-6095	282	2	bayesian	bayesian	NOUN
cana-6095	282	3	conjugate	conjugate	VERB
cana-6095	282	4	gradient	gradient	ADJ
cana-6095	282	5	method	method	NOUN
cana-6095	282	6	.	.	PUNCT
cana-6095	283	1	bayesian	bayesian	NOUN
cana-6095	283	2	analysis	analysis	NOUN
cana-6095	283	3	,	,	PUNCT
cana-6095	283	4	14(3	14(3	NUM
cana-6095	283	5	)	)	PUNCT
cana-6095	283	6	,	,	PUNCT
cana-6095	283	7	937	937	NUM
cana-6095	283	8	-	-	SYM
cana-6095	283	9	1012	1012	NUM
cana-6095	283	10	.	.	PUNCT
cana-6095	284	1	29	29	NUM
cana-6095	284	2	.	.	PUNCT
cana-6095	285	1	gunter	gunter	NOUN
cana-6095	285	2	,	,	PUNCT
cana-6095	285	3	t.	t.	PROPN
cana-6095	285	4	,	,	PUNCT
cana-6095	285	5	osborne	osborne	PROPN
cana-6095	285	6	,	,	PUNCT
cana-6095	285	7	m.	m.	NOUN
cana-6095	285	8	a.	a.	PROPN
cana-6095	285	9	,	,	PUNCT
cana-6095	285	10	garnett	garnett	PROPN
cana-6095	285	11	,	,	PUNCT
cana-6095	285	12	r.	r.	PROPN
cana-6095	285	13	,	,	PUNCT
cana-6095	285	14	hennig	hennig	PROPN
cana-6095	285	15	,	,	PUNCT
cana-6095	285	16	p.	p.	PROPN
cana-6095	285	17	,	,	PUNCT
cana-6095	285	18	&	&	CCONJ
cana-6095	285	19	roberts	roberts	PROPN
cana-6095	285	20	,	,	PUNCT
cana-6095	285	21	s.	s.	PROPN
cana-6095	285	22	j.	j.	PROPN
cana-6095	285	23	(	(	PUNCT
cana-6095	285	24	2014	2014	NUM
cana-6095	285	25	)	)	PUNCT
cana-6095	285	26	.	.	PUNCT
cana-6095	286	1	sampling	sample	VERB
cana-6095	286	2	for	for	ADP
cana-6095	286	3	inference	inference	NOUN
cana-6095	286	4	in	in	ADP
cana-6095	286	5	probabilistic	probabilistic	ADJ
cana-6095	286	6	models	model	NOUN
cana-6095	286	7	with	with	ADP
cana-6095	286	8	fast	fast	ADJ
cana-6095	286	9	bayesian	bayesian	NOUN
cana-6095	286	10	quadrature	quadrature	NOUN
cana-6095	286	11	.	.	PUNCT
cana-6095	287	1	advances	advance	NOUN
cana-6095	287	2	in	in	ADP
cana-6095	287	3	neural	neural	ADJ
cana-6095	287	4	information	information	NOUN
cana-6095	287	5	processing	processing	NOUN
cana-6095	287	6	systems	system	NOUN
cana-6095	287	7	(	(	PUNCT
cana-6095	287	8	neurips	neurip	NOUN
cana-6095	287	9	)	)	PUNCT
cana-6095	287	10	.	.	PUNCT
cana-6095	288	1	30	30	NUM
cana-6095	288	2	.	.	X
cana-6095	288	3	karvonen	karvonen	PROPN
cana-6095	288	4	,	,	PUNCT
cana-6095	288	5	t.	t.	PROPN
cana-6095	288	6	,	,	PUNCT
cana-6095	288	7	&	&	CCONJ
cana-6095	288	8	särkkä	särkkä	PROPN
cana-6095	288	9	,	,	PUNCT
cana-6095	288	10	s.	s.	PROPN
cana-6095	288	11	(	(	PUNCT
cana-6095	288	12	2018	2018	NUM
cana-6095	288	13	)	)	PUNCT
cana-6095	288	14	.	.	PUNCT
cana-6095	289	1	fully	fully	ADV
cana-6095	289	2	symmetric	symmetric	ADJ
cana-6095	289	3	kernel	kernel	PROPN
cana-6095	289	4	quadrature	quadrature	NOUN
cana-6095	289	5	.	.	PUNCT
cana-6095	290	1	siam	siam	PROPN
cana-6095	290	2	journal	journal	PROPN
cana-6095	290	3	on	on	ADP
cana-6095	290	4	scientific	scientific	ADJ
cana-6095	290	5	computing	computing	NOUN
cana-6095	290	6	,	,	PUNCT
cana-6095	290	7	40(2	40(2	NUM
cana-6095	290	8	)	)	PUNCT
cana-6095	290	9	,	,	PUNCT
cana-6095	290	10	a697	a697	PROPN
cana-6095	290	11	-	-	PUNCT
cana-6095	290	12	a720	a720	PROPN
cana-6095	290	13	.	.	PROPN
cana-6095	291	1	31	31	NUM
cana-6095	291	2	.	.	PUNCT
cana-6095	292	1	oates	oates	PROPN
cana-6095	292	2	,	,	PUNCT
cana-6095	292	3	c.	c.	PROPN
cana-6095	292	4	j.	j.	PROPN
cana-6095	292	5	,	,	PUNCT
cana-6095	292	6	girolami	girolami	PROPN
cana-6095	292	7	,	,	PUNCT
cana-6095	292	8	m.	m.	NOUN
cana-6095	292	9	,	,	PUNCT
cana-6095	292	10	&	&	CCONJ
cana-6095	292	11	chopin	chopin	PROPN
cana-6095	292	12	,	,	PUNCT
cana-6095	292	13	n.	n.	NOUN
cana-6095	292	14	(	(	PUNCT
cana-6095	292	15	2017	2017	NUM
cana-6095	292	16	)	)	PUNCT
cana-6095	292	17	.	.	PUNCT
cana-6095	293	1	control	control	NOUN
cana-6095	293	2	functionals	functional	NOUN
cana-6095	293	3	for	for	ADP
cana-6095	293	4	monte	monte	PROPN
cana-6095	293	5	carlo	carlo	PROPN
cana-6095	293	6	integration	integration	NOUN
cana-6095	293	7	.	.	PUNCT
cana-6095	294	1	journal	journal	NOUN
cana-6095	294	2	of	of	ADP
cana-6095	294	3	the	the	DET
cana-6095	294	4	royal	royal	ADJ
cana-6095	294	5	statistical	statistical	ADJ
cana-6095	294	6	society	society	NOUN
cana-6095	294	7	:	:	PUNCT
cana-6095	294	8	series	series	PROPN
cana-6095	294	9	b	b	PROPN
cana-6095	294	10	(	(	PUNCT
cana-6095	294	11	statistical	statistical	ADJ
cana-6095	294	12	methodology	methodology	NOUN
cana-6095	294	13	)	)	PUNCT
cana-6095	294	14	,	,	PUNCT
cana-6095	294	15	79(3	79(3	NUM
cana-6095	294	16	)	)	PUNCT
cana-6095	294	17	,	,	PUNCT
cana-6095	294	18	695	695	NUM
cana-6095	294	19	-	-	SYM
cana-6095	294	20	718	718	NUM
cana-6095	294	21	.	.	PUNCT
cana-6095	295	1	32	32	NUM
cana-6095	295	2	.	.	PUNCT
cana-6095	296	1	cao	cao	PROPN
cana-6095	296	2	,	,	PUNCT
cana-6095	296	3	y.	y.	PROPN
cana-6095	296	4	,	,	PUNCT
cana-6095	296	5	oates	oates	PROPN
cana-6095	296	6	,	,	PUNCT
cana-6095	296	7	c.	c.	PROPN
cana-6095	296	8	j.	j.	PROPN
cana-6095	296	9	,	,	PUNCT
cana-6095	296	10	&	&	CCONJ
cana-6095	296	11	girolami	girolami	PROPN
cana-6095	296	12	,	,	PUNCT
cana-6095	296	13	m.	m.	NOUN
cana-6095	296	14	(	(	PUNCT
cana-6095	296	15	2022	2022	NUM
cana-6095	296	16	)	)	PUNCT
cana-6095	296	17	.	.	PUNCT
cana-6095	297	1	bayesian	bayesian	PROPN
cana-6095	297	2	stein	stein	PROPN
cana-6095	297	3	networks	network	NOUN
cana-6095	297	4	for	for	ADP
cana-6095	297	5	numerical	numerical	ADJ
cana-6095	297	6	integration	integration	NOUN
cana-6095	297	7	.	.	PUNCT
cana-6095	298	1	proceedings	proceeding	NOUN
cana-6095	298	2	of	of	ADP
cana-6095	298	3	the	the	DET
cana-6095	298	4	39th	39th	ADJ
cana-6095	298	5	international	international	ADJ
cana-6095	298	6	conference	conference	NOUN
cana-6095	298	7	on	on	ADP
cana-6095	298	8	machine	machine	NOUN
cana-6095	298	9	learning	learning	NOUN
cana-6095	298	10	(	(	PUNCT
cana-6095	298	11	icml	icml	PROPN
cana-6095	298	12	)	)	PUNCT
cana-6095	298	13	.	.	PUNCT
cana-6095	299	1	(	(	PUNCT
cana-6095	299	2	directly	directly	ADV
cana-6095	299	3	references	reference	VERB
cana-6095	299	4	the	the	DET
cana-6095	299	5	bayesian	bayesian	NOUN
cana-6095	299	6	stein	stein	PROPN
cana-6095	299	7	networks	network	NOUN
cana-6095	299	8	mentioned	mention	VERB
cana-6095	299	9	)	)	PUNCT
cana-6095	299	10	.	.	PUNCT
cana-6095	300	1	33	33	NUM
cana-6095	300	2	.	.	PUNCT
cana-6095	301	1	bessa	bessa	NOUN
cana-6095	301	2	,	,	PUNCT
cana-6095	301	3	m.	m.	NOUN
cana-6095	301	4	a.	a.	PROPN
cana-6095	301	5	,	,	PUNCT
cana-6095	301	6	bostanabad	bostanabad	PROPN
cana-6095	301	7	,	,	PUNCT
cana-6095	301	8	r.	r.	PROPN
cana-6095	301	9	,	,	PUNCT
cana-6095	301	10	liu	liu	PROPN
cana-6095	301	11	,	,	PUNCT
cana-6095	301	12	z.	z.	PROPN
cana-6095	301	13	,	,	PUNCT
cana-6095	301	14	hu	hu	PROPN
cana-6095	301	15	,	,	PUNCT
cana-6095	301	16	a.	a.	NOUN
cana-6095	301	17	,	,	PUNCT
cana-6095	301	18	apley	apley	PROPN
cana-6095	301	19	,	,	PUNCT
cana-6095	301	20	d.	d.	PROPN
cana-6095	301	21	w.	w.	PROPN
cana-6095	301	22	,	,	PUNCT
cana-6095	301	23	brinson	brinson	PROPN
cana-6095	301	24	,	,	PUNCT
cana-6095	301	25	c.	c.	PROPN
cana-6095	301	26	,	,	PUNCT
cana-6095	301	27	...	...	PUNCT
cana-6095	301	28	&	&	CCONJ
cana-6095	301	29	liu	liu	PROPN
cana-6095	301	30	,	,	PUNCT
cana-6095	301	31	w.	w.	PROPN
cana-6095	301	32	k.	k.	PROPN
cana-6095	301	33	(	(	PUNCT
cana-6095	301	34	2017	2017	NUM
cana-6095	301	35	)	)	PUNCT
cana-6095	301	36	.	.	PUNCT
cana-6095	302	1	a	a	DET
cana-6095	302	2	framework	framework	NOUN
cana-6095	302	3	for	for	ADP
cana-6095	302	4	data	data	NOUN
cana-6095	302	5	-	-	PUNCT
cana-6095	302	6	driven	drive	VERB
cana-6095	302	7	analysis	analysis	NOUN
cana-6095	302	8	of	of	ADP
cana-6095	302	9	materials	material	NOUN
cana-6095	302	10	under	under	ADP
cana-6095	302	11	uncertainty	uncertainty	NOUN
cana-6095	302	12	:	:	PUNCT
cana-6095	302	13	countering	counter	VERB
cana-6095	302	14	the	the	DET
cana-6095	302	15	curse	curse	NOUN
cana-6095	302	16	of	of	ADP
cana-6095	302	17	dimensionality	dimensionality	NOUN
cana-6095	302	18	.	.	PUNCT
cana-6095	303	1	computer	computer	NOUN
cana-6095	303	2	methods	method	NOUN
cana-6095	303	3	in	in	ADP
cana-6095	303	4	applied	applied	ADJ
cana-6095	303	5	mechanics	mechanic	NOUN
cana-6095	303	6	and	and	CCONJ
cana-6095	303	7	engineering	engineering	NOUN
cana-6095	303	8	,	,	PUNCT
cana-6095	303	9	320	320	NUM
cana-6095	303	10	,	,	PUNCT
cana-6095	303	11	633	633	NUM
cana-6095	303	12	-	-	SYM
cana-6095	303	13	667	667	NUM
cana-6095	303	14	.	.	PUNCT
cana-6095	304	1	(	(	PUNCT
cana-6095	304	2	key	key	ADJ
cana-6095	304	3	paper	paper	NOUN
cana-6095	304	4	on	on	ADP
cana-6095	304	5	data	data	NOUN
cana-6095	304	6	-	-	PUNCT
cana-6095	304	7	driven	drive	VERB
cana-6095	304	8	materials	material	NOUN
cana-6095	304	9	uq	uq	NOUN
cana-6095	304	10	)	)	PUNCT
cana-6095	304	11	.	.	PUNCT
cana-6095	305	1	34	34	NUM
cana-6095	305	2	.	.	PUNCT
cana-6095	305	3	kalidindi	kalidindi	PROPN
cana-6095	305	4	,	,	PUNCT
cana-6095	305	5	s.	s.	PROPN
cana-6095	305	6	r.	r.	PROPN
cana-6095	305	7	(	(	PUNCT
cana-6095	305	8	2015	2015	NUM
cana-6095	305	9	)	)	PUNCT
cana-6095	305	10	.	.	PUNCT
cana-6095	306	1	data	datum	NOUN
cana-6095	306	2	science	science	NOUN
cana-6095	306	3	and	and	CCONJ
cana-6095	306	4	cyber	cyber	NOUN
cana-6095	306	5	-	-	PUNCT
cana-6095	306	6	infrastructure	infrastructure	NOUN
cana-6095	306	7	:	:	PUNCT
cana-6095	306	8	critical	critical	ADJ
cana-6095	306	9	enablers	enabler	NOUN
cana-6095	306	10	for	for	ADP
cana-6095	306	11	accelerated	accelerate	VERB
cana-6095	306	12	development	development	NOUN
cana-6095	306	13	of	of	ADP
cana-6095	306	14	hierarchical	hierarchical	ADJ
cana-6095	306	15	materials	material	NOUN
cana-6095	306	16	.	.	PUNCT
cana-6095	307	1	international	international	ADJ
cana-6095	307	2	materials	material	NOUN
cana-6095	307	3	reviews	review	NOUN
cana-6095	307	4	,	,	PUNCT
cana-6095	307	5	60(3	60(3	NOUN
cana-6095	307	6	)	)	PUNCT
cana-6095	307	7	,	,	PUNCT
cana-6095	307	8	150	150	NUM
cana-6095	307	9	-	-	SYM
cana-6095	307	10	168	168	NUM
cana-6095	307	11	.	.	PUNCT
cana-6095	308	1	(	(	PUNCT
cana-6095	308	2	foundational	foundational	ADJ
cana-6095	308	3	for	for	ADP
cana-6095	308	4	materials	material	NOUN
cana-6095	308	5	informatics	informatic	NOUN
cana-6095	308	6	)	)	PUNCT
cana-6095	308	7	.	.	PUNCT
cana-6095	309	1	35	35	NUM
cana-6095	309	2	.	.	PUNCT
cana-6095	310	1	liu	liu	PROPN
cana-6095	310	2	,	,	PUNCT
cana-6095	310	3	z.	z.	PROPN
cana-6095	310	4	,	,	PUNCT
cana-6095	310	5	bessa	bessa	PROPN
cana-6095	310	6	,	,	PUNCT
cana-6095	310	7	m.	m.	NOUN
cana-6095	310	8	a.	a.	PROPN
cana-6095	310	9	,	,	PUNCT
cana-6095	310	10	&	&	CCONJ
cana-6095	310	11	liu	liu	PROPN
cana-6095	310	12	,	,	PUNCT
cana-6095	310	13	w.	w.	PROPN
cana-6095	310	14	k.	k.	PROPN
cana-6095	310	15	(	(	PUNCT
cana-6095	310	16	2016	2016	NUM
cana-6095	310	17	)	)	PUNCT
cana-6095	310	18	.	.	PUNCT
cana-6095	311	1	self	self	NOUN
cana-6095	311	2	-	-	PUNCT
cana-6095	311	3	consistent	consistent	ADJ
cana-6095	311	4	clustering	clustering	ADJ
cana-6095	311	5	analysis	analysis	NOUN
cana-6095	311	6	:	:	PUNCT
cana-6095	311	7	an	an	DET
cana-6095	311	8	efficient	efficient	ADJ
cana-6095	311	9	multi	multi	ADJ
cana-6095	311	10	-	-	ADJ
cana-6095	311	11	scale	scale	ADJ
cana-6095	311	12	scheme	scheme	NOUN
cana-6095	311	13	for	for	ADP
cana-6095	311	14	inelastic	inelastic	ADJ
cana-6095	311	15	composite	composite	ADJ
cana-6095	311	16	materials	material	NOUN
cana-6095	311	17	.	.	PUNCT
cana-6095	312	1	computer	computer	NOUN
cana-6095	312	2	methods	method	NOUN
cana-6095	312	3	in	in	ADP
cana-6095	312	4	applied	applied	ADJ
cana-6095	312	5	mechanics	mechanic	NOUN
cana-6095	312	6	and	and	CCONJ
cana-6095	312	7	engineering	engineering	NOUN
cana-6095	312	8	,	,	PUNCT
cana-6095	312	9	306	306	NUM
cana-6095	312	10	,	,	PUNCT
cana-6095	312	11	319	319	NUM
cana-6095	312	12	-	-	SYM
cana-6095	312	13	341	341	NUM
cana-6095	312	14	.	.	NUM
cana-6095	313	1	36	36	NUM
cana-6095	313	2	.	.	PUNCT
cana-6095	314	1	ranganathan	ranganathan	PROPN
cana-6095	314	2	,	,	PUNCT
cana-6095	314	3	r.	r.	PROPN
cana-6095	314	4	,	,	PUNCT
cana-6095	314	5	&	&	CCONJ
cana-6095	314	6	farimani	farimani	PROPN
cana-6095	314	7	,	,	PUNCT
cana-6095	314	8	a.	a.	PROPN
cana-6095	314	9	b.	b.	PROPN
cana-6095	314	10	(	(	PUNCT
cana-6095	314	11	2021	2021	NUM
cana-6095	314	12	)	)	PUNCT
cana-6095	314	13	.	.	PUNCT
cana-6095	315	1	a	a	DET
cana-6095	315	2	bayesian	bayesian	NOUN
cana-6095	315	3	framework	framework	NOUN
cana-6095	315	4	for	for	ADP
cana-6095	315	5	materials	material	NOUN
cana-6095	315	6	knowledge	knowledge	NOUN
cana-6095	315	7	systems	system	NOUN
cana-6095	315	8	.	.	PUNCT
cana-6095	316	1	npj	npj	PROPN
cana-6095	316	2	computational	computational	ADJ
cana-6095	316	3	materials	material	NOUN
cana-6095	316	4	,	,	PUNCT
cana-6095	316	5	7(1	7(1	NUM
cana-6095	316	6	)	)	PUNCT
cana-6095	316	7	,	,	PUNCT
cana-6095	316	8	1	1	NUM
cana-6095	316	9	-	-	SYM
cana-6095	316	10	10	10	NUM
cana-6095	316	11	.	.	PUNCT
cana-6095	317	1	37	37	NUM
cana-6095	317	2	.	.	PUNCT
cana-6095	318	1	wang	wang	PROPN
cana-6095	318	2	,	,	PUNCT
cana-6095	318	3	k.	k.	PROPN
cana-6095	318	4	,	,	PUNCT
cana-6095	318	5	&	&	CCONJ
cana-6095	318	6	sun	sun	PROPN
cana-6095	318	7	,	,	PUNCT
cana-6095	318	8	w.	w.	PROPN
cana-6095	318	9	(	(	PUNCT
cana-6095	318	10	2018	2018	NUM
cana-6095	318	11	)	)	PUNCT
cana-6095	318	12	.	.	PUNCT
cana-6095	319	1	a	a	DET
cana-6095	319	2	multiscale	multiscale	ADJ
cana-6095	319	3	multi	multi	ADJ
cana-6095	319	4	-	-	ADJ
cana-6095	319	5	axis	axis	ADJ
cana-6095	319	6	constitutive	constitutive	ADJ
cana-6095	319	7	model	model	NOUN
cana-6095	319	8	for	for	ADP
cana-6095	319	9	the	the	DET
cana-6095	319	10	nonlinear	nonlinear	ADJ
cana-6095	319	11	analysis	analysis	NOUN
cana-6095	319	12	of	of	ADP
cana-6095	319	13	composite	composite	ADJ
cana-6095	319	14	structures	structure	NOUN
cana-6095	319	15	.	.	PUNCT
cana-6095	320	1	journal	journal	NOUN
cana-6095	320	2	of	of	ADP
cana-6095	320	3	applied	apply	VERB
cana-6095	320	4	mechanics	mechanic	NOUN
cana-6095	320	5	,	,	PUNCT
cana-6095	320	6	85(7	85(7	NUM
cana-6095	320	7	)	)	PUNCT
cana-6095	320	8	.	.	PUNCT
cana-6095	321	1	38	38	NUM
cana-6095	321	2	.	.	PUNCT
cana-6095	322	1	louizos	louizos	PROPN
cana-6095	322	2	,	,	PUNCT
cana-6095	322	3	c.	c.	PROPN
cana-6095	322	4	,	,	PUNCT
cana-6095	322	5	&	&	CCONJ
cana-6095	322	6	welling	welling	PROPN
cana-6095	322	7	,	,	PUNCT
cana-6095	322	8	m.	m.	NOUN
cana-6095	322	9	(	(	PUNCT
cana-6095	322	10	2017	2017	NUM
cana-6095	322	11	)	)	PUNCT
cana-6095	322	12	.	.	PUNCT
cana-6095	323	1	multiplicative	multiplicative	ADJ
cana-6095	323	2	normalizing	normalizing	ADJ
cana-6095	323	3	flows	flow	NOUN
cana-6095	323	4	for	for	ADP
cana-6095	323	5	variational	variational	ADJ
cana-6095	323	6	bayesian	bayesian	NOUN
cana-6095	323	7	neural	neural	ADJ
cana-6095	323	8	networks	network	NOUN
cana-6095	323	9	.	.	PUNCT
cana-6095	324	1	proceedings	proceeding	NOUN
cana-6095	324	2	of	of	ADP
cana-6095	324	3	the	the	DET
cana-6095	324	4	34th	34th	ADJ
cana-6095	324	5	international	international	ADJ
cana-6095	324	6	conference	conference	NOUN
cana-6095	324	7	on	on	ADP
cana-6095	324	8	machine	machine	NOUN
cana-6095	324	9	learning	learning	NOUN
cana-6095	324	10	(	(	PUNCT
cana-6095	324	11	icml	icml	PROPN
cana-6095	324	12	)	)	PUNCT
cana-6095	324	13	.	.	PUNCT
cana-6095	325	1	(	(	PUNCT
cana-6095	325	2	uses	use	VERB
cana-6095	325	3	normalizing	normalize	VERB
cana-6095	325	4	flows	flow	NOUN
cana-6095	325	5	for	for	ADP
cana-6095	325	6	more	more	ADJ
cana-6095	325	7	expressive	expressive	ADJ
cana-6095	325	8	posteriors	posterior	NOUN
cana-6095	325	9	)	)	PUNCT
cana-6095	325	10	.	.	PUNCT
cana-6095	326	1	39	39	NUM
cana-6095	326	2	.	.	PUNCT
cana-6095	327	1	mishkin	mishkin	PROPN
cana-6095	327	2	,	,	PUNCT
cana-6095	327	3	d.	d.	PROPN
cana-6095	327	4	,	,	PUNCT
cana-6095	327	5	sergievskiy	sergievskiy	PROPN
cana-6095	327	6	,	,	PUNCT
cana-6095	327	7	n.	n.	NOUN
cana-6095	327	8	,	,	PUNCT
cana-6095	327	9	&	&	CCONJ
cana-6095	327	10	matas	matas	PROPN
cana-6095	327	11	,	,	PUNCT
cana-6095	327	12	j.	j.	PROPN
cana-6095	327	13	(	(	PUNCT
cana-6095	327	14	2018	2018	NUM
cana-6095	327	15	)	)	PUNCT
cana-6095	327	16	.	.	PUNCT
cana-6095	328	1	systematic	systematic	ADJ
cana-6095	328	2	evaluation	evaluation	NOUN
cana-6095	328	3	of	of	ADP
cana-6095	328	4	convolution	convolution	NOUN
cana-6095	328	5	neural	neural	ADJ
cana-6095	328	6	network	network	NOUN
cana-6095	328	7	advances	advance	NOUN
cana-6095	328	8	on	on	ADP
cana-6095	328	9	the	the	DET
cana-6095	328	10	imagenet	imagenet	NOUN
cana-6095	328	11	.	.	PUNCT
cana-6095	329	1	computer	computer	NOUN
cana-6095	329	2	vision	vision	NOUN
cana-6095	329	3	and	and	CCONJ
cana-6095	329	4	image	image	NOUN
cana-6095	329	5	understanding	understanding	NOUN
cana-6095	329	6	,	,	PUNCT
cana-6095	329	7	161	161	NUM
cana-6095	329	8	,	,	PUNCT
cana-6095	329	9	11	11	NUM
cana-6095	329	10	-	-	SYM
cana-6095	329	11	19	19	NUM
cana-6095	329	12	.	.	PUNCT
cana-6095	329	13	communications	communication	NOUN
cana-6095	329	14	on	on	ADP
cana-6095	329	15	applied	apply	VERB
cana-6095	329	16	nonlinear	nonlinear	ADJ
cana-6095	329	17	analysis	analysis	NOUN
cana-6095	329	18	issn	issn	NOUN
cana-6095	329	19	:	:	PUNCT
cana-6095	329	20	1074	1074	NUM
cana-6095	329	21	-	-	PUNCT
cana-6095	329	22	133x	133x	NUM
cana-6095	329	23	vol	vol	NOUN
cana-6095	329	24	30	30	NUM
cana-6095	329	25	no	no	NOUN
cana-6095	329	26	.	.	NOUN
cana-6095	329	27	3	3	NUM
cana-6095	329	28	(	(	PUNCT
cana-6095	329	29	2023	2023	NUM
cana-6095	329	30	)	)	PUNCT
cana-6095	329	31	66	66	NUM
cana-6095	329	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-6095	329	33	40	40	NUM
cana-6095	329	34	.	.	PUNCT
cana-6095	330	1	ritter	ritter	PROPN
cana-6095	330	2	,	,	PUNCT
cana-6095	330	3	h.	h.	PROPN
cana-6095	330	4	,	,	PUNCT
cana-6095	330	5	botev	botev	NOUN
cana-6095	330	6	,	,	PUNCT
cana-6095	330	7	a.	a.	NOUN
cana-6095	330	8	,	,	PUNCT
cana-6095	330	9	&	&	CCONJ
cana-6095	330	10	barber	barber	PROPN
cana-6095	330	11	,	,	PUNCT
cana-6095	330	12	d.	d.	PROPN
cana-6095	330	13	(	(	PUNCT
cana-6095	330	14	2018	2018	NUM
cana-6095	330	15	)	)	PUNCT
cana-6095	330	16	.	.	PUNCT
cana-6095	331	1	a	a	DET
cana-6095	331	2	scalable	scalable	ADJ
cana-6095	331	3	laplace	laplace	NOUN
cana-6095	331	4	approximation	approximation	NOUN
cana-6095	331	5	for	for	ADP
cana-6095	331	6	neural	neural	ADJ
cana-6095	331	7	networks	network	NOUN
cana-6095	331	8	.	.	PUNCT
cana-6095	332	1	international	international	ADJ
cana-6095	332	2	conference	conference	NOUN
cana-6095	332	3	on	on	ADP
cana-6095	332	4	learning	learn	VERB
cana-6095	332	5	representations	representation	NOUN
cana-6095	332	6	(	(	PUNCT
cana-6095	332	7	iclr	iclr	NOUN
cana-6095	332	8	)	)	PUNCT
cana-6095	332	9	.	.	PUNCT
cana-6095	333	1	41	41	NUM
cana-6095	333	2	.	.	PUNCT
cana-6095	334	1	sun	sun	PROPN
cana-6095	334	2	,	,	PUNCT
cana-6095	334	3	s.	s.	PROPN
cana-6095	334	4	,	,	PUNCT
cana-6095	334	5	zhang	zhang	PROPN
cana-6095	334	6	,	,	PUNCT
cana-6095	334	7	g.	g.	PROPN
cana-6095	334	8	,	,	PUNCT
cana-6095	334	9	shi	shi	PROPN
cana-6095	334	10	,	,	PUNCT
cana-6095	334	11	j.	j.	PROPN
cana-6095	334	12	,	,	PUNCT
cana-6095	334	13	&	&	CCONJ
cana-6095	334	14	grosse	grosse	PROPN
cana-6095	334	15	,	,	PUNCT
cana-6095	334	16	r.	r.	PROPN
cana-6095	334	17	(	(	PUNCT
cana-6095	334	18	2019	2019	NUM
cana-6095	334	19	)	)	PUNCT
cana-6095	334	20	.	.	PUNCT
cana-6095	335	1	functional	functional	ADJ
cana-6095	335	2	variational	variational	ADJ
cana-6095	335	3	bayesian	bayesian	NOUN
cana-6095	335	4	neural	neural	ADJ
cana-6095	335	5	networks	network	NOUN
cana-6095	335	6	.	.	PUNCT
cana-6095	336	1	international	international	ADJ
cana-6095	336	2	conference	conference	NOUN
cana-6095	336	3	on	on	ADP
cana-6095	336	4	learning	learn	VERB
cana-6095	336	5	representations	representation	NOUN
cana-6095	336	6	(	(	PUNCT
cana-6095	336	7	iclr	iclr	NOUN
cana-6095	336	8	)	)	PUNCT
cana-6095	336	9	.	.	PUNCT
cana-6095	337	1	(	(	PUNCT
cana-6095	337	2	explores	explore	VERB
cana-6095	337	3	functional	functional	ADJ
cana-6095	337	4	approaches	approach	NOUN
cana-6095	337	5	for	for	ADP
cana-6095	337	6	bnns	bnn	NOUN
cana-6095	337	7	)	)	PUNCT
cana-6095	337	8	.	.	PUNCT
cana-6095	338	1	42	42	NUM
cana-6095	338	2	.	.	X
cana-6095	339	1	zhang	zhang	PROPN
cana-6095	339	2	,	,	PUNCT
cana-6095	339	3	g.	g.	PROPN
cana-6095	339	4	,	,	PUNCT
cana-6095	339	5	sun	sun	PROPN
cana-6095	339	6	,	,	PUNCT
cana-6095	339	7	s.	s.	PROPN
cana-6095	339	8	,	,	PUNCT
cana-6095	339	9	duvenaud	duvenaud	PROPN
cana-6095	339	10	,	,	PUNCT
cana-6095	339	11	d.	d.	PROPN
cana-6095	339	12	,	,	PUNCT
cana-6095	339	13	&	&	CCONJ
cana-6095	339	14	grosse	grosse	PROPN
cana-6095	339	15	,	,	PUNCT
cana-6095	339	16	r.	r.	PROPN
cana-6095	339	17	(	(	PUNCT
cana-6095	339	18	2018	2018	NUM
cana-6095	339	19	)	)	PUNCT
cana-6095	339	20	.	.	PUNCT
cana-6095	340	1	noisy	noisy	ADJ
cana-6095	340	2	natural	natural	ADJ
cana-6095	340	3	gradient	gradient	NOUN
cana-6095	340	4	as	as	ADP
cana-6095	340	5	variational	variational	ADJ
cana-6095	340	6	inference	inference	NOUN
cana-6095	340	7	.	.	PUNCT
cana-6095	341	1	proceedings	proceeding	NOUN
cana-6095	341	2	of	of	ADP
cana-6095	341	3	the	the	DET
cana-6095	341	4	35th	35th	ADJ
cana-6095	341	5	international	international	ADJ
cana-6095	341	6	conference	conference	NOUN
cana-6095	341	7	on	on	ADP
cana-6095	341	8	machine	machine	NOUN
cana-6095	341	9	learning	learning	NOUN
cana-6095	341	10	(	(	PUNCT
cana-6095	341	11	icml	icml	PROPN
cana-6095	341	12	)	)	PUNCT
cana-6095	341	13	.	.	PUNCT
cana-6095	342	1	43	43	NUM
cana-6095	342	2	.	.	PUNCT
cana-6095	343	1	guo	guo	PROPN
cana-6095	343	2	,	,	PUNCT
cana-6095	343	3	c.	c.	PROPN
cana-6095	343	4	,	,	PUNCT
cana-6095	343	5	pleiss	pleiss	NOUN
cana-6095	343	6	,	,	PUNCT
cana-6095	343	7	g.	g.	PROPN
cana-6095	343	8	,	,	PUNCT
cana-6095	343	9	sun	sun	NOUN
cana-6095	343	10	,	,	PUNCT
cana-6095	343	11	y.	y.	PROPN
cana-6095	343	12	,	,	PUNCT
cana-6095	343	13	&	&	CCONJ
cana-6095	343	14	weinberger	weinberger	PROPN
cana-6095	343	15	,	,	PUNCT
cana-6095	343	16	k.	k.	PROPN
cana-6095	343	17	q.	q.	PROPN
cana-6095	343	18	(	(	PUNCT
cana-6095	343	19	2017	2017	NUM
cana-6095	343	20	)	)	PUNCT
cana-6095	343	21	.	.	PUNCT
cana-6095	344	1	on	on	ADP
cana-6095	344	2	calibration	calibration	NOUN
cana-6095	344	3	of	of	ADP
cana-6095	344	4	modern	modern	ADJ
cana-6095	344	5	neural	neural	ADJ
cana-6095	344	6	networks	network	NOUN
cana-6095	344	7	.	.	PUNCT
cana-6095	345	1	proceedings	proceeding	NOUN
cana-6095	345	2	of	of	ADP
cana-6095	345	3	the	the	DET
cana-6095	345	4	34th	34th	ADJ
cana-6095	345	5	international	international	ADJ
cana-6095	345	6	conference	conference	NOUN
cana-6095	345	7	on	on	ADP
cana-6095	345	8	machine	machine	NOUN
cana-6095	345	9	learning	learning	NOUN
cana-6095	345	10	(	(	PUNCT
cana-6095	345	11	icml	icml	PROPN
cana-6095	345	12	)	)	PUNCT
cana-6095	345	13	.	.	PUNCT
cana-6095	346	1	(	(	PUNCT
cana-6095	346	2	seminal	seminal	ADJ
cana-6095	346	3	paper	paper	NOUN
cana-6095	346	4	on	on	ADP
cana-6095	346	5	modern	modern	ADJ
cana-6095	346	6	nns	nn	NOUN
cana-6095	346	7	being	be	AUX
cana-6095	346	8	miscalibrated	miscalibrated	ADJ
cana-6095	346	9	)	)	PUNCT
cana-6095	346	10	.	.	PUNCT
cana-6095	347	1	44	44	NUM
cana-6095	347	2	.	.	PUNCT
cana-6095	347	3	grosse	grosse	PROPN
cana-6095	347	4	,	,	PUNCT
cana-6095	347	5	r.	r.	PROPN
cana-6095	347	6	b.	b.	PROPN
cana-6095	347	7	,	,	PUNCT
cana-6095	347	8	ancha	ancha	PROPN
cana-6095	347	9	,	,	PUNCT
cana-6095	347	10	s.	s.	PROPN
cana-6095	347	11	,	,	PUNCT
cana-6095	347	12	&	&	CCONJ
cana-6095	347	13	roy	roy	PROPN
cana-6095	347	14	,	,	PUNCT
cana-6095	347	15	d.	d.	PROPN
cana-6095	347	16	m.	m.	PROPN
cana-6095	347	17	(	(	PUNCT
cana-6095	347	18	2016	2016	NUM
cana-6095	347	19	)	)	PUNCT
cana-6095	347	20	.	.	PUNCT
cana-6095	348	1	measuring	measure	VERB
cana-6095	348	2	the	the	DET
cana-6095	348	3	reliability	reliability	NOUN
cana-6095	348	4	of	of	ADP
cana-6095	348	5	mcmc	mcmc	PROPN
cana-6095	348	6	inference	inference	PROPN
cana-6095	348	7	with	with	ADP
cana-6095	348	8	bidirectional	bidirectional	ADJ
cana-6095	348	9	monte	monte	PROPN
cana-6095	348	10	carlo	carlo	PROPN
cana-6095	348	11	.	.	PUNCT
cana-6095	349	1	advances	advance	NOUN
cana-6095	349	2	in	in	ADP
cana-6095	349	3	neural	neural	ADJ
cana-6095	349	4	information	information	NOUN
cana-6095	349	5	processing	processing	NOUN
cana-6095	349	6	systems	system	NOUN
cana-6095	349	7	(	(	PUNCT
cana-6095	349	8	neurips	neurip	NOUN
cana-6095	349	9	)	)	PUNCT
cana-6095	349	10	.	.	PUNCT
cana-6095	350	1	45	45	NUM
cana-6095	350	2	.	.	PUNCT
cana-6095	350	3	ovadia	ovadia	PROPN
cana-6095	350	4	,	,	PUNCT
cana-6095	350	5	y.	y.	NOUN
cana-6095	350	6	,	,	PUNCT
cana-6095	350	7	fertig	fertig	PROPN
cana-6095	350	8	,	,	PUNCT
cana-6095	350	9	e.	e.	PROPN
cana-6095	350	10	,	,	PUNCT
cana-6095	350	11	ren	ren	PROPN
cana-6095	350	12	,	,	PUNCT
cana-6095	350	13	j.	j.	PROPN
cana-6095	350	14	,	,	PUNCT
cana-6095	350	15	nado	nado	PROPN
cana-6095	350	16	,	,	PUNCT
cana-6095	350	17	z.	z.	PROPN
cana-6095	350	18	,	,	PUNCT
cana-6095	350	19	sculley	sculley	NOUN
cana-6095	350	20	,	,	PUNCT
cana-6095	350	21	d.	d.	PROPN
cana-6095	350	22	,	,	PUNCT
cana-6095	350	23	nowozin	nowozin	PROPN
cana-6095	350	24	,	,	PUNCT
cana-6095	350	25	s.	s.	PROPN
cana-6095	350	26	,	,	PUNCT
cana-6095	350	27	...	...	PUNCT
cana-6095	350	28	&	&	CCONJ
cana-6095	350	29	snoek	snoek	PROPN
cana-6095	350	30	,	,	PUNCT
cana-6095	350	31	j.	j.	PROPN
cana-6095	350	32	(	(	PUNCT
cana-6095	350	33	2019	2019	NUM
cana-6095	350	34	)	)	PUNCT
cana-6095	350	35	.	.	PUNCT
cana-6095	351	1	can	can	AUX
cana-6095	351	2	you	you	PRON
cana-6095	351	3	trust	trust	VERB
cana-6095	351	4	your	your	PRON
cana-6095	351	5	model	model	NOUN
cana-6095	351	6	's	's	PART
cana-6095	351	7	uncertainty	uncertainty	NOUN
cana-6095	351	8	?	?	PUNCT
cana-6095	352	1	evaluating	evaluate	VERB
cana-6095	352	2	predictive	predictive	ADJ
cana-6095	352	3	uncertainty	uncertainty	NOUN
cana-6095	352	4	under	under	ADP
cana-6095	352	5	dataset	dataset	NOUN
cana-6095	352	6	shift	shift	NOUN
cana-6095	352	7	.	.	PUNCT
cana-6095	353	1	advances	advance	NOUN
cana-6095	353	2	in	in	ADP
cana-6095	353	3	neural	neural	ADJ
cana-6095	353	4	information	information	NOUN
cana-6095	353	5	processing	processing	NOUN
cana-6095	353	6	systems	system	NOUN
cana-6095	353	7	(	(	PUNCT
cana-6095	353	8	neurips	neurip	NOUN
cana-6095	353	9	)	)	PUNCT
cana-6095	353	10	.	.	PUNCT
cana-6095	354	1	(	(	PUNCT
cana-6095	354	2	important	important	ADJ
cana-6095	354	3	empirical	empirical	ADJ
cana-6095	354	4	study	study	NOUN
cana-6095	354	5	of	of	ADP
cana-6095	354	6	uq	uq	NOUN
cana-6095	354	7	methods	method	NOUN
cana-6095	354	8	under	under	ADP
cana-6095	354	9	distribution	distribution	NOUN
cana-6095	354	10	shift	shift	NOUN
cana-6095	354	11	)	)	PUNCT
cana-6095	354	12	.	.	PUNCT
cana-6095	355	1	46	46	NUM
cana-6095	355	2	.	.	PUNCT
cana-6095	356	1	snoek	snoek	PROPN
cana-6095	356	2	,	,	PUNCT
cana-6095	356	3	j.	j.	PROPN
cana-6095	356	4	,	,	PUNCT
cana-6095	356	5	larochelle	larochelle	PROPN
cana-6095	356	6	,	,	PUNCT
cana-6095	356	7	h.	h.	PROPN
cana-6095	356	8	,	,	PUNCT
cana-6095	356	9	&	&	CCONJ
cana-6095	356	10	adams	adams	PROPN
cana-6095	356	11	,	,	PUNCT
cana-6095	356	12	r.	r.	PROPN
cana-6095	356	13	p.	p.	PROPN
cana-6095	356	14	(	(	PUNCT
cana-6095	356	15	2012	2012	NUM
cana-6095	356	16	)	)	PUNCT
cana-6095	356	17	.	.	PUNCT
cana-6095	357	1	practical	practical	ADJ
cana-6095	357	2	bayesian	bayesian	NOUN
cana-6095	357	3	optimization	optimization	NOUN
cana-6095	357	4	of	of	ADP
cana-6095	357	5	machine	machine	NOUN
cana-6095	357	6	learning	learn	VERB
cana-6095	357	7	algorithms	algorithm	NOUN
cana-6095	357	8	.	.	PUNCT
cana-6095	358	1	advances	advance	NOUN
cana-6095	358	2	in	in	ADP
cana-6095	358	3	neural	neural	ADJ
cana-6095	358	4	information	information	NOUN
cana-6095	358	5	processing	processing	NOUN
cana-6095	358	6	systems	system	NOUN
cana-6095	358	7	(	(	PUNCT
cana-6095	358	8	neurips	neurip	NOUN
cana-6095	358	9	)	)	PUNCT
cana-6095	358	10	.	.	PUNCT
cana-6095	359	1	47	47	NUM
cana-6095	359	2	.	.	PUNCT
cana-6095	359	3	wilson	wilson	PROPN
cana-6095	359	4	,	,	PUNCT
cana-6095	359	5	a.	a.	PROPN
cana-6095	359	6	g.	g.	PROPN
cana-6095	359	7	,	,	PUNCT
cana-6095	359	8	&	&	CCONJ
cana-6095	359	9	izmailov	izmailov	PROPN
cana-6095	359	10	,	,	PUNCT
cana-6095	359	11	p.	p.	NOUN
cana-6095	359	12	(	(	PUNCT
cana-6095	359	13	2020	2020	NUM
cana-6095	359	14	)	)	PUNCT
cana-6095	359	15	.	.	PUNCT
cana-6095	360	1	bayesian	bayesian	NOUN
cana-6095	360	2	deep	deep	ADJ
cana-6095	360	3	learning	learning	NOUN
cana-6095	360	4	and	and	CCONJ
cana-6095	360	5	a	a	DET
cana-6095	360	6	probabilistic	probabilistic	ADJ
cana-6095	360	7	perspective	perspective	NOUN
cana-6095	360	8	of	of	ADP
cana-6095	360	9	generalization	generalization	NOUN
cana-6095	360	10	.	.	PUNCT
cana-6095	361	1	advances	advance	NOUN
cana-6095	361	2	in	in	ADP
cana-6095	361	3	neural	neural	ADJ
cana-6095	361	4	information	information	NOUN
cana-6095	361	5	processing	processing	NOUN
cana-6095	361	6	systems	system	NOUN
cana-6095	361	7	(	(	PUNCT
cana-6095	361	8	neurips	neurip	NOUN
cana-6095	361	9	)	)	PUNCT
cana-6095	361	10	.	.	PUNCT
cana-6095	362	1	(	(	PUNCT
cana-6095	362	2	theoretical	theoretical	ADJ
cana-6095	362	3	work	work	NOUN
cana-6095	362	4	connecting	connect	VERB
cana-6095	362	5	bnns	bnn	NOUN
cana-6095	362	6	to	to	ADP
cana-6095	362	7	generalization	generalization	NOUN
cana-6095	362	8	)	)	PUNCT
cana-6095	362	9	.	.	PUNCT