id	sid	tid	token	lemma	pos
ajst-27525	1	1	academic	academic	ADJ
ajst-27525	1	2	journal	journal	NOUN
ajst-27525	1	3	of	of	ADP
ajst-27525	1	4	science	science	NOUN
ajst-27525	1	5	and	and	CCONJ
ajst-27525	1	6	technology	technology	NOUN
ajst-27525	1	7	issn	issn	NOUN
ajst-27525	1	8	:	:	PUNCT
ajst-27525	1	9	2771	2771	NUM
ajst-27525	1	10	-	-	SYM
ajst-27525	1	11	3032	3032	NUM
ajst-27525	1	12	|	|	NOUN
ajst-27525	1	13	vol	vol	NOUN
ajst-27525	1	14	.	.	PROPN
ajst-27525	1	15	13	13	NUM
ajst-27525	1	16	,	,	PUNCT
ajst-27525	1	17	no	no	INTJ
ajst-27525	1	18	.	.	NOUN
ajst-27525	1	19	2	2	NUM
ajst-27525	1	20	,	,	PUNCT
ajst-27525	1	21	2024	2024	NUM
ajst-27525	1	22	182	182	NUM
ajst-27525	1	23	feasibility	feasibility	NOUN
ajst-27525	1	24	study	study	NOUN
ajst-27525	1	25	of	of	ADP
ajst-27525	1	26	solving	solve	VERB
ajst-27525	1	27	oil‐water	oil‐water	ADP
ajst-27525	1	28	two‐phase	two‐phase	DET
ajst-27525	1	29	flow	flow	NOUN
ajst-27525	1	30	equations	equation	NOUN
ajst-27525	1	31	using	use	VERB
ajst-27525	1	32	fourier	fourier	ADJ
ajst-27525	1	33	neural	neural	ADJ
ajst-27525	1	34	operator	operator	NOUN
ajst-27525	1	35	rong	rong	PROPN
ajst-27525	1	36	zhong	zhong	PROPN
ajst-27525	1	37	school	school	PROPN
ajst-27525	1	38	of	of	ADP
ajst-27525	1	39	petroleum	petroleum	NOUN
ajst-27525	1	40	engineering	engineering	NOUN
ajst-27525	1	41	,	,	PUNCT
ajst-27525	1	42	xi'an	xi'an	PROPN
ajst-27525	1	43	shiyou	shiyou	PROPN
ajst-27525	1	44	university	university	PROPN
ajst-27525	1	45	,	,	PUNCT
ajst-27525	1	46	xi'an	xi'an	PROPN
ajst-27525	1	47	,	,	PUNCT
ajst-27525	1	48	shaanxi	shaanxi	PROPN
ajst-27525	1	49	,	,	PUNCT
ajst-27525	1	50	710065	710065	NUM
ajst-27525	1	51	,	,	PUNCT
ajst-27525	1	52	china	china	PROPN
ajst-27525	1	53	abstract	abstract	PROPN
ajst-27525	1	54	:	:	PUNCT
ajst-27525	1	55	in	in	ADP
ajst-27525	1	56	petroleum	petroleum	NOUN
ajst-27525	1	57	reservoir	reservoir	PROPN
ajst-27525	1	58	engineering	engineering	NOUN
ajst-27525	1	59	,	,	PUNCT
ajst-27525	1	60	deep	deep	ADJ
ajst-27525	1	61	learning	learning	NOUN
ajst-27525	1	62	shows	show	VERB
ajst-27525	1	63	promising	promise	VERB
ajst-27525	1	64	potential	potential	NOUN
ajst-27525	1	65	for	for	ADP
ajst-27525	1	66	solving	solve	VERB
ajst-27525	1	67	partial	partial	ADJ
ajst-27525	1	68	differential	differential	ADJ
ajst-27525	1	69	equations	equation	NOUN
ajst-27525	1	70	(	(	PUNCT
ajst-27525	1	71	pdes	pde	NOUN
ajst-27525	1	72	)	)	PUNCT
ajst-27525	1	73	in	in	ADP
ajst-27525	1	74	reservoir	reservoir	PROPN
ajst-27525	1	75	numerical	numerical	PROPN
ajst-27525	1	76	simulations	simulation	NOUN
ajst-27525	1	77	.	.	PUNCT
ajst-27525	2	1	however	however	ADV
ajst-27525	2	2	,	,	PUNCT
ajst-27525	2	3	traditional	traditional	ADJ
ajst-27525	2	4	neural	neural	ADJ
ajst-27525	2	5	network	network	NOUN
ajst-27525	2	6	-	-	PUNCT
ajst-27525	2	7	based	base	VERB
ajst-27525	2	8	methods	method	NOUN
ajst-27525	2	9	for	for	ADP
ajst-27525	2	10	pde	pde	NOUN
ajst-27525	2	11	solutions	solution	NOUN
ajst-27525	2	12	are	be	AUX
ajst-27525	2	13	often	often	ADV
ajst-27525	2	14	limited	limit	VERB
ajst-27525	2	15	,	,	PUNCT
ajst-27525	2	16	typically	typically	ADV
ajst-27525	2	17	requiring	require	VERB
ajst-27525	2	18	retraining	retrain	VERB
ajst-27525	2	19	for	for	ADP
ajst-27525	2	20	different	different	ADJ
ajst-27525	2	21	equations	equation	NOUN
ajst-27525	2	22	.	.	PUNCT
ajst-27525	3	1	this	this	DET
ajst-27525	3	2	study	study	NOUN
ajst-27525	3	3	introduces	introduce	VERB
ajst-27525	3	4	the	the	DET
ajst-27525	3	5	fourier	fourier	ADJ
ajst-27525	3	6	neural	neural	ADJ
ajst-27525	3	7	operator	operator	NOUN
ajst-27525	3	8	(	(	PUNCT
ajst-27525	3	9	fno	fno	PROPN
ajst-27525	3	10	)	)	PUNCT
ajst-27525	3	11	approach	approach	NOUN
ajst-27525	3	12	,	,	PUNCT
ajst-27525	3	13	incorporating	incorporate	VERB
ajst-27525	3	14	the	the	DET
ajst-27525	3	15	fast	fast	ADJ
ajst-27525	3	16	fourier	fourier	NOUN
ajst-27525	3	17	transform	transform	NOUN
ajst-27525	3	18	mechanism	mechanism	NOUN
ajst-27525	3	19	to	to	PART
ajst-27525	3	20	facilitate	facilitate	VERB
ajst-27525	3	21	operator	operator	NOUN
ajst-27525	3	22	learning	learning	NOUN
ajst-27525	3	23	.	.	PUNCT
ajst-27525	4	1	we	we	PRON
ajst-27525	4	2	conduct	conduct	VERB
ajst-27525	4	3	a	a	DET
ajst-27525	4	4	feasibility	feasibility	NOUN
ajst-27525	4	5	analysis	analysis	NOUN
ajst-27525	4	6	of	of	ADP
ajst-27525	4	7	using	use	VERB
ajst-27525	4	8	fno	fno	PROPN
ajst-27525	4	9	for	for	ADP
ajst-27525	4	10	solving	solve	VERB
ajst-27525	4	11	two	two	NUM
ajst-27525	4	12	-	-	PUNCT
ajst-27525	4	13	dimensional	dimensional	ADJ
ajst-27525	4	14	oil	oil	NOUN
ajst-27525	4	15	-	-	PUNCT
ajst-27525	4	16	water	water	NOUN
ajst-27525	4	17	two	two	NUM
ajst-27525	4	18	-	-	PUNCT
ajst-27525	4	19	phase	phase	NOUN
ajst-27525	4	20	flow	flow	NOUN
ajst-27525	4	21	pdes	pde	NOUN
ajst-27525	4	22	.	.	PUNCT
ajst-27525	5	1	through	through	ADP
ajst-27525	5	2	extensive	extensive	ADJ
ajst-27525	5	3	literature	literature	PROPN
ajst-27525	5	4	review	review	NOUN
ajst-27525	5	5	,	,	PUNCT
ajst-27525	5	6	we	we	PRON
ajst-27525	5	7	summarize	summarize	VERB
ajst-27525	5	8	the	the	DET
ajst-27525	5	9	current	current	ADJ
ajst-27525	5	10	state	state	NOUN
ajst-27525	5	11	and	and	CCONJ
ajst-27525	5	12	limitations	limitation	NOUN
ajst-27525	5	13	of	of	ADP
ajst-27525	5	14	deep	deep	ADJ
ajst-27525	5	15	learning	learning	NOUN
ajst-27525	5	16	in	in	ADP
ajst-27525	5	17	oil	oil	NOUN
ajst-27525	5	18	-	-	PUNCT
ajst-27525	5	19	water	water	NOUN
ajst-27525	5	20	two	two	NUM
ajst-27525	5	21	-	-	PUNCT
ajst-27525	5	22	phase	phase	NOUN
ajst-27525	5	23	flow	flow	NOUN
ajst-27525	5	24	modeling	modeling	NOUN
ajst-27525	5	25	,	,	PUNCT
ajst-27525	5	26	highlighting	highlight	VERB
ajst-27525	5	27	the	the	DET
ajst-27525	5	28	application	application	NOUN
ajst-27525	5	29	and	and	CCONJ
ajst-27525	5	30	advancements	advancement	NOUN
ajst-27525	5	31	of	of	ADP
ajst-27525	5	32	neural	neural	ADJ
ajst-27525	5	33	operators	operator	NOUN
ajst-27525	5	34	for	for	ADP
ajst-27525	5	35	pde	pde	NOUN
ajst-27525	5	36	solutions	solution	NOUN
ajst-27525	5	37	.	.	PUNCT
ajst-27525	6	1	this	this	DET
ajst-27525	6	2	study	study	NOUN
ajst-27525	6	3	demonstrates	demonstrate	VERB
ajst-27525	6	4	the	the	DET
ajst-27525	6	5	potential	potential	NOUN
ajst-27525	6	6	of	of	ADP
ajst-27525	6	7	fno	fno	PROPN
ajst-27525	6	8	to	to	PART
ajst-27525	6	9	solve	solve	VERB
ajst-27525	6	10	high	high	ADJ
ajst-27525	6	11	-	-	PUNCT
ajst-27525	6	12	dimensional	dimensional	ADJ
ajst-27525	6	13	oil	oil	NOUN
ajst-27525	6	14	-	-	PUNCT
ajst-27525	6	15	water	water	NOUN
ajst-27525	6	16	two	two	NUM
ajst-27525	6	17	-	-	PUNCT
ajst-27525	6	18	phase	phase	NOUN
ajst-27525	6	19	flow	flow	NOUN
ajst-27525	6	20	equations	equation	NOUN
ajst-27525	6	21	,	,	PUNCT
ajst-27525	6	22	offering	offer	VERB
ajst-27525	6	23	valuable	valuable	ADJ
ajst-27525	6	24	insights	insight	NOUN
ajst-27525	6	25	into	into	ADP
ajst-27525	6	26	intelligent	intelligent	ADJ
ajst-27525	6	27	predictions	prediction	NOUN
ajst-27525	6	28	for	for	ADP
ajst-27525	6	29	complex	complex	ADJ
ajst-27525	6	30	subsurface	subsurface	NOUN
ajst-27525	6	31	reservoirs	reservoir	NOUN
ajst-27525	6	32	and	and	CCONJ
ajst-27525	6	33	presenting	present	VERB
ajst-27525	6	34	new	new	ADJ
ajst-27525	6	35	methods	method	NOUN
ajst-27525	6	36	and	and	CCONJ
ajst-27525	6	37	perspectives	perspective	NOUN
ajst-27525	6	38	for	for	ADP
ajst-27525	6	39	further	further	ADJ
ajst-27525	6	40	development	development	NOUN
ajst-27525	6	41	in	in	ADP
ajst-27525	6	42	reservoir	reservoir	PROPN
ajst-27525	6	43	numerical	numerical	PROPN
ajst-27525	6	44	modeling	modeling	PROPN
ajst-27525	6	45	.	.	PUNCT
ajst-27525	7	1	keywords	keyword	NOUN
ajst-27525	7	2	:	:	PUNCT
ajst-27525	7	3	deep	deep	ADJ
ajst-27525	7	4	learning	learning	NOUN
ajst-27525	7	5	;	;	PUNCT
ajst-27525	7	6	neural	neural	ADJ
ajst-27525	7	7	operators	operator	NOUN
ajst-27525	7	8	;	;	PUNCT
ajst-27525	7	9	fno	fno	PROPN
ajst-27525	7	10	;	;	PUNCT
ajst-27525	7	11	oil	oil	NOUN
ajst-27525	7	12	-	-	PUNCT
ajst-27525	7	13	water	water	NOUN
ajst-27525	7	14	two	two	NUM
ajst-27525	7	15	-	-	PUNCT
ajst-27525	7	16	phase	phase	NOUN
ajst-27525	7	17	flow	flow	NOUN
ajst-27525	7	18	;	;	PUNCT
ajst-27525	7	19	partial	partial	ADJ
ajst-27525	7	20	differential	differential	NOUN
ajst-27525	7	21	equations	equation	NOUN
ajst-27525	7	22	.	.	PUNCT
ajst-27525	8	1	1	1	X
ajst-27525	8	2	.	.	X
ajst-27525	8	3	introduction	introduction	NOUN
ajst-27525	8	4	reservoir	reservoir	PROPN
ajst-27525	8	5	numerical	numerical	PROPN
ajst-27525	8	6	simulation	simulation	PROPN
ajst-27525	8	7	is	be	AUX
ajst-27525	8	8	an	an	DET
ajst-27525	8	9	essential	essential	ADJ
ajst-27525	8	10	component	component	NOUN
ajst-27525	8	11	in	in	ADP
ajst-27525	8	12	petroleum	petroleum	NOUN
ajst-27525	8	13	development	development	NOUN
ajst-27525	8	14	and	and	CCONJ
ajst-27525	8	15	production	production	NOUN
ajst-27525	8	16	.	.	PUNCT
ajst-27525	9	1	traditional	traditional	ADJ
ajst-27525	9	2	reservoir	reservoir	PROPN
ajst-27525	9	3	simulation	simulation	NOUN
ajst-27525	9	4	techniques	technique	NOUN
ajst-27525	9	5	are	be	AUX
ajst-27525	9	6	grounded	ground	VERB
ajst-27525	9	7	in	in	ADP
ajst-27525	9	8	physicsbased	physicsbase	VERB
ajst-27525	9	9	methods	method	NOUN
ajst-27525	9	10	that	that	PRON
ajst-27525	9	11	approximate	approximate	ADJ
ajst-27525	9	12	solutions	solution	NOUN
ajst-27525	9	13	for	for	ADP
ajst-27525	9	14	partial	partial	ADJ
ajst-27525	9	15	differential	differential	ADJ
ajst-27525	9	16	equations	equation	NOUN
ajst-27525	9	17	(	(	PUNCT
ajst-27525	9	18	pdes	pde	NOUN
ajst-27525	9	19	)	)	PUNCT
ajst-27525	9	20	using	use	VERB
ajst-27525	9	21	finite	finite	ADJ
ajst-27525	9	22	difference	difference	NOUN
ajst-27525	9	23	methods	method	NOUN
ajst-27525	9	24	(	(	PUNCT
ajst-27525	9	25	dm	dm	NOUN
ajst-27525	9	26	)	)	PUNCT
ajst-27525	9	27	,	,	PUNCT
ajst-27525	9	28	finite	finite	PROPN
ajst-27525	9	29	element	element	NOUN
ajst-27525	9	30	methods	method	NOUN
ajst-27525	9	31	(	(	PUNCT
ajst-27525	9	32	fem	fem	NOUN
ajst-27525	9	33	)	)	PUNCT
ajst-27525	9	34	,	,	PUNCT
ajst-27525	9	35	or	or	CCONJ
ajst-27525	9	36	boundary	boundary	ADJ
ajst-27525	9	37	element	element	NOUN
ajst-27525	9	38	methods	method	NOUN
ajst-27525	9	39	(	(	PUNCT
ajst-27525	9	40	bem	bem	PROPN
ajst-27525	9	41	)	)	PUNCT
ajst-27525	9	42	.	.	PUNCT
ajst-27525	10	1	the	the	DET
ajst-27525	10	2	finite	finite	ADJ
ajst-27525	10	3	difference	difference	NOUN
ajst-27525	10	4	and	and	CCONJ
ajst-27525	10	5	finite	finite	ADJ
ajst-27525	10	6	element	element	NOUN
ajst-27525	10	7	methods	method	NOUN
ajst-27525	10	8	primarily	primarily	ADV
ajst-27525	10	9	address	address	VERB
ajst-27525	10	10	pde	pde	NOUN
ajst-27525	10	11	problems	problem	NOUN
ajst-27525	10	12	on	on	ADP
ajst-27525	10	13	bounded	bounded	ADJ
ajst-27525	10	14	domains	domain	NOUN
ajst-27525	10	15	,	,	PUNCT
ajst-27525	10	16	while	while	SCONJ
ajst-27525	10	17	boundary	boundary	ADJ
ajst-27525	10	18	element	element	NOUN
ajst-27525	10	19	methods	method	NOUN
ajst-27525	10	20	are	be	AUX
ajst-27525	10	21	used	use	VERB
ajst-27525	10	22	for	for	ADP
ajst-27525	10	23	unbounded	unbounded	ADJ
ajst-27525	10	24	domains	domain	NOUN
ajst-27525	10	25	.	.	PUNCT
ajst-27525	11	1	however	however	ADV
ajst-27525	11	2	,	,	PUNCT
ajst-27525	11	3	for	for	ADP
ajst-27525	11	4	large	large	ADJ
ajst-27525	11	5	-	-	PUNCT
ajst-27525	11	6	scale	scale	NOUN
ajst-27525	11	7	,	,	PUNCT
ajst-27525	11	8	high	high	ADJ
ajst-27525	11	9	-	-	PUNCT
ajst-27525	11	10	precision	precision	NOUN
ajst-27525	11	11	,	,	PUNCT
ajst-27525	11	12	and	and	CCONJ
ajst-27525	11	13	high	high	ADV
ajst-27525	11	14	-	-	PUNCT
ajst-27525	11	15	dimensional	dimensional	ADJ
ajst-27525	11	16	problems	problem	NOUN
ajst-27525	11	17	,	,	PUNCT
ajst-27525	11	18	these	these	DET
ajst-27525	11	19	grid	grid	NOUN
ajst-27525	11	20	-	-	PUNCT
ajst-27525	11	21	based	base	VERB
ajst-27525	11	22	traditional	traditional	ADJ
ajst-27525	11	23	methods	method	NOUN
ajst-27525	11	24	often	often	ADV
ajst-27525	11	25	demand	demand	VERB
ajst-27525	11	26	substantial	substantial	ADJ
ajst-27525	11	27	memory	memory	NOUN
ajst-27525	11	28	and	and	CCONJ
ajst-27525	11	29	computational	computational	ADJ
ajst-27525	11	30	resources	resource	NOUN
ajst-27525	11	31	.	.	PUNCT
ajst-27525	12	1	with	with	ADP
ajst-27525	12	2	the	the	DET
ajst-27525	12	3	rapid	rapid	ADJ
ajst-27525	12	4	advancement	advancement	NOUN
ajst-27525	12	5	of	of	ADP
ajst-27525	12	6	artificial	artificial	ADJ
ajst-27525	12	7	intelligence	intelligence	NOUN
ajst-27525	12	8	,	,	PUNCT
ajst-27525	12	9	machine	machine	NOUN
ajst-27525	12	10	learning	learning	NOUN
ajst-27525	12	11	is	be	AUX
ajst-27525	12	12	increasingly	increasingly	ADV
ajst-27525	12	13	applied	apply	VERB
ajst-27525	12	14	to	to	ADP
ajst-27525	12	15	reservoir	reservoir	NOUN
ajst-27525	12	16	engineering	engineering	NOUN
ajst-27525	12	17	challenges	challenge	NOUN
ajst-27525	12	18	with	with	ADP
ajst-27525	12	19	complex	complex	ADJ
ajst-27525	12	20	physical	physical	ADJ
ajst-27525	12	21	interpretations	interpretation	NOUN
ajst-27525	12	22	,	,	PUNCT
ajst-27525	12	23	offering	offer	VERB
ajst-27525	12	24	new	new	ADJ
ajst-27525	12	25	approaches	approach	NOUN
ajst-27525	12	26	to	to	PART
ajst-27525	12	27	solve	solve	VERB
ajst-27525	12	28	pdes	pde	NOUN
ajst-27525	12	29	governing	govern	VERB
ajst-27525	12	30	oil	oil	NOUN
ajst-27525	12	31	-	-	PUNCT
ajst-27525	12	32	water	water	NOUN
ajst-27525	12	33	two	two	NUM
ajst-27525	12	34	-	-	PUNCT
ajst-27525	12	35	phase	phase	NOUN
ajst-27525	12	36	flow	flow	NOUN
ajst-27525	12	37	.	.	PUNCT
ajst-27525	13	1	current	current	ADJ
ajst-27525	13	2	mainstream	mainstream	NOUN
ajst-27525	13	3	deep	deep	ADJ
ajst-27525	13	4	learning	learning	NOUN
ajst-27525	13	5	approaches	approach	NOUN
ajst-27525	13	6	for	for	ADP
ajst-27525	13	7	pde	pde	NOUN
ajst-27525	13	8	solutions	solution	NOUN
ajst-27525	13	9	are	be	AUX
ajst-27525	13	10	classified	classify	VERB
ajst-27525	13	11	into	into	ADP
ajst-27525	13	12	data	data	NOUN
ajst-27525	13	13	-	-	PUNCT
ajst-27525	13	14	driven	drive	VERB
ajst-27525	13	15	and	and	CCONJ
ajst-27525	13	16	physics	physics	NOUN
ajst-27525	13	17	-	-	PUNCT
ajst-27525	13	18	constrained	constrain	VERB
ajst-27525	13	19	methods	method	NOUN
ajst-27525	13	20	.	.	PUNCT
ajst-27525	14	1	the	the	DET
ajst-27525	14	2	former	former	ADJ
ajst-27525	14	3	uses	use	VERB
ajst-27525	14	4	deep	deep	ADJ
ajst-27525	14	5	learning	learn	VERB
ajst-27525	14	6	algorithms	algorithm	NOUN
ajst-27525	14	7	to	to	PART
ajst-27525	14	8	train	train	VERB
ajst-27525	14	9	on	on	ADP
ajst-27525	14	10	datasets	dataset	NOUN
ajst-27525	14	11	derived	derive	VERB
ajst-27525	14	12	from	from	ADP
ajst-27525	14	13	numerical	numerical	ADJ
ajst-27525	14	14	simulators	simulator	NOUN
ajst-27525	14	15	,	,	PUNCT
ajst-27525	14	16	implicitly	implicitly	ADV
ajst-27525	14	17	solving	solve	VERB
ajst-27525	14	18	pdes	pde	NOUN
ajst-27525	14	19	.	.	PUNCT
ajst-27525	15	1	however	however	ADV
ajst-27525	15	2	,	,	PUNCT
ajst-27525	15	3	data	data	NOUN
ajst-27525	15	4	-	-	PUNCT
ajst-27525	15	5	driven	drive	VERB
ajst-27525	15	6	methods	method	NOUN
ajst-27525	15	7	often	often	ADV
ajst-27525	15	8	overlook	overlook	VERB
ajst-27525	15	9	the	the	DET
ajst-27525	15	10	underlying	underlying	ADJ
ajst-27525	15	11	physical	physical	ADJ
ajst-27525	15	12	laws	law	NOUN
ajst-27525	15	13	embedded	embed	VERB
ajst-27525	15	14	in	in	ADP
ajst-27525	15	15	the	the	DET
ajst-27525	15	16	data	datum	NOUN
ajst-27525	15	17	,	,	PUNCT
ajst-27525	15	18	resulting	result	VERB
ajst-27525	15	19	in	in	ADP
ajst-27525	15	20	lower	low	ADJ
ajst-27525	15	21	stability	stability	NOUN
ajst-27525	15	22	and	and	CCONJ
ajst-27525	15	23	accuracy	accuracy	NOUN
ajst-27525	15	24	,	,	PUNCT
ajst-27525	15	25	and	and	CCONJ
ajst-27525	15	26	limiting	limit	VERB
ajst-27525	15	27	their	their	PRON
ajst-27525	15	28	capacity	capacity	NOUN
ajst-27525	15	29	for	for	ADP
ajst-27525	15	30	long	long	ADJ
ajst-27525	15	31	-	-	PUNCT
ajst-27525	15	32	term	term	NOUN
ajst-27525	15	33	and	and	CCONJ
ajst-27525	15	34	effective	effective	ADJ
ajst-27525	15	35	predictions	prediction	NOUN
ajst-27525	15	36	.	.	PUNCT
ajst-27525	16	1	physics	physics	NOUN
ajst-27525	16	2	-	-	PUNCT
ajst-27525	16	3	constrained	constrain	VERB
ajst-27525	16	4	methods	method	NOUN
ajst-27525	16	5	,	,	PUNCT
ajst-27525	16	6	on	on	ADP
ajst-27525	16	7	the	the	DET
ajst-27525	16	8	other	other	ADJ
ajst-27525	16	9	hand	hand	NOUN
ajst-27525	16	10	,	,	PUNCT
ajst-27525	16	11	embed	embed	VERB
ajst-27525	16	12	physical	physical	ADJ
ajst-27525	16	13	laws	law	NOUN
ajst-27525	16	14	as	as	ADP
ajst-27525	16	15	regularization	regularization	NOUN
ajst-27525	16	16	terms	term	NOUN
ajst-27525	16	17	within	within	ADP
ajst-27525	16	18	neural	neural	ADJ
ajst-27525	16	19	networks	network	NOUN
ajst-27525	16	20	,	,	PUNCT
ajst-27525	16	21	improving	improve	VERB
ajst-27525	16	22	accuracy	accuracy	NOUN
ajst-27525	16	23	but	but	CCONJ
ajst-27525	16	24	still	still	ADV
ajst-27525	16	25	facing	face	VERB
ajst-27525	16	26	limitations	limitation	NOUN
ajst-27525	16	27	in	in	ADP
ajst-27525	16	28	handling	handle	VERB
ajst-27525	16	29	high	high	ADV
ajst-27525	16	30	-	-	PUNCT
ajst-27525	16	31	dimensional	dimensional	ADJ
ajst-27525	16	32	and	and	CCONJ
ajst-27525	16	33	nonlinear	nonlinear	ADJ
ajst-27525	16	34	equations	equation	NOUN
ajst-27525	16	35	.	.	PUNCT
ajst-27525	17	1	both	both	DET
ajst-27525	17	2	approaches	approach	NOUN
ajst-27525	17	3	predominantly	predominantly	ADV
ajst-27525	17	4	focus	focus	VERB
ajst-27525	17	5	on	on	ADP
ajst-27525	17	6	learning	learn	VERB
ajst-27525	17	7	mappings	mapping	NOUN
ajst-27525	17	8	within	within	ADP
ajst-27525	17	9	finite	finite	ADJ
ajst-27525	17	10	-	-	ADJ
ajst-27525	17	11	dimensional	dimensional	ADJ
ajst-27525	17	12	euclidean	euclidean	ADJ
ajst-27525	17	13	spaces	space	NOUN
ajst-27525	17	14	or	or	CCONJ
ajst-27525	17	15	between	between	SCONJ
ajst-27525	17	16	finite	finite	PROPN
ajst-27525	17	17	sets.neural	sets.neural	PROPN
ajst-27525	17	18	operators	operator	NOUN
ajst-27525	17	19	provide	provide	VERB
ajst-27525	17	20	a	a	DET
ajst-27525	17	21	generalization	generalization	NOUN
ajst-27525	17	22	of	of	ADP
ajst-27525	17	23	neural	neural	ADJ
ajst-27525	17	24	networks	network	NOUN
ajst-27525	17	25	that	that	PRON
ajst-27525	17	26	can	can	AUX
ajst-27525	17	27	learn	learn	VERB
ajst-27525	17	28	mappings	mapping	NOUN
ajst-27525	17	29	between	between	ADP
ajst-27525	17	30	infinitedimensional	infinitedimensional	ADJ
ajst-27525	17	31	function	function	NOUN
ajst-27525	17	32	spaces	space	NOUN
ajst-27525	17	33	,	,	PUNCT
ajst-27525	17	34	formulating	formulate	VERB
ajst-27525	17	35	these	these	DET
ajst-27525	17	36	operators	operator	NOUN
ajst-27525	17	37	as	as	ADP
ajst-27525	17	38	combinations	combination	NOUN
ajst-27525	17	39	of	of	ADP
ajst-27525	17	40	linear	linear	ADJ
ajst-27525	17	41	integral	integral	ADJ
ajst-27525	17	42	operators	operator	NOUN
ajst-27525	17	43	and	and	CCONJ
ajst-27525	17	44	nonlinear	nonlinear	ADJ
ajst-27525	17	45	activation	activation	NOUN
ajst-27525	17	46	functions	function	NOUN
ajst-27525	17	47	,	,	PUNCT
ajst-27525	17	48	which	which	PRON
ajst-27525	17	49	enable	enable	VERB
ajst-27525	17	50	them	they	PRON
ajst-27525	17	51	to	to	PART
ajst-27525	17	52	capture	capture	VERB
ajst-27525	17	53	the	the	DET
ajst-27525	17	54	mapping	mapping	NOUN
ajst-27525	17	55	processes	process	NOUN
ajst-27525	17	56	for	for	ADP
ajst-27525	17	57	pde	pde	NOUN
ajst-27525	17	58	solutions	solution	NOUN
ajst-27525	17	59	.	.	PUNCT
ajst-27525	18	1	among	among	ADP
ajst-27525	18	2	these	these	PRON
ajst-27525	18	3	,	,	PUNCT
ajst-27525	18	4	the	the	DET
ajst-27525	18	5	fourier	fourier	ADJ
ajst-27525	18	6	neural	neural	ADJ
ajst-27525	18	7	operator	operator	NOUN
ajst-27525	18	8	(	(	PUNCT
ajst-27525	18	9	fno	fno	PROPN
ajst-27525	18	10	)	)	PUNCT
ajst-27525	18	11	combines	combine	VERB
ajst-27525	18	12	universal	universal	ADJ
ajst-27525	18	13	approximation	approximation	NOUN
ajst-27525	18	14	capability	capability	NOUN
ajst-27525	18	15	with	with	ADP
ajst-27525	18	16	discretization	discretization	NOUN
ajst-27525	18	17	invariance	invariance	NOUN
ajst-27525	18	18	,	,	PUNCT
ajst-27525	18	19	allowing	allow	VERB
ajst-27525	18	20	it	it	PRON
ajst-27525	18	21	to	to	PART
ajst-27525	18	22	approximate	approximate	VERB
ajst-27525	18	23	any	any	DET
ajst-27525	18	24	given	give	VERB
ajst-27525	18	25	nonlinear	nonlinear	ADJ
ajst-27525	18	26	continuous	continuous	ADJ
ajst-27525	18	27	operator	operator	NOUN
ajst-27525	18	28	and	and	CCONJ
ajst-27525	18	29	to	to	PART
ajst-27525	18	30	share	share	VERB
ajst-27525	18	31	model	model	NOUN
ajst-27525	18	32	parameters	parameter	NOUN
ajst-27525	18	33	across	across	ADP
ajst-27525	18	34	different	different	ADJ
ajst-27525	18	35	discretizations	discretization	NOUN
ajst-27525	18	36	within	within	ADP
ajst-27525	18	37	the	the	DET
ajst-27525	18	38	underlying	underlie	VERB
ajst-27525	18	39	function	function	NOUN
ajst-27525	18	40	space.[1,2	space.[1,2	ADP
ajst-27525	18	41	]	]	X
ajst-27525	19	1	this	this	DET
ajst-27525	19	2	study	study	NOUN
ajst-27525	19	3	focuses	focus	VERB
ajst-27525	19	4	on	on	ADP
ajst-27525	19	5	applying	apply	VERB
ajst-27525	19	6	the	the	DET
ajst-27525	19	7	fourier	fourier	ADJ
ajst-27525	19	8	neural	neural	ADJ
ajst-27525	19	9	operator	operator	NOUN
ajst-27525	19	10	(	(	PUNCT
ajst-27525	19	11	fno	fno	PROPN
ajst-27525	19	12	)	)	PUNCT
ajst-27525	19	13	to	to	ADP
ajst-27525	19	14	the	the	DET
ajst-27525	19	15	oil	oil	NOUN
ajst-27525	19	16	-	-	PUNCT
ajst-27525	19	17	water	water	NOUN
ajst-27525	19	18	two	two	NUM
ajst-27525	19	19	-	-	PUNCT
ajst-27525	19	20	phase	phase	NOUN
ajst-27525	19	21	flow	flow	NOUN
ajst-27525	19	22	equations	equation	NOUN
ajst-27525	19	23	in	in	ADP
ajst-27525	19	24	reservoir	reservoir	PROPN
ajst-27525	19	25	simulation	simulation	PROPN
ajst-27525	19	26	.	.	PUNCT
ajst-27525	20	1	the	the	DET
ajst-27525	20	2	fno	fno	PROPN
ajst-27525	20	3	offers	offer	VERB
ajst-27525	20	4	an	an	DET
ajst-27525	20	5	efficient	efficient	ADJ
ajst-27525	20	6	framework	framework	NOUN
ajst-27525	20	7	for	for	ADP
ajst-27525	20	8	solving	solve	VERB
ajst-27525	20	9	pdes	pde	NOUN
ajst-27525	20	10	,	,	PUNCT
ajst-27525	20	11	overcoming	overcome	VERB
ajst-27525	20	12	the	the	DET
ajst-27525	20	13	limitations	limitation	NOUN
ajst-27525	20	14	of	of	ADP
ajst-27525	20	15	traditional	traditional	ADJ
ajst-27525	20	16	datadriven	datadriven	ADJ
ajst-27525	20	17	and	and	CCONJ
ajst-27525	20	18	physics	physics	NOUN
ajst-27525	20	19	-	-	PUNCT
ajst-27525	20	20	constrained	constrain	VERB
ajst-27525	20	21	methods	method	NOUN
ajst-27525	20	22	while	while	SCONJ
ajst-27525	20	23	combining	combine	VERB
ajst-27525	20	24	the	the	DET
ajst-27525	20	25	advantages	advantage	NOUN
ajst-27525	20	26	of	of	ADP
ajst-27525	20	27	these	these	DET
ajst-27525	20	28	approaches	approach	NOUN
ajst-27525	20	29	.	.	PUNCT
ajst-27525	21	1	specifically	specifically	ADV
ajst-27525	21	2	,	,	PUNCT
ajst-27525	21	3	the	the	DET
ajst-27525	21	4	study	study	NOUN
ajst-27525	21	5	investigates	investigate	VERB
ajst-27525	21	6	the	the	DET
ajst-27525	21	7	applicability	applicability	NOUN
ajst-27525	21	8	of	of	ADP
ajst-27525	21	9	fno	fno	PROPN
ajst-27525	21	10	to	to	PART
ajst-27525	21	11	solve	solve	VERB
ajst-27525	21	12	and	and	CCONJ
ajst-27525	21	13	invert	invert	VERB
ajst-27525	21	14	oilwater	oilwater	ADJ
ajst-27525	21	15	two	two	NUM
ajst-27525	21	16	-	-	PUNCT
ajst-27525	21	17	phase	phase	NOUN
ajst-27525	21	18	flow	flow	NOUN
ajst-27525	21	19	pdes	pde	NOUN
ajst-27525	21	20	,	,	PUNCT
ajst-27525	21	21	analyzing	analyze	VERB
ajst-27525	21	22	the	the	DET
ajst-27525	21	23	impact	impact	NOUN
ajst-27525	21	24	of	of	ADP
ajst-27525	21	25	data	datum	NOUN
ajst-27525	21	26	volume	volume	NOUN
ajst-27525	21	27	,	,	PUNCT
ajst-27525	21	28	hyperparameters	hyperparameter	NOUN
ajst-27525	21	29	,	,	PUNCT
ajst-27525	21	30	and	and	CCONJ
ajst-27525	21	31	other	other	ADJ
ajst-27525	21	32	factors	factor	NOUN
ajst-27525	21	33	on	on	ADP
ajst-27525	21	34	the	the	DET
ajst-27525	21	35	solution	solution	NOUN
ajst-27525	21	36	process	process	NOUN
ajst-27525	21	37	.	.	PUNCT
ajst-27525	22	1	this	this	DET
ajst-27525	22	2	research	research	NOUN
ajst-27525	22	3	provides	provide	VERB
ajst-27525	22	4	a	a	DET
ajst-27525	22	5	feasibility	feasibility	NOUN
ajst-27525	22	6	study	study	NOUN
ajst-27525	22	7	of	of	ADP
ajst-27525	22	8	fno	fno	PROPN
ajst-27525	22	9	’s	’s	PART
ajst-27525	22	10	potential	potential	NOUN
ajst-27525	22	11	to	to	PART
ajst-27525	22	12	solve	solve	VERB
ajst-27525	22	13	oil	oil	NOUN
ajst-27525	22	14	-	-	PUNCT
ajst-27525	22	15	water	water	NOUN
ajst-27525	22	16	two	two	NUM
ajst-27525	22	17	-	-	PUNCT
ajst-27525	22	18	phase	phase	NOUN
ajst-27525	22	19	pdes	pde	NOUN
ajst-27525	22	20	and	and	CCONJ
ajst-27525	22	21	their	their	PRON
ajst-27525	22	22	inversion	inversion	NOUN
ajst-27525	22	23	problems	problem	NOUN
ajst-27525	22	24	effectively	effectively	ADV
ajst-27525	22	25	.	.	PUNCT
ajst-27525	23	1	2	2	X
ajst-27525	23	2	.	.	X
ajst-27525	23	3	current	current	ADJ
ajst-27525	23	4	research	research	NOUN
ajst-27525	23	5	status	status	NOUN
ajst-27525	23	6	of	of	ADP
ajst-27525	23	7	solving	solve	VERB
ajst-27525	23	8	partial	partial	ADJ
ajst-27525	23	9	differential	differential	ADJ
ajst-27525	23	10	equations	equation	NOUN
ajst-27525	23	11	with	with	ADP
ajst-27525	23	12	neural	neural	ADJ
ajst-27525	23	13	networks	network	NOUN
ajst-27525	23	14	traditional	traditional	ADJ
ajst-27525	23	15	methods	method	NOUN
ajst-27525	23	16	for	for	ADP
ajst-27525	23	17	solving	solve	VERB
ajst-27525	23	18	partial	partial	ADJ
ajst-27525	23	19	differential	differential	ADJ
ajst-27525	23	20	equations	equation	NOUN
ajst-27525	23	21	(	(	PUNCT
ajst-27525	23	22	pdes	pde	NOUN
ajst-27525	23	23	)	)	PUNCT
ajst-27525	23	24	require	require	VERB
ajst-27525	23	25	grid	grid	NOUN
ajst-27525	23	26	discretization	discretization	NOUN
ajst-27525	23	27	and	and	CCONJ
ajst-27525	23	28	nonlinear	nonlinear	ADJ
ajst-27525	23	29	equation	equation	NOUN
ajst-27525	23	30	solving	solving	NOUN
ajst-27525	23	31	,	,	PUNCT
ajst-27525	23	32	making	make	VERB
ajst-27525	23	33	the	the	DET
ajst-27525	23	34	process	process	NOUN
ajst-27525	23	35	technically	technically	ADV
ajst-27525	23	36	challenging	challenging	ADJ
ajst-27525	23	37	,	,	PUNCT
ajst-27525	23	38	computationally	computationally	ADV
ajst-27525	23	39	expensive	expensive	ADJ
ajst-27525	23	40	,	,	PUNCT
ajst-27525	23	41	and	and	CCONJ
ajst-27525	23	42	often	often	ADV
ajst-27525	23	43	unsuitable	unsuitable	ADJ
ajst-27525	23	44	for	for	ADP
ajst-27525	23	45	solving	solve	VERB
ajst-27525	23	46	inverse	inverse	NOUN
ajst-27525	23	47	problems	problem	NOUN
ajst-27525	23	48	.	.	PUNCT
ajst-27525	24	1	deep	deep	ADJ
ajst-27525	24	2	learning	learning	NOUN
ajst-27525	24	3	-	-	PUNCT
ajst-27525	24	4	based	base	VERB
ajst-27525	24	5	methods	method	NOUN
ajst-27525	24	6	for	for	ADP
ajst-27525	24	7	pdes	pde	NOUN
ajst-27525	24	8	can	can	AUX
ajst-27525	24	9	perform	perform	VERB
ajst-27525	24	10	automatic	automatic	ADJ
ajst-27525	24	11	differentiation	differentiation	NOUN
ajst-27525	24	12	in	in	ADP
ajst-27525	24	13	both	both	DET
ajst-27525	24	14	time	time	NOUN
ajst-27525	24	15	and	and	CCONJ
ajst-27525	24	16	space	space	NOUN
ajst-27525	24	17	,	,	PUNCT
ajst-27525	24	18	effectively	effectively	ADV
ajst-27525	24	19	addressing	address	VERB
ajst-27525	24	20	nonlinear	nonlinear	ADJ
ajst-27525	24	21	problems	problem	NOUN
ajst-27525	24	22	and	and	CCONJ
ajst-27525	24	23	enabling	enable	VERB
ajst-27525	24	24	solutions	solution	NOUN
ajst-27525	24	25	for	for	ADP
ajst-27525	24	26	more	more	ADV
ajst-27525	24	27	complex	complex	ADJ
ajst-27525	24	28	,	,	PUNCT
ajst-27525	24	29	higher	higher	ADV
ajst-27525	24	30	-	-	PUNCT
ajst-27525	24	31	dimensional	dimensional	ADJ
ajst-27525	24	32	pdes	pde	NOUN
ajst-27525	24	33	.	.	PUNCT
ajst-27525	25	1	at	at	ADP
ajst-27525	25	2	present	present	ADJ
ajst-27525	25	3	,	,	PUNCT
ajst-27525	25	4	mainstream	mainstream	ADJ
ajst-27525	25	5	neural	neural	ADJ
ajst-27525	25	6	network	network	NOUN
ajst-27525	25	7	-	-	PUNCT
ajst-27525	25	8	based	base	VERB
ajst-27525	25	9	pde	pde	NOUN
ajst-27525	25	10	-	-	PUNCT
ajst-27525	25	11	solving	solve	VERB
ajst-27525	25	12	approaches	approach	NOUN
ajst-27525	25	13	include	include	VERB
ajst-27525	25	14	data	datum	NOUN
ajst-27525	25	15	-	-	PUNCT
ajst-27525	25	16	driven	drive	VERB
ajst-27525	25	17	,	,	PUNCT
ajst-27525	25	18	physics	physics	NOUN
ajst-27525	25	19	-	-	PUNCT
ajst-27525	25	20	informed	inform	VERB
ajst-27525	25	21	,	,	PUNCT
ajst-27525	25	22	and	and	CCONJ
ajst-27525	25	23	neural	neural	ADJ
ajst-27525	25	24	operator	operator	NOUN
ajst-27525	25	25	methods	method	NOUN
ajst-27525	25	26	.	.	PUNCT
ajst-27525	26	1	the	the	DET
ajst-27525	26	2	data	data	NOUN
ajst-27525	26	3	-	-	PUNCT
ajst-27525	26	4	driven	drive	VERB
ajst-27525	26	5	approach	approach	NOUN
ajst-27525	26	6	relies	rely	VERB
ajst-27525	26	7	solely	solely	ADV
ajst-27525	26	8	on	on	ADP
ajst-27525	26	9	labeled	label	VERB
ajst-27525	26	10	data	data	NOUN
ajst-27525	26	11	constraints	constraint	NOUN
ajst-27525	26	12	,	,	PUNCT
ajst-27525	26	13	while	while	SCONJ
ajst-27525	26	14	the	the	DET
ajst-27525	26	15	physics	physics	NOUN
ajst-27525	26	16	-	-	PUNCT
ajst-27525	26	17	informed	inform	VERB
ajst-27525	26	18	approach	approach	NOUN
ajst-27525	26	19	combines	combine	VERB
ajst-27525	26	20	constraints	constraint	NOUN
ajst-27525	26	21	from	from	ADP
ajst-27525	26	22	labeled	label	VERB
ajst-27525	26	23	data	datum	NOUN
ajst-27525	26	24	with	with	ADP
ajst-27525	26	25	those	those	PRON
ajst-27525	26	26	from	from	ADP
ajst-27525	26	27	pdes	pde	NOUN
ajst-27525	26	28	.	.	PUNCT
ajst-27525	27	1	the	the	DET
ajst-27525	27	2	following	follow	VERB
ajst-27525	27	3	sections	section	NOUN
ajst-27525	27	4	provide	provide	VERB
ajst-27525	27	5	a	a	DET
ajst-27525	27	6	brief	brief	ADJ
ajst-27525	27	7	overview	overview	NOUN
ajst-27525	27	8	of	of	ADP
ajst-27525	27	9	datadriven	datadriven	ADJ
ajst-27525	27	10	and	and	CCONJ
ajst-27525	27	11	physics	physics	NOUN
ajst-27525	27	12	-	-	PUNCT
ajst-27525	27	13	informed	inform	VERB
ajst-27525	27	14	methods	method	NOUN
ajst-27525	27	15	,	,	PUNCT
ajst-27525	27	16	as	as	ADV
ajst-27525	27	17	well	well	ADV
ajst-27525	27	18	as	as	ADP
ajst-27525	27	19	the	the	DET
ajst-27525	27	20	fourier	fourier	ADJ
ajst-27525	27	21	neural	neural	ADJ
ajst-27525	27	22	operator	operator	NOUN
ajst-27525	27	23	(	(	PUNCT
ajst-27525	27	24	fno	fno	PROPN
ajst-27525	27	25	)	)	PUNCT
ajst-27525	27	26	and	and	CCONJ
ajst-27525	27	27	its	its	PRON
ajst-27525	27	28	derivatives	derivative	NOUN
ajst-27525	27	29	.	.	PUNCT
ajst-27525	28	1	183	183	NUM
ajst-27525	28	2	2.1	2.1	NUM
ajst-27525	28	3	.	.	PUNCT
ajst-27525	29	1	data	data	NOUN
ajst-27525	29	2	-	-	PUNCT
ajst-27525	29	3	driven	drive	VERB
ajst-27525	29	4	and	and	CCONJ
ajst-27525	29	5	physics	physics	NOUN
ajst-27525	29	6	-	-	PUNCT
ajst-27525	29	7	informed	inform	VERB
ajst-27525	29	8	methods	method	NOUN
ajst-27525	29	9	in	in	ADP
ajst-27525	29	10	1943	1943	NUM
ajst-27525	29	11	,	,	PUNCT
ajst-27525	29	12	mcculloch	mcculloch	NOUN
ajst-27525	29	13	and	and	CCONJ
ajst-27525	29	14	pitts	pitt	NOUN
ajst-27525	29	15	[	[	X
ajst-27525	29	16	4	4	NUM
ajst-27525	29	17	]	]	PUNCT
ajst-27525	29	18	introduced	introduce	VERB
ajst-27525	29	19	artificial	artificial	ADJ
ajst-27525	29	20	neural	neural	ADJ
ajst-27525	29	21	networks	network	NOUN
ajst-27525	29	22	and	and	CCONJ
ajst-27525	29	23	their	their	PRON
ajst-27525	29	24	mathematical	mathematical	ADJ
ajst-27525	29	25	models	model	NOUN
ajst-27525	29	26	,	,	PUNCT
ajst-27525	29	27	marking	mark	VERB
ajst-27525	29	28	the	the	DET
ajst-27525	29	29	beginning	beginning	NOUN
ajst-27525	29	30	of	of	ADP
ajst-27525	29	31	neural	neural	ADJ
ajst-27525	29	32	network	network	NOUN
ajst-27525	29	33	research	research	NOUN
ajst-27525	29	34	.	.	PUNCT
ajst-27525	30	1	since	since	SCONJ
ajst-27525	30	2	neural	neural	ADJ
ajst-27525	30	3	networks	network	NOUN
ajst-27525	30	4	essentially	essentially	ADV
ajst-27525	30	5	map	map	VERB
ajst-27525	30	6	inputs	input	NOUN
ajst-27525	30	7	to	to	ADP
ajst-27525	30	8	outputs	output	NOUN
ajst-27525	30	9	via	via	ADP
ajst-27525	30	10	composite	composite	ADJ
ajst-27525	30	11	functions	function	NOUN
ajst-27525	30	12	,	,	PUNCT
ajst-27525	30	13	they	they	PRON
ajst-27525	30	14	can	can	AUX
ajst-27525	30	15	be	be	AUX
ajst-27525	30	16	used	use	VERB
ajst-27525	30	17	to	to	PART
ajst-27525	30	18	approximate	approximate	VERB
ajst-27525	30	19	continuous	continuous	ADJ
ajst-27525	30	20	nonlinear	nonlinear	ADJ
ajst-27525	30	21	functions	function	NOUN
ajst-27525	30	22	.	.	PUNCT
ajst-27525	31	1	automatic	automatic	ADJ
ajst-27525	31	2	differentiation	differentiation	NOUN
ajst-27525	31	3	in	in	ADP
ajst-27525	31	4	artificial	artificial	ADJ
ajst-27525	31	5	neural	neural	ADJ
ajst-27525	31	6	networks	network	NOUN
ajst-27525	31	7	,	,	PUNCT
ajst-27525	31	8	which	which	PRON
ajst-27525	31	9	computes	compute	VERB
ajst-27525	31	10	derivatives	derivative	NOUN
ajst-27525	31	11	precisely	precisely	ADV
ajst-27525	31	12	using	use	VERB
ajst-27525	31	13	the	the	DET
ajst-27525	31	14	chain	chain	NOUN
ajst-27525	31	15	rule	rule	NOUN
ajst-27525	31	16	,	,	PUNCT
ajst-27525	31	17	can	can	AUX
ajst-27525	31	18	replace	replace	VERB
ajst-27525	31	19	complex	complex	ADJ
ajst-27525	31	20	gradient	gradient	ADJ
ajst-27525	31	21	calculations	calculation	NOUN
ajst-27525	31	22	in	in	ADP
ajst-27525	31	23	pdes	pde	NOUN
ajst-27525	31	24	.	.	PUNCT
ajst-27525	32	1	in	in	ADP
ajst-27525	32	2	1986	1986	NUM
ajst-27525	32	3	,	,	PUNCT
ajst-27525	32	4	rumelhart	rumelhart	PROPN
ajst-27525	32	5	et	et	PROPN
ajst-27525	32	6	al	al	PROPN
ajst-27525	32	7	.	.	PROPN
ajst-27525	32	8	introduced	introduce	VERB
ajst-27525	32	9	the	the	DET
ajst-27525	32	10	backpropagation	backpropagation	NOUN
ajst-27525	32	11	algorithm	algorithm	NOUN
ajst-27525	32	12	,	,	PUNCT
ajst-27525	32	13	laying	lay	VERB
ajst-27525	32	14	the	the	DET
ajst-27525	32	15	groundwork	groundwork	NOUN
ajst-27525	32	16	for	for	ADP
ajst-27525	32	17	neural	neural	ADJ
ajst-27525	32	18	networks	network	NOUN
ajst-27525	32	19	in	in	ADP
ajst-27525	32	20	solving	solve	VERB
ajst-27525	32	21	pdes	pde	NOUN
ajst-27525	32	22	.	.	PUNCT
ajst-27525	33	1	wornik	wornik	PROPN
ajst-27525	33	2	et	et	PROPN
ajst-27525	33	3	al	al	PROPN
ajst-27525	33	4	.	.	PUNCT
ajst-27525	34	1	[	[	X
ajst-27525	34	2	7	7	X
ajst-27525	34	3	]	]	PUNCT
ajst-27525	34	4	demonstrated	demonstrate	VERB
ajst-27525	34	5	in	in	ADP
ajst-27525	34	6	1990	1990	NUM
ajst-27525	34	7	that	that	SCONJ
ajst-27525	34	8	multilayer	multilayer	ADJ
ajst-27525	34	9	neural	neural	ADJ
ajst-27525	34	10	networks	network	NOUN
ajst-27525	34	11	could	could	AUX
ajst-27525	34	12	approximate	approximate	VERB
ajst-27525	34	13	any	any	DET
ajst-27525	34	14	function	function	NOUN
ajst-27525	34	15	and	and	CCONJ
ajst-27525	34	16	its	its	PRON
ajst-27525	34	17	derivatives	derivative	NOUN
ajst-27525	34	18	,	,	PUNCT
ajst-27525	34	19	providing	provide	VERB
ajst-27525	34	20	theoretical	theoretical	ADJ
ajst-27525	34	21	support	support	NOUN
ajst-27525	34	22	for	for	ADP
ajst-27525	34	23	neural	neural	ADJ
ajst-27525	34	24	networks	network	NOUN
ajst-27525	34	25	in	in	ADP
ajst-27525	34	26	solving	solve	VERB
ajst-27525	34	27	differential	differential	ADJ
ajst-27525	34	28	equations	equation	NOUN
ajst-27525	34	29	.	.	PUNCT
ajst-27525	35	1	in	in	ADP
ajst-27525	35	2	1994	1994	NUM
ajst-27525	35	3	,	,	PUNCT
ajst-27525	35	4	meade	meade	PROPN
ajst-27525	35	5	et	et	PROPN
ajst-27525	35	6	al	al	PROPN
ajst-27525	35	7	.	.	PROPN
ajst-27525	35	8	introduced	introduce	VERB
ajst-27525	35	9	differential	differential	ADJ
ajst-27525	35	10	equations	equation	NOUN
ajst-27525	35	11	,	,	PUNCT
ajst-27525	35	12	initial	initial	ADJ
ajst-27525	35	13	conditions	condition	NOUN
ajst-27525	35	14	,	,	PUNCT
ajst-27525	35	15	and	and	CCONJ
ajst-27525	35	16	boundary	boundary	ADJ
ajst-27525	35	17	conditions	condition	NOUN
ajst-27525	35	18	into	into	ADP
ajst-27525	35	19	the	the	DET
ajst-27525	35	20	loss	loss	NOUN
ajst-27525	35	21	function	function	NOUN
ajst-27525	35	22	to	to	PART
ajst-27525	35	23	minimize	minimize	VERB
ajst-27525	35	24	residuals	residual	NOUN
ajst-27525	35	25	,	,	PUNCT
ajst-27525	35	26	enabling	enable	VERB
ajst-27525	35	27	approximate	approximate	ADJ
ajst-27525	35	28	solutions	solution	NOUN
ajst-27525	35	29	to	to	ADP
ajst-27525	35	30	equations	equation	NOUN
ajst-27525	35	31	.	.	PUNCT
ajst-27525	36	1	in	in	ADP
ajst-27525	36	2	1996	1996	NUM
ajst-27525	36	3	,	,	PUNCT
ajst-27525	36	4	li	li	PROPN
ajst-27525	37	1	[	[	X
ajst-27525	37	2	8	8	NUM
ajst-27525	37	3	]	]	PUNCT
ajst-27525	37	4	demonstrated	demonstrate	VERB
ajst-27525	37	5	that	that	SCONJ
ajst-27525	37	6	hidden	hide	VERB
ajst-27525	37	7	layers	layer	NOUN
ajst-27525	37	8	in	in	ADP
ajst-27525	37	9	neural	neural	ADJ
ajst-27525	37	10	networks	network	NOUN
ajst-27525	37	11	could	could	AUX
ajst-27525	37	12	approximate	approximate	VERB
ajst-27525	37	13	multivariate	multivariate	NOUN
ajst-27525	37	14	polynomials	polynomial	NOUN
ajst-27525	37	15	and	and	CCONJ
ajst-27525	37	16	their	their	PRON
ajst-27525	37	17	derivatives	derivative	NOUN
ajst-27525	37	18	;	;	PUNCT
ajst-27525	37	19	further	far	ADV
ajst-27525	37	20	,	,	PUNCT
ajst-27525	37	21	in	in	ADP
ajst-27525	37	22	1998	1998	NUM
ajst-27525	37	23	,	,	PUNCT
ajst-27525	37	24	lagaris	lagaris	PROPN
ajst-27525	37	25	et	et	PROPN
ajst-27525	37	26	al	al	PROPN
ajst-27525	37	27	.	.	PUNCT
ajst-27525	38	1	[	[	X
ajst-27525	38	2	9	9	NUM
ajst-27525	38	3	]	]	PUNCT
ajst-27525	38	4	independently	independently	ADV
ajst-27525	38	5	represented	represent	VERB
ajst-27525	38	6	initial	initial	ADJ
ajst-27525	38	7	and	and	CCONJ
ajst-27525	38	8	boundary	boundary	ADJ
ajst-27525	38	9	conditions	condition	NOUN
ajst-27525	38	10	,	,	PUNCT
ajst-27525	38	11	opening	open	VERB
ajst-27525	38	12	new	new	ADJ
ajst-27525	38	13	avenues	avenue	NOUN
ajst-27525	38	14	for	for	ADP
ajst-27525	38	15	solving	solve	VERB
ajst-27525	38	16	pdes	pde	NOUN
ajst-27525	38	17	.	.	PUNCT
ajst-27525	39	1	in	in	ADP
ajst-27525	39	2	2001	2001	NUM
ajst-27525	39	3	,	,	PUNCT
ajst-27525	39	4	aarts	aart	NOUN
ajst-27525	39	5	and	and	CCONJ
ajst-27525	39	6	van	van	PROPN
ajst-27525	39	7	[	[	X
ajst-27525	39	8	10	10	NUM
ajst-27525	39	9	]	]	PUNCT
ajst-27525	39	10	used	use	VERB
ajst-27525	39	11	single	single	ADJ
ajst-27525	39	12	-	-	PUNCT
ajst-27525	39	13	hidden	hide	VERB
ajst-27525	39	14	-	-	PUNCT
ajst-27525	39	15	layer	layer	NOUN
ajst-27525	39	16	feedforward	feedforward	NOUN
ajst-27525	39	17	networks	network	NOUN
ajst-27525	39	18	to	to	PART
ajst-27525	39	19	represent	represent	VERB
ajst-27525	39	20	differential	differential	ADJ
ajst-27525	39	21	operators	operator	NOUN
ajst-27525	39	22	of	of	ADP
ajst-27525	39	23	different	different	ADJ
ajst-27525	39	24	orders	order	NOUN
ajst-27525	39	25	for	for	ADP
ajst-27525	39	26	training	train	VERB
ajst-27525	39	27	pde	pde	NOUN
ajst-27525	39	28	solutions	solution	NOUN
ajst-27525	39	29	,	,	PUNCT
ajst-27525	39	30	while	while	SCONJ
ajst-27525	39	31	in	in	ADP
ajst-27525	39	32	2005	2005	NUM
ajst-27525	39	33	,	,	PUNCT
ajst-27525	39	34	ramuhalli	ramuhalli	VERB
ajst-27525	39	35	et	et	PROPN
ajst-27525	39	36	al	al	PROPN
ajst-27525	39	37	.	.	PUNCT
ajst-27525	40	1	[	[	X
ajst-27525	40	2	11	11	NUM
ajst-27525	40	3	]	]	PUNCT
ajst-27525	40	4	combined	combine	VERB
ajst-27525	40	5	finite	finite	PROPN
ajst-27525	40	6	element	element	NOUN
ajst-27525	40	7	modules	module	NOUN
ajst-27525	40	8	with	with	ADP
ajst-27525	40	9	neural	neural	ADJ
ajst-27525	40	10	networks	network	NOUN
ajst-27525	40	11	,	,	PUNCT
ajst-27525	40	12	introducing	introduce	VERB
ajst-27525	40	13	the	the	DET
ajst-27525	40	14	finite	finite	ADJ
ajst-27525	40	15	element	element	NOUN
ajst-27525	40	16	neural	neural	ADJ
ajst-27525	40	17	network	network	NOUN
ajst-27525	40	18	.	.	PUNCT
ajst-27525	41	1	due	due	ADP
ajst-27525	41	2	to	to	ADP
ajst-27525	41	3	the	the	DET
ajst-27525	41	4	limitations	limitation	NOUN
ajst-27525	41	5	of	of	ADP
ajst-27525	41	6	early	early	ADJ
ajst-27525	41	7	multilayer	multilayer	NOUN
ajst-27525	41	8	fully	fully	ADV
ajst-27525	41	9	connected	connect	VERB
ajst-27525	41	10	neural	neural	ADJ
ajst-27525	41	11	networks	network	NOUN
ajst-27525	41	12	,	,	PUNCT
ajst-27525	41	13	which	which	PRON
ajst-27525	41	14	could	could	AUX
ajst-27525	41	15	only	only	ADV
ajst-27525	41	16	solve	solve	VERB
ajst-27525	41	17	simple	simple	ADJ
ajst-27525	41	18	equations	equation	NOUN
ajst-27525	41	19	,	,	PUNCT
ajst-27525	41	20	neural	neural	ADJ
ajst-27525	41	21	network	network	NOUN
ajst-27525	41	22	methods	method	NOUN
ajst-27525	41	23	for	for	ADP
ajst-27525	41	24	pde	pde	NOUN
ajst-27525	41	25	solutions	solution	NOUN
ajst-27525	41	26	did	do	AUX
ajst-27525	41	27	not	not	PART
ajst-27525	41	28	gain	gain	VERB
ajst-27525	41	29	significant	significant	ADJ
ajst-27525	41	30	attention	attention	NOUN
ajst-27525	41	31	.	.	PUNCT
ajst-27525	42	1	in	in	ADP
ajst-27525	42	2	2018	2018	NUM
ajst-27525	42	3	,	,	PUNCT
ajst-27525	42	4	long	long	ADV
ajst-27525	42	5	et	et	PROPN
ajst-27525	42	6	al	al	PROPN
ajst-27525	42	7	.	.	PUNCT
ajst-27525	43	1	[	[	X
ajst-27525	43	2	3	3	X
ajst-27525	43	3	]	]	PUNCT
ajst-27525	43	4	proposed	propose	VERB
ajst-27525	43	5	a	a	DET
ajst-27525	43	6	data	data	NOUN
ajst-27525	43	7	-	-	PUNCT
ajst-27525	43	8	driven	drive	VERB
ajst-27525	43	9	neural	neural	ADJ
ajst-27525	43	10	network	network	NOUN
ajst-27525	43	11	(	(	PUNCT
ajst-27525	43	12	pde	pde	NOUN
ajst-27525	43	13	-	-	PUNCT
ajst-27525	43	14	net	net	NOUN
ajst-27525	43	15	)	)	PUNCT
ajst-27525	43	16	,	,	PUNCT
ajst-27525	43	17	introducing	introduce	VERB
ajst-27525	43	18	euler	euler	NOUN
ajst-27525	43	19	discretization	discretization	NOUN
ajst-27525	43	20	for	for	ADP
ajst-27525	43	21	time	time	NOUN
ajst-27525	43	22	derivatives	derivative	NOUN
ajst-27525	43	23	and	and	CCONJ
ajst-27525	43	24	approximating	approximate	VERB
ajst-27525	43	25	differential	differential	ADJ
ajst-27525	43	26	operators	operator	NOUN
ajst-27525	43	27	as	as	ADP
ajst-27525	43	28	constrained	constrain	VERB
ajst-27525	43	29	convolution	convolution	NOUN
ajst-27525	43	30	kernels	kernel	NOUN
ajst-27525	43	31	,	,	PUNCT
ajst-27525	43	32	allowing	allow	VERB
ajst-27525	43	33	the	the	DET
ajst-27525	43	34	neural	neural	ADJ
ajst-27525	43	35	network	network	NOUN
ajst-27525	43	36	to	to	ADP
ajst-27525	43	37	better	well	ADJ
ajst-27525	43	38	approximate	approximate	ADJ
ajst-27525	43	39	pdes	pde	NOUN
ajst-27525	43	40	.	.	PUNCT
ajst-27525	44	1	zha	zha	NOUN
ajst-27525	44	2	et	et	NOUN
ajst-27525	44	3	al	al	PROPN
ajst-27525	44	4	.	.	PUNCT
ajst-27525	45	1	[	[	X
ajst-27525	45	2	12	12	NUM
ajst-27525	45	3	]	]	PUNCT
ajst-27525	45	4	extended	extend	VERB
ajst-27525	45	5	the	the	DET
ajst-27525	45	6	constrained	constrain	VERB
ajst-27525	45	7	convolution	convolution	NOUN
ajst-27525	45	8	kernels	kernel	NOUN
ajst-27525	45	9	to	to	ADP
ajst-27525	45	10	three	three	NUM
ajst-27525	45	11	dimensions	dimension	NOUN
ajst-27525	45	12	,	,	PUNCT
ajst-27525	45	13	and	and	CCONJ
ajst-27525	45	14	liu	liu	PROPN
ajst-27525	45	15	et	et	PROPN
ajst-27525	45	16	al	al	PROPN
ajst-27525	45	17	.	.	PUNCT
ajst-27525	46	1	[	[	X
ajst-27525	46	2	13	13	NUM
ajst-27525	46	3	]	]	PUNCT
ajst-27525	46	4	proposed	propose	VERB
ajst-27525	46	5	a	a	DET
ajst-27525	46	6	universal	universal	ADJ
ajst-27525	46	7	differential	differential	ADJ
ajst-27525	46	8	equation	equation	NOUN
ajst-27525	46	9	solver	solver	ADV
ajst-27525	46	10	based	base	VERB
ajst-27525	46	11	on	on	ADP
ajst-27525	46	12	fully	fully	ADV
ajst-27525	46	13	connected	connect	VERB
ajst-27525	46	14	neural	neural	ADJ
ajst-27525	46	15	networks	network	NOUN
ajst-27525	46	16	for	for	ADP
ajst-27525	46	17	solving	solve	VERB
ajst-27525	46	18	initialboundary	initialboundary	ADJ
ajst-27525	46	19	value	value	NOUN
ajst-27525	46	20	problems	problem	NOUN
ajst-27525	46	21	.	.	PUNCT
ajst-27525	47	1	addressing	address	VERB
ajst-27525	47	2	high	high	ADJ
ajst-27525	47	3	-	-	PUNCT
ajst-27525	47	4	dimensional	dimensional	ADJ
ajst-27525	47	5	pdes	pde	NOUN
ajst-27525	47	6	in	in	ADP
ajst-27525	47	7	data	data	NOUN
ajst-27525	47	8	-	-	PUNCT
ajst-27525	47	9	driven	drive	VERB
ajst-27525	47	10	settings	setting	NOUN
ajst-27525	47	11	,	,	PUNCT
ajst-27525	47	12	han	han	PROPN
ajst-27525	47	13	and	and	CCONJ
ajst-27525	47	14	jentzen	jentzen	PROPN
ajst-27525	47	15	et	et	PROPN
ajst-27525	47	16	al	al	PROPN
ajst-27525	47	17	.	.	PUNCT
ajst-27525	48	1	[	[	X
ajst-27525	48	2	14,15	14,15	NUM
ajst-27525	48	3	]	]	PUNCT
ajst-27525	48	4	developed	develop	VERB
ajst-27525	48	5	a	a	DET
ajst-27525	48	6	deep	deep	ADJ
ajst-27525	48	7	learning	learning	NOUN
ajst-27525	48	8	-	-	PUNCT
ajst-27525	48	9	based	base	VERB
ajst-27525	48	10	solver	solver	NOUN
ajst-27525	48	11	for	for	ADP
ajst-27525	48	12	parabolic	parabolic	ADJ
ajst-27525	48	13	pdes	pde	NOUN
ajst-27525	48	14	by	by	ADP
ajst-27525	48	15	approximating	approximate	VERB
ajst-27525	48	16	gradient	gradient	ADJ
ajst-27525	48	17	operators	operator	NOUN
ajst-27525	48	18	.	.	PUNCT
ajst-27525	49	1	recently	recently	ADV
ajst-27525	49	2	,	,	PUNCT
ajst-27525	49	3	sirignano	sirignano	PROPN
ajst-27525	49	4	et	et	PROPN
ajst-27525	49	5	al	al	PROPN
ajst-27525	49	6	.	.	PUNCT
ajst-27525	50	1	[	[	X
ajst-27525	50	2	16	16	NUM
ajst-27525	50	3	]	]	PUNCT
ajst-27525	50	4	proposed	propose	VERB
ajst-27525	50	5	the	the	DET
ajst-27525	50	6	deep	deep	ADJ
ajst-27525	50	7	galerkin	galerkin	ADJ
ajst-27525	50	8	method	method	NOUN
ajst-27525	50	9	(	(	PUNCT
ajst-27525	50	10	dgm	dgm	PROPN
ajst-27525	50	11	)	)	PUNCT
ajst-27525	50	12	,	,	PUNCT
ajst-27525	50	13	a	a	DET
ajst-27525	50	14	physics	physics	NOUN
ajst-27525	50	15	-	-	PUNCT
ajst-27525	50	16	informed	inform	VERB
ajst-27525	50	17	neural	neural	ADJ
ajst-27525	50	18	network	network	NOUN
ajst-27525	50	19	fundamentally	fundamentally	ADV
ajst-27525	50	20	based	base	VERB
ajst-27525	50	21	on	on	ADP
ajst-27525	50	22	the	the	DET
ajst-27525	50	23	galerkin	galerkin	ADJ
ajst-27525	50	24	method	method	NOUN
ajst-27525	50	25	for	for	ADP
ajst-27525	50	26	second	second	ADJ
ajst-27525	50	27	-	-	PUNCT
ajst-27525	50	28	order	order	NOUN
ajst-27525	50	29	differential	differential	NOUN
ajst-27525	50	30	operator	operator	NOUN
ajst-27525	50	31	computations	computation	NOUN
ajst-27525	50	32	.	.	PUNCT
ajst-27525	51	1	kani	kani	PROPN
ajst-27525	51	2	et	et	PROPN
ajst-27525	51	3	al	al	PROPN
ajst-27525	51	4	.	.	PUNCT
ajst-27525	52	1	[	[	X
ajst-27525	52	2	17	17	NUM
ajst-27525	52	3	]	]	PUNCT
ajst-27525	52	4	integrated	integrated	ADJ
ajst-27525	52	5	physics	physics	NOUN
ajst-27525	52	6	-	-	PUNCT
ajst-27525	52	7	informed	inform	VERB
ajst-27525	52	8	constraints	constraint	NOUN
ajst-27525	52	9	with	with	ADP
ajst-27525	52	10	deep	deep	ADJ
ajst-27525	52	11	residual	residual	ADJ
ajst-27525	52	12	recurrent	recurrent	ADJ
ajst-27525	52	13	neural	neural	ADJ
ajst-27525	52	14	networks	network	NOUN
ajst-27525	52	15	,	,	PUNCT
ajst-27525	52	16	introducing	introduce	VERB
ajst-27525	52	17	orthogonal	orthogonal	ADJ
ajst-27525	52	18	decomposition	decomposition	NOUN
ajst-27525	52	19	and	and	CCONJ
ajst-27525	52	20	discrete	discrete	ADJ
ajst-27525	52	21	empirical	empirical	ADJ
ajst-27525	52	22	interpolation	interpolation	NOUN
ajst-27525	52	23	methods	method	NOUN
ajst-27525	52	24	to	to	PART
ajst-27525	52	25	optimize	optimize	VERB
ajst-27525	52	26	computational	computational	ADJ
ajst-27525	52	27	complexity	complexity	NOUN
ajst-27525	52	28	in	in	ADP
ajst-27525	52	29	high	high	ADJ
ajst-27525	52	30	-	-	PUNCT
ajst-27525	52	31	fidelity	fidelity	NOUN
ajst-27525	52	32	numerical	numerical	ADJ
ajst-27525	52	33	simulations	simulation	NOUN
ajst-27525	52	34	.	.	PUNCT
ajst-27525	53	1	in	in	ADP
ajst-27525	53	2	2019	2019	NUM
ajst-27525	53	3	,	,	PUNCT
ajst-27525	53	4	raissi	raissi	ADJ
ajst-27525	53	5	et	et	PROPN
ajst-27525	53	6	al	al	PROPN
ajst-27525	53	7	.	.	PUNCT
ajst-27525	54	1	[	[	X
ajst-27525	54	2	18	18	NUM
ajst-27525	54	3	]	]	PUNCT
ajst-27525	54	4	introduced	introduce	VERB
ajst-27525	54	5	physics	physics	NOUN
ajst-27525	54	6	-	-	PUNCT
ajst-27525	54	7	informed	inform	VERB
ajst-27525	54	8	neural	neural	ADJ
ajst-27525	54	9	networks	network	NOUN
ajst-27525	54	10	(	(	PUNCT
ajst-27525	54	11	pinns	pinn	NOUN
ajst-27525	54	12	)	)	PUNCT
ajst-27525	54	13	,	,	PUNCT
ajst-27525	54	14	a	a	DET
ajst-27525	54	15	method	method	NOUN
ajst-27525	54	16	that	that	PRON
ajst-27525	54	17	combines	combine	VERB
ajst-27525	54	18	datadriven	datadriven	ADJ
ajst-27525	54	19	and	and	CCONJ
ajst-27525	54	20	physics	physics	NOUN
ajst-27525	54	21	-	-	PUNCT
ajst-27525	54	22	informed	inform	VERB
ajst-27525	54	23	constraints	constraint	NOUN
ajst-27525	54	24	.	.	PUNCT
ajst-27525	55	1	by	by	ADP
ajst-27525	55	2	constructing	construct	VERB
ajst-27525	55	3	residuals	residual	NOUN
ajst-27525	55	4	from	from	ADP
ajst-27525	55	5	control	control	NOUN
ajst-27525	55	6	equations	equation	NOUN
ajst-27525	55	7	and	and	CCONJ
ajst-27525	55	8	boundary	boundary	ADJ
ajst-27525	55	9	conditions	condition	NOUN
ajst-27525	55	10	,	,	PUNCT
ajst-27525	55	11	pinns	pinn	NOUN
ajst-27525	55	12	embed	embed	VERB
ajst-27525	55	13	physics	physics	NOUN
ajst-27525	55	14	laws	law	NOUN
ajst-27525	55	15	in	in	ADP
ajst-27525	55	16	regularized	regularize	VERB
ajst-27525	55	17	form	form	NOUN
ajst-27525	55	18	within	within	ADP
ajst-27525	55	19	the	the	DET
ajst-27525	55	20	loss	loss	NOUN
ajst-27525	55	21	function	function	NOUN
ajst-27525	55	22	,	,	PUNCT
ajst-27525	55	23	enhancing	enhance	VERB
ajst-27525	55	24	the	the	DET
ajst-27525	55	25	efficiency	efficiency	NOUN
ajst-27525	55	26	and	and	CCONJ
ajst-27525	55	27	accuracy	accuracy	NOUN
ajst-27525	55	28	of	of	ADP
ajst-27525	55	29	equation	equation	NOUN
ajst-27525	55	30	solutions	solution	NOUN
ajst-27525	55	31	.	.	PUNCT
ajst-27525	56	1	since	since	SCONJ
ajst-27525	56	2	then	then	ADV
ajst-27525	56	3	,	,	PUNCT
ajst-27525	56	4	various	various	ADJ
ajst-27525	56	5	studies	study	NOUN
ajst-27525	56	6	based	base	VERB
ajst-27525	56	7	on	on	ADP
ajst-27525	56	8	pinns	pinn	NOUN
ajst-27525	56	9	have	have	AUX
ajst-27525	56	10	flourished	flourish	VERB
ajst-27525	56	11	.	.	PUNCT
ajst-27525	57	1	meng	meng	PROPN
ajst-27525	57	2	et	et	PROPN
ajst-27525	57	3	al	al	PROPN
ajst-27525	57	4	.	.	PUNCT
ajst-27525	58	1	[	[	X
ajst-27525	58	2	19	19	NUM
ajst-27525	58	3	]	]	PUNCT
ajst-27525	58	4	proposed	propose	VERB
ajst-27525	58	5	the	the	DET
ajst-27525	58	6	parareal	parareal	NOUN
ajst-27525	58	7	physics	physics	NOUN
ajst-27525	58	8	-	-	PUNCT
ajst-27525	58	9	informed	inform	VERB
ajst-27525	58	10	neural	neural	ADJ
ajst-27525	58	11	network	network	NOUN
ajst-27525	58	12	(	(	PUNCT
ajst-27525	58	13	ppinn	ppinn	PROPN
ajst-27525	58	14	)	)	PUNCT
ajst-27525	58	15	,	,	PUNCT
ajst-27525	58	16	which	which	PRON
ajst-27525	58	17	divides	divide	VERB
ajst-27525	58	18	long	long	ADJ
ajst-27525	58	19	-	-	PUNCT
ajst-27525	58	20	time	time	NOUN
ajst-27525	58	21	problems	problem	NOUN
ajst-27525	58	22	into	into	ADP
ajst-27525	58	23	several	several	ADJ
ajst-27525	58	24	independent	independent	ADJ
ajst-27525	58	25	shorttime	shorttime	NOUN
ajst-27525	58	26	problems	problem	NOUN
ajst-27525	58	27	to	to	PART
ajst-27525	58	28	improve	improve	VERB
ajst-27525	58	29	solution	solution	NOUN
ajst-27525	58	30	efficiency	efficiency	NOUN
ajst-27525	58	31	.	.	PUNCT
ajst-27525	59	1	jagtap	jagtap	PROPN
ajst-27525	59	2	et	et	PROPN
ajst-27525	59	3	al	al	PROPN
ajst-27525	59	4	.	.	PUNCT
ajst-27525	60	1	[	[	X
ajst-27525	60	2	20	20	NUM
ajst-27525	60	3	]	]	PUNCT
ajst-27525	60	4	introduced	introduce	VERB
ajst-27525	60	5	adaptive	adaptive	ADJ
ajst-27525	60	6	activation	activation	NOUN
ajst-27525	60	7	functions	function	NOUN
ajst-27525	60	8	to	to	PART
ajst-27525	60	9	replace	replace	VERB
ajst-27525	60	10	conventional	conventional	ADJ
ajst-27525	60	11	ones	one	NOUN
ajst-27525	60	12	in	in	ADP
ajst-27525	60	13	pinns	pinn	NOUN
ajst-27525	60	14	,	,	PUNCT
ajst-27525	60	15	resulting	result	VERB
ajst-27525	60	16	in	in	ADP
ajst-27525	60	17	enhanced	enhanced	ADJ
ajst-27525	60	18	solution	solution	NOUN
ajst-27525	60	19	efficiency	efficiency	NOUN
ajst-27525	60	20	,	,	PUNCT
ajst-27525	60	21	accuracy	accuracy	NOUN
ajst-27525	60	22	,	,	PUNCT
ajst-27525	60	23	and	and	CCONJ
ajst-27525	60	24	robustness	robustness	NOUN
ajst-27525	60	25	.	.	PUNCT
ajst-27525	61	1	recently	recently	ADV
ajst-27525	61	2	,	,	PUNCT
ajst-27525	61	3	fraces	frace	NOUN
ajst-27525	61	4	et	et	PROPN
ajst-27525	61	5	al	al	PROPN
ajst-27525	61	6	.	.	PUNCT
ajst-27525	62	1	[	[	X
ajst-27525	62	2	21	21	NUM
ajst-27525	62	3	]	]	PUNCT
ajst-27525	62	4	addressed	address	VERB
ajst-27525	62	5	uncertainty	uncertainty	NOUN
ajst-27525	62	6	quantification	quantification	NOUN
ajst-27525	62	7	in	in	ADP
ajst-27525	62	8	reservoir	reservoir	NOUN
ajst-27525	62	9	engineering	engineering	NOUN
ajst-27525	62	10	by	by	ADP
ajst-27525	62	11	introducing	introduce	VERB
ajst-27525	62	12	a	a	DET
ajst-27525	62	13	parametrized	parametrized	ADJ
ajst-27525	62	14	physics	physics	NOUN
ajst-27525	62	15	-	-	PUNCT
ajst-27525	62	16	informed	inform	VERB
ajst-27525	62	17	neural	neural	ADJ
ajst-27525	62	18	network	network	NOUN
ajst-27525	62	19	(	(	PUNCT
ajst-27525	62	20	p	p	NOUN
ajst-27525	62	21	-	-	PUNCT
ajst-27525	62	22	pinn	pinn	NOUN
ajst-27525	62	23	)	)	PUNCT
ajst-27525	62	24	,	,	PUNCT
ajst-27525	62	25	using	use	VERB
ajst-27525	62	26	two	two	NUM
ajst-27525	62	27	-	-	PUNCT
ajst-27525	62	28	phase	phase	NOUN
ajst-27525	62	29	oil	oil	NOUN
ajst-27525	62	30	-	-	PUNCT
ajst-27525	62	31	water	water	NOUN
ajst-27525	62	32	pdes	pde	NOUN
ajst-27525	62	33	to	to	PART
ajst-27525	62	34	validate	validate	VERB
ajst-27525	62	35	the	the	DET
ajst-27525	62	36	model	model	NOUN
ajst-27525	62	37	’s	’s	PART
ajst-27525	62	38	superior	superior	ADJ
ajst-27525	62	39	performance	performance	NOUN
ajst-27525	62	40	.	.	PUNCT
ajst-27525	63	1	2.2	2.2	NUM
ajst-27525	63	2	.	.	PUNCT
ajst-27525	64	1	fourier	fourier	PROPN
ajst-27525	64	2	neural	neural	ADJ
ajst-27525	64	3	operator	operator	NOUN
ajst-27525	64	4	in	in	ADP
ajst-27525	64	5	1989	1989	NUM
ajst-27525	64	6	,	,	PUNCT
ajst-27525	64	7	hornik	hornik	VERB
ajst-27525	64	8	et	et	PROPN
ajst-27525	64	9	al	al	PROPN
ajst-27525	64	10	.	.	PUNCT
ajst-27525	65	1	[	[	X
ajst-27525	65	2	25	25	NUM
ajst-27525	65	3	]	]	PUNCT
ajst-27525	65	4	introduced	introduce	VERB
ajst-27525	65	5	the	the	DET
ajst-27525	65	6	concept	concept	NOUN
ajst-27525	65	7	that	that	SCONJ
ajst-27525	65	8	multilayer	multilayer	ADJ
ajst-27525	65	9	feedforward	feedforward	NOUN
ajst-27525	65	10	neural	neural	ADJ
ajst-27525	65	11	networks	network	NOUN
ajst-27525	65	12	could	could	AUX
ajst-27525	65	13	serve	serve	VERB
ajst-27525	65	14	as	as	ADP
ajst-27525	65	15	universal	universal	ADJ
ajst-27525	65	16	function	function	NOUN
ajst-27525	65	17	approximators	approximator	NOUN
ajst-27525	65	18	.	.	PUNCT
ajst-27525	66	1	they	they	PRON
ajst-27525	66	2	demonstrated	demonstrate	VERB
ajst-27525	66	3	that	that	SCONJ
ajst-27525	66	4	,	,	PUNCT
ajst-27525	66	5	with	with	ADP
ajst-27525	66	6	a	a	DET
ajst-27525	66	7	sufficient	sufficient	ADJ
ajst-27525	66	8	number	number	NOUN
ajst-27525	66	9	of	of	ADP
ajst-27525	66	10	hidden	hidden	ADJ
ajst-27525	66	11	units	unit	NOUN
ajst-27525	66	12	,	,	PUNCT
ajst-27525	66	13	feedforward	feedforward	ADJ
ajst-27525	66	14	neural	neural	ADJ
ajst-27525	66	15	networks	network	NOUN
ajst-27525	66	16	could	could	AUX
ajst-27525	66	17	approximate	approximate	VERB
ajst-27525	66	18	any	any	DET
ajst-27525	66	19	borel	borel	NOUN
ajst-27525	66	20	-	-	PUNCT
ajst-27525	66	21	measurable	measurable	ADJ
ajst-27525	66	22	function	function	NOUN
ajst-27525	66	23	in	in	ADP
ajst-27525	66	24	a	a	DET
ajst-27525	66	25	finite	finite	ADJ
ajst-27525	66	26	-	-	ADJ
ajst-27525	66	27	dimensional	dimensional	ADJ
ajst-27525	66	28	space	space	NOUN
ajst-27525	66	29	to	to	ADP
ajst-27525	66	30	arbitrary	arbitrary	ADJ
ajst-27525	66	31	accuracy	accuracy	NOUN
ajst-27525	66	32	,	,	PUNCT
ajst-27525	66	33	effectively	effectively	ADV
ajst-27525	66	34	approximating	approximate	VERB
ajst-27525	66	35	any	any	DET
ajst-27525	66	36	continuous	continuous	ADJ
ajst-27525	66	37	nonlinear	nonlinear	ADJ
ajst-27525	66	38	function	function	NOUN
ajst-27525	66	39	.	.	PUNCT
ajst-27525	67	1	this	this	DET
ajst-27525	67	2	universal	universal	ADJ
ajst-27525	67	3	approximation	approximation	NOUN
ajst-27525	67	4	theorem	theorem	NOUN
ajst-27525	67	5	,	,	PUNCT
ajst-27525	67	6	proven	prove	VERB
ajst-27525	67	7	with	with	ADP
ajst-27525	67	8	fourier	fouri	ADJ
ajst-27525	67	9	transform	transform	NOUN
ajst-27525	67	10	methods	method	NOUN
ajst-27525	67	11	,	,	PUNCT
ajst-27525	67	12	laid	lay	VERB
ajst-27525	67	13	the	the	DET
ajst-27525	67	14	foundation	foundation	NOUN
ajst-27525	67	15	for	for	ADP
ajst-27525	67	16	the	the	DET
ajst-27525	67	17	later	later	ADJ
ajst-27525	67	18	development	development	NOUN
ajst-27525	67	19	of	of	ADP
ajst-27525	67	20	neural	neural	ADJ
ajst-27525	67	21	operators	operator	NOUN
ajst-27525	67	22	.	.	PUNCT
ajst-27525	68	1	in	in	ADP
ajst-27525	68	2	2019	2019	NUM
ajst-27525	68	3	,	,	PUNCT
ajst-27525	68	4	lu	lu	PROPN
ajst-27525	68	5	et	et	PROPN
ajst-27525	68	6	al	al	PROPN
ajst-27525	68	7	.	.	PUNCT
ajst-27525	69	1	[	[	X
ajst-27525	69	2	26	26	NUM
ajst-27525	69	3	]	]	PUNCT
ajst-27525	69	4	proposed	propose	VERB
ajst-27525	69	5	the	the	DET
ajst-27525	69	6	deep	deep	ADJ
ajst-27525	69	7	operator	operator	NOUN
ajst-27525	69	8	network	network	NOUN
ajst-27525	69	9	(	(	PUNCT
ajst-27525	69	10	deeponet	deeponet	NOUN
ajst-27525	69	11	)	)	PUNCT
ajst-27525	69	12	,	,	PUNCT
ajst-27525	69	13	an	an	DET
ajst-27525	69	14	architecture	architecture	NOUN
ajst-27525	69	15	capable	capable	ADJ
ajst-27525	69	16	of	of	ADP
ajst-27525	69	17	efficiently	efficiently	ADV
ajst-27525	69	18	learning	learn	VERB
ajst-27525	69	19	operators	operator	NOUN
ajst-27525	69	20	from	from	ADP
ajst-27525	69	21	relatively	relatively	ADV
ajst-27525	69	22	small	small	ADJ
ajst-27525	69	23	datasets	dataset	NOUN
ajst-27525	69	24	.	.	PUNCT
ajst-27525	70	1	the	the	DET
ajst-27525	70	2	deeponet	deeponet	NOUN
ajst-27525	70	3	consists	consist	VERB
ajst-27525	70	4	of	of	ADP
ajst-27525	70	5	two	two	NUM
ajst-27525	70	6	sub	sub	NOUN
ajst-27525	70	7	-	-	NOUN
ajst-27525	70	8	networks	network	NOUN
ajst-27525	70	9	:	:	PUNCT
ajst-27525	70	10	one	one	NUM
ajst-27525	70	11	encodes	encode	VERB
ajst-27525	70	12	the	the	DET
ajst-27525	70	13	input	input	NOUN
ajst-27525	70	14	function	function	NOUN
ajst-27525	70	15	,	,	PUNCT
ajst-27525	70	16	and	and	CCONJ
ajst-27525	70	17	the	the	DET
ajst-27525	70	18	other	other	ADJ
ajst-27525	70	19	encodes	encode	VERB
ajst-27525	70	20	the	the	DET
ajst-27525	70	21	spatial	spatial	ADJ
ajst-27525	70	22	locations	location	NOUN
ajst-27525	70	23	of	of	ADP
ajst-27525	70	24	the	the	DET
ajst-27525	70	25	output	output	NOUN
ajst-27525	70	26	function	function	NOUN
ajst-27525	70	27	.	.	PUNCT
ajst-27525	71	1	experimental	experimental	ADJ
ajst-27525	71	2	results	result	NOUN
ajst-27525	71	3	showed	show	VERB
ajst-27525	71	4	that	that	SCONJ
ajst-27525	71	5	deeponets	deeponet	NOUN
ajst-27525	71	6	significantly	significantly	ADV
ajst-27525	71	7	reduced	reduce	VERB
ajst-27525	71	8	generalization	generalization	NOUN
ajst-27525	71	9	errors	error	NOUN
ajst-27525	71	10	,	,	PUNCT
ajst-27525	71	11	establishing	establish	VERB
ajst-27525	71	12	a	a	DET
ajst-27525	71	13	theoretical	theoretical	ADJ
ajst-27525	71	14	basis	basis	NOUN
ajst-27525	71	15	for	for	ADP
ajst-27525	71	16	further	further	ADJ
ajst-27525	71	17	neural	neural	ADJ
ajst-27525	71	18	operator	operator	NOUN
ajst-27525	71	19	research	research	NOUN
ajst-27525	71	20	.	.	PUNCT
ajst-27525	72	1	in	in	ADP
ajst-27525	72	2	2020	2020	NUM
ajst-27525	72	3	,	,	PUNCT
ajst-27525	72	4	li	li	PROPN
ajst-27525	72	5	et	et	PROPN
ajst-27525	72	6	al	al	PROPN
ajst-27525	72	7	.	.	PUNCT
ajst-27525	73	1	[	[	X
ajst-27525	73	2	27	27	NUM
ajst-27525	73	3	]	]	PUNCT
ajst-27525	73	4	introduced	introduce	VERB
ajst-27525	73	5	the	the	DET
ajst-27525	73	6	fourier	fourier	ADJ
ajst-27525	73	7	neural	neural	ADJ
ajst-27525	73	8	operator	operator	NOUN
ajst-27525	73	9	(	(	PUNCT
ajst-27525	73	10	fno	fno	PROPN
ajst-27525	73	11	)	)	PUNCT
ajst-27525	73	12	,	,	PUNCT
ajst-27525	73	13	a	a	DET
ajst-27525	73	14	neural	neural	ADJ
ajst-27525	73	15	operator	operator	NOUN
ajst-27525	73	16	model	model	NOUN
ajst-27525	73	17	with	with	ADP
ajst-27525	73	18	a	a	DET
ajst-27525	73	19	fixed	fix	VERB
ajst-27525	73	20	number	number	NOUN
ajst-27525	73	21	of	of	ADP
ajst-27525	73	22	parameters	parameter	NOUN
ajst-27525	73	23	that	that	PRON
ajst-27525	73	24	also	also	ADV
ajst-27525	73	25	meets	meet	VERB
ajst-27525	73	26	discretization	discretization	NOUN
ajst-27525	73	27	invariance	invariance	NOUN
ajst-27525	73	28	.	.	PUNCT
ajst-27525	74	1	compared	compare	VERB
ajst-27525	74	2	to	to	ADP
ajst-27525	74	3	traditional	traditional	ADJ
ajst-27525	74	4	pde	pde	NOUN
ajst-27525	74	5	solvers	solver	NOUN
ajst-27525	74	6	,	,	PUNCT
ajst-27525	74	7	the	the	DET
ajst-27525	74	8	fno	fno	PROPN
ajst-27525	74	9	operates	operate	VERB
ajst-27525	74	10	three	three	NUM
ajst-27525	74	11	orders	order	NOUN
ajst-27525	74	12	of	of	ADP
ajst-27525	74	13	magnitude	magnitude	NOUN
ajst-27525	74	14	faster	fast	ADV
ajst-27525	74	15	while	while	SCONJ
ajst-27525	74	16	achieving	achieve	VERB
ajst-27525	74	17	higher	high	ADJ
ajst-27525	74	18	accuracy	accuracy	NOUN
ajst-27525	74	19	at	at	ADP
ajst-27525	74	20	fixed	fix	VERB
ajst-27525	74	21	resolutions	resolution	NOUN
ajst-27525	74	22	.	.	PUNCT
ajst-27525	75	1	the	the	DET
ajst-27525	75	2	fno	fno	PROPN
ajst-27525	75	3	replaces	replace	VERB
ajst-27525	75	4	finite	finite	ADJ
ajst-27525	75	5	-	-	ADJ
ajst-27525	75	6	dimensional	dimensional	ADJ
ajst-27525	75	7	linear	linear	ADJ
ajst-27525	75	8	layers	layer	NOUN
ajst-27525	75	9	in	in	ADP
ajst-27525	75	10	neural	neural	ADJ
ajst-27525	75	11	networks	network	NOUN
ajst-27525	75	12	with	with	ADP
ajst-27525	75	13	linear	linear	PROPN
ajst-27525	75	14	operators	operator	NOUN
ajst-27525	75	15	acting	act	VERB
ajst-27525	75	16	on	on	ADP
ajst-27525	75	17	function	function	NOUN
ajst-27525	75	18	spaces	space	NOUN
ajst-27525	75	19	.	.	PUNCT
ajst-27525	76	1	research	research	NOUN
ajst-27525	76	2	further	far	ADV
ajst-27525	76	3	demonstrated	demonstrate	VERB
ajst-27525	76	4	that	that	SCONJ
ajst-27525	76	5	neural	neural	ADJ
ajst-27525	76	6	operators	operator	NOUN
ajst-27525	76	7	are	be	AUX
ajst-27525	76	8	universal	universal	ADJ
ajst-27525	76	9	approximators	approximator	NOUN
ajst-27525	76	10	for	for	ADP
ajst-27525	76	11	continuous	continuous	ADJ
ajst-27525	76	12	operators	operator	NOUN
ajst-27525	76	13	between	between	ADP
ajst-27525	76	14	banach	banach	NOUN
ajst-27525	76	15	spaces	space	NOUN
ajst-27525	76	16	,	,	PUNCT
ajst-27525	76	17	capable	capable	ADJ
ajst-27525	76	18	of	of	ADP
ajst-27525	76	19	uniformly	uniformly	ADV
ajst-27525	76	20	approximating	approximate	VERB
ajst-27525	76	21	any	any	DET
ajst-27525	76	22	continuous	continuous	ADJ
ajst-27525	76	23	operator	operator	NOUN
ajst-27525	76	24	defined	define	VERB
ajst-27525	76	25	on	on	ADP
ajst-27525	76	26	banach	banach	NOUN
ajst-27525	76	27	spaces	space	NOUN
ajst-27525	76	28	.	.	PUNCT
ajst-27525	77	1	neural	neural	ADJ
ajst-27525	77	2	operators	operator	NOUN
ajst-27525	77	3	,	,	PUNCT
ajst-27525	77	4	including	include	VERB
ajst-27525	77	5	the	the	DET
ajst-27525	77	6	fno	fno	PROPN
ajst-27525	77	7	,	,	PUNCT
ajst-27525	77	8	are	be	AUX
ajst-27525	77	9	currently	currently	ADV
ajst-27525	77	10	the	the	DET
ajst-27525	77	11	only	only	ADJ
ajst-27525	77	12	models	model	NOUN
ajst-27525	77	13	known	know	VERB
ajst-27525	77	14	to	to	PART
ajst-27525	77	15	possess	possess	VERB
ajst-27525	77	16	both	both	DET
ajst-27525	77	17	discretization	discretization	NOUN
ajst-27525	77	18	invariance	invariance	NOUN
ajst-27525	77	19	and	and	CCONJ
ajst-27525	77	20	universal	universal	ADJ
ajst-27525	77	21	approximation	approximation	NOUN
ajst-27525	77	22	properties	property	NOUN
ajst-27525	77	23	.	.	PUNCT
ajst-27525	78	1	zhang	zhang	PROPN
ajst-27525	78	2	et	et	PROPN
ajst-27525	78	3	al	al	PROPN
ajst-27525	78	4	.	.	PUNCT
ajst-27525	79	1	[	[	X
ajst-27525	79	2	28	28	NUM
ajst-27525	79	3	]	]	PUNCT
ajst-27525	79	4	applied	apply	VERB
ajst-27525	79	5	fno	fno	PROPN
ajst-27525	79	6	to	to	ADP
ajst-27525	79	7	the	the	DET
ajst-27525	79	8	field	field	NOUN
ajst-27525	79	9	of	of	ADP
ajst-27525	79	10	reservoir	reservoir	PROPN
ajst-27525	79	11	engineering	engineering	NOUN
ajst-27525	79	12	,	,	PUNCT
ajst-27525	79	13	developing	develop	VERB
ajst-27525	79	14	an	an	DET
ajst-27525	79	15	fno	fno	PROPN
ajst-27525	79	16	-	-	PUNCT
ajst-27525	79	17	based	base	VERB
ajst-27525	79	18	fuzzy	fuzzy	ADJ
ajst-27525	79	19	neural	neural	ADJ
ajst-27525	79	20	network	network	NOUN
ajst-27525	79	21	model	model	NOUN
ajst-27525	79	22	to	to	PART
ajst-27525	79	23	solve	solve	VERB
ajst-27525	79	24	two	two	NUM
ajst-27525	79	25	-	-	PUNCT
ajst-27525	79	26	dimensional	dimensional	ADJ
ajst-27525	79	27	oil	oil	NOUN
ajst-27525	79	28	-	-	PUNCT
ajst-27525	79	29	water	water	NOUN
ajst-27525	79	30	two	two	NUM
ajst-27525	79	31	-	-	PUNCT
ajst-27525	79	32	phase	phase	NOUN
ajst-27525	79	33	pdes	pde	NOUN
ajst-27525	79	34	in	in	ADP
ajst-27525	79	35	subsurface	subsurface	NOUN
ajst-27525	79	36	reservoirs	reservoir	NOUN
ajst-27525	79	37	.	.	PUNCT
ajst-27525	80	1	this	this	DET
ajst-27525	80	2	model	model	NOUN
ajst-27525	80	3	uses	use	VERB
ajst-27525	80	4	fast	fast	ADJ
ajst-27525	80	5	fourier	fourier	NOUN
ajst-27525	80	6	transform	transform	NOUN
ajst-27525	80	7	(	(	PUNCT
ajst-27525	80	8	fft	fft	PROPN
ajst-27525	80	9	)	)	PUNCT
ajst-27525	80	10	to	to	PART
ajst-27525	80	11	extract	extract	VERB
ajst-27525	80	12	information	information	NOUN
ajst-27525	80	13	from	from	ADP
ajst-27525	80	14	the	the	DET
ajst-27525	80	15	fourier	fourier	NOUN
ajst-27525	80	16	space	space	NOUN
ajst-27525	80	17	,	,	PUNCT
ajst-27525	80	18	approximating	approximate	VERB
ajst-27525	80	19	differential	differential	ADJ
ajst-27525	80	20	operators	operator	NOUN
ajst-27525	80	21	and	and	CCONJ
ajst-27525	80	22	enhancing	enhance	VERB
ajst-27525	80	23	the	the	DET
ajst-27525	80	24	model	model	NOUN
ajst-27525	80	25	’s	’s	PART
ajst-27525	80	26	efficiency	efficiency	NOUN
ajst-27525	80	27	,	,	PUNCT
ajst-27525	80	28	accuracy	accuracy	NOUN
ajst-27525	80	29	,	,	PUNCT
ajst-27525	80	30	and	and	CCONJ
ajst-27525	80	31	generalization	generalization	NOUN
ajst-27525	80	32	capability	capability	NOUN
ajst-27525	80	33	.	.	PUNCT
ajst-27525	81	1	recently	recently	ADV
ajst-27525	81	2	,	,	PUNCT
ajst-27525	81	3	du	du	PROPN
ajst-27525	81	4	et	et	PROPN
ajst-27525	81	5	al	al	PROPN
ajst-27525	81	6	.	.	PUNCT
ajst-27525	82	1	[	[	X
ajst-27525	82	2	29	29	NUM
ajst-27525	82	3	]	]	PUNCT
ajst-27525	82	4	introduced	introduce	VERB
ajst-27525	82	5	a	a	DET
ajst-27525	82	6	modified	modify	VERB
ajst-27525	82	7	version	version	NOUN
ajst-27525	82	8	of	of	ADP
ajst-27525	82	9	fno	fno	PROPN
ajst-27525	82	10	,	,	PUNCT
ajst-27525	82	11	the	the	DET
ajst-27525	82	12	global	global	ADJ
ajst-27525	82	13	-	-	PUNCT
ajst-27525	82	14	local	local	ADJ
ajst-27525	82	15	fourier	fourier	NOUN
ajst-27525	82	16	neural	neural	ADJ
ajst-27525	82	17	operator	operator	NOUN
ajst-27525	82	18	,	,	PUNCT
ajst-27525	82	19	designed	design	VERB
ajst-27525	82	20	to	to	PART
ajst-27525	82	21	predict	predict	VERB
ajst-27525	82	22	magnetohydrodynamics	magnetohydrodynamic	NOUN
ajst-27525	82	23	(	(	PUNCT
ajst-27525	82	24	mhd	mhd	NOUN
ajst-27525	82	25	)	)	PUNCT
ajst-27525	82	26	.	.	PUNCT
ajst-27525	83	1	their	their	PRON
ajst-27525	83	2	results	result	NOUN
ajst-27525	83	3	demonstrated	demonstrate	VERB
ajst-27525	83	4	that	that	SCONJ
ajst-27525	83	5	this	this	DET
ajst-27525	83	6	new	new	ADJ
ajst-27525	83	7	model	model	NOUN
ajst-27525	83	8	not	not	PART
ajst-27525	83	9	only	only	ADV
ajst-27525	83	10	accelerated	accelerate	VERB
ajst-27525	83	11	simulations	simulation	NOUN
ajst-27525	83	12	but	but	CCONJ
ajst-27525	83	13	also	also	ADV
ajst-27525	83	14	significantly	significantly	ADV
ajst-27525	83	15	improved	improve	VERB
ajst-27525	83	16	predictive	predictive	ADJ
ajst-27525	83	17	capabilities	capability	NOUN
ajst-27525	83	18	.	.	PUNCT
ajst-27525	84	1	3	3	X
ajst-27525	84	2	.	.	X
ajst-27525	84	3	overview	overview	NOUN
ajst-27525	84	4	of	of	ADP
ajst-27525	84	5	the	the	DET
ajst-27525	84	6	fourier	fourier	NOUN
ajst-27525	84	7	neural	neural	ADJ
ajst-27525	84	8	operator	operator	NOUN
ajst-27525	84	9	3.1	3.1	NUM
ajst-27525	84	10	.	.	PUNCT
ajst-27525	84	11	basic	basic	ADJ
ajst-27525	84	12	principle	principle	NOUN
ajst-27525	84	13	of	of	ADP
ajst-27525	84	14	fno	fno	PROPN
ajst-27525	84	15	the	the	DET
ajst-27525	84	16	fourier	fourier	NOUN
ajst-27525	84	17	neural	neural	ADJ
ajst-27525	84	18	operator	operator	NOUN
ajst-27525	84	19	(	(	PUNCT
ajst-27525	84	20	fno	fno	PROPN
ajst-27525	84	21	)	)	PUNCT
ajst-27525	84	22	leverages	leverage	VERB
ajst-27525	84	23	the	the	DET
ajst-27525	84	24	fast	fast	ADJ
ajst-27525	84	25	fourier	fourier	NOUN
ajst-27525	84	26	transform	transform	NOUN
ajst-27525	84	27	(	(	PUNCT
ajst-27525	84	28	fft	fft	PROPN
ajst-27525	84	29	)	)	PUNCT
ajst-27525	84	30	to	to	PART
ajst-27525	84	31	compute	compute	VERB
ajst-27525	84	32	complex	complex	ADJ
ajst-27525	84	33	linear	linear	ADJ
ajst-27525	84	34	integral	integral	ADJ
ajst-27525	84	35	operators	operator	NOUN
ajst-27525	84	36	by	by	ADP
ajst-27525	84	37	parameterizing	parameterize	VERB
ajst-27525	84	38	the	the	DET
ajst-27525	84	39	kernel	kernel	NOUN
ajst-27525	84	40	in	in	ADP
ajst-27525	84	41	fourier	fourier	ADJ
ajst-27525	84	42	space	space	NOUN
ajst-27525	84	43	rather	rather	ADV
ajst-27525	84	44	than	than	ADP
ajst-27525	84	45	working	work	VERB
ajst-27525	84	46	directly	directly	ADV
ajst-27525	84	47	in	in	ADP
ajst-27525	84	48	the	the	DET
ajst-27525	84	49	domain	domain	NOUN
ajst-27525	84	50	ddd	ddd	NOUN
ajst-27525	84	51	.	.	PUNCT
ajst-27525	85	1	let	let	VERB
ajst-27525	85	2	xxx	xxx	NOUN
ajst-27525	85	3	denote	denote	VERB
ajst-27525	85	4	the	the	DET
ajst-27525	85	5	kernel	kernel	PROPN
ajst-27525	85	6	integral	integral	ADJ
ajst-27525	85	7	operator	operator	NOUN
ajst-27525	85	8	.	.	PUNCT
ajst-27525	86	1	184	184	NUM
ajst-27525	86	2	table	table	NOUN
ajst-27525	86	3	1	1	NUM
ajst-27525	86	4	.	.	PUNCT
ajst-27525	86	5	solving	solving	NOUN
ajst-27525	86	6	and	and	CCONJ
ajst-27525	86	7	classification	classification	NOUN
ajst-27525	86	8	of	of	ADP
ajst-27525	86	9	partial	partial	ADJ
ajst-27525	86	10	differential	differential	ADJ
ajst-27525	86	11	equations	equation	NOUN
ajst-27525	86	12	based	base	VERB
ajst-27525	86	13	on	on	ADP
ajst-27525	86	14	neural	neural	ADJ
ajst-27525	86	15	networks	network	NOUN
ajst-27525	86	16	categorization	categorization	NOUN
ajst-27525	86	17	author	author	NOUN
ajst-27525	86	18	(	(	PUNCT
ajst-27525	86	19	year	year	NOUN
ajst-27525	86	20	)	)	PUNCT
ajst-27525	86	21	）	）	PROPN
ajst-27525	86	22	method	method	NOUN
ajst-27525	86	23	(	(	PUNCT
ajst-27525	86	24	model	model	NOUN
ajst-27525	86	25	)	)	PUNCT
ajst-27525	86	26	pde	pde	PROPN
ajst-27525	86	27	data	data	NOUN
ajst-27525	86	28	-	-	PUNCT
ajst-27525	86	29	driven	drive	VERB
ajst-27525	86	30	[	[	X
ajst-27525	86	31	14]rudy	14]rudy	NUM
ajst-27525	86	32	et	et	NOUN
ajst-27525	86	33	al.(2017	al.(2017	NOUN
ajst-27525	86	34	)	)	PUNCT
ajst-27525	86	35	sparse	sparse	ADJ
ajst-27525	86	36	regression	regression	NOUN
ajst-27525	86	37	navier	navier	NOUN
ajst-27525	86	38	-	-	PUNCT
ajst-27525	86	39	stokes	stoke	NOUN
ajst-27525	86	40	equations	equation	NOUN
ajst-27525	86	41	;	;	PUNCT
ajst-27525	86	42	diffusion	diffusion	NOUN
ajst-27525	86	43	equation	equation	NOUN
ajst-27525	86	44	;	;	PUNCT
ajst-27525	86	45	kuramoto	kuramoto	NOUN
ajst-27525	86	46	-	-	PUNCT
ajst-27525	86	47	sivashinsky	sivashinsky	NOUN
ajst-27525	86	48	equation	equation	NOUN
ajst-27525	86	49	[	[	X
ajst-27525	86	50	17]bar	17]bar	NUM
ajst-27525	86	51	-	-	PUNCT
ajst-27525	86	52	sinai	sinai	PROPN
ajst-27525	86	53	et	et	PROPN
ajst-27525	86	54	al	al	PROPN
ajst-27525	86	55	.	.	PROPN
ajst-27525	87	1	(	(	PUNCT
ajst-27525	87	2	2019	2019	NUM
ajst-27525	87	3	)	)	PUNCT
ajst-27525	87	4	subgrid	subgrid	ADJ
ajst-27525	87	5	-	-	PUNCT
ajst-27525	87	6	scale	scale	NOUN
ajst-27525	87	7	modeling	modeling	NOUN
ajst-27525	87	8	burgers	burger	NOUN
ajst-27525	87	9	’	'	PUNCT
ajst-27525	87	10	equation	equation	NOUN
ajst-27525	87	11	[	[	X
ajst-27525	87	12	20]kadeethum(2021	20]kadeethum(2021	NUM
ajst-27525	87	13	)	)	PUNCT
ajst-27525	87	14	cgan	cgan	VERB
ajst-27525	87	15	quasi	quasi	NOUN
ajst-27525	87	16	-	-	ADJ
ajst-27525	87	17	static	static	ADJ
ajst-27525	87	18	or	or	CCONJ
ajst-27525	87	19	steady	steady	ADJ
ajst-27525	87	20	-	-	PUNCT
ajst-27525	87	21	state	state	NOUN
ajst-27525	87	22	problems	problem	NOUN
ajst-27525	87	23	physical	physical	ADJ
ajst-27525	87	24	constraints	constraint	NOUN
ajst-27525	87	25	[	[	X
ajst-27525	87	26	18]raissi	18]raissi	NUM
ajst-27525	87	27	et	et	NOUN
ajst-27525	87	28	al.(2019	al.(2019	PROPN
ajst-27525	87	29	)	)	PUNCT
ajst-27525	87	30	pinn	pinn	NOUN
ajst-27525	87	31	burgers	burger	NOUN
ajst-27525	87	32	equation	equation	NOUN
ajst-27525	87	33	;	;	PUNCT
ajst-27525	87	34	schrodinger	schrodinger	ADJ
ajst-27525	87	35	equation	equation	NOUN
ajst-27525	87	36	;	;	PUNCT
ajst-27525	87	37	allen	allen	PROPN
ajst-27525	87	38	–	–	PUNCT
ajst-27525	87	39	cahn	cahn	NOUN
ajst-27525	87	40	equation	equation	NOUN
ajst-27525	87	41	;	;	PUNCT
ajst-27525	87	42	navier	navier	NOUN
ajst-27525	87	43	–	–	PUNCT
ajst-27525	87	44	stokes	stoke	NOUN
ajst-27525	87	45	equation	equation	NOUN
ajst-27525	87	46	.	.	PUNCT
ajst-27525	88	1	[	[	X
ajst-27525	88	2	19]meng	19]meng	NUM
ajst-27525	88	3	et	et	NOUN
ajst-27525	88	4	al.(2020	al.(2020	PROPN
ajst-27525	88	5	)	)	PUNCT
ajst-27525	88	6	ppinn	ppinn	NOUN
ajst-27525	88	7	burgers	burger	NOUN
ajst-27525	88	8	equation	equation	NOUN
ajst-27525	88	9	;	;	PUNCT
ajst-27525	88	10	diffusion	diffusion	NOUN
ajst-27525	88	11	–	–	PUNCT
ajst-27525	88	12	reaction	reaction	NOUN
ajst-27525	88	13	equation	equation	NOUN
ajst-27525	88	14	.	.	PUNCT
ajst-27525	89	1	[	[	X
ajst-27525	89	2	21]fraces	21]fraces	NUM
ajst-27525	89	3	et	et	NOUN
ajst-27525	89	4	al.(2023	al.(2023	PROPN
ajst-27525	89	5	)	)	PUNCT
ajst-27525	89	6	p	p	NOUN
ajst-27525	89	7	-	-	PUNCT
ajst-27525	89	8	pinn	pinn	NOUN
ajst-27525	89	9	buckley	buckley	NOUN
ajst-27525	89	10	-	-	PUNCT
ajst-27525	89	11	leverett	leverett	PROPN
ajst-27525	89	12	problem	problem	NOUN
ajst-27525	89	13	neural	neural	ADJ
ajst-27525	89	14	operator	operator	NOUN
ajst-27525	90	1	[	[	X
ajst-27525	90	2	26]lu	26]lu	NUM
ajst-27525	90	3	l	l	X
ajst-27525	90	4	et	et	NOUN
ajst-27525	90	5	al.(2019	al.(2019	NOUN
ajst-27525	90	6	)	)	PUNCT
ajst-27525	90	7	deeponet	deeponet	NOUN
ajst-27525	90	8	diffusion	diffusion	NOUN
ajst-27525	90	9	-	-	PUNCT
ajst-27525	90	10	reaction	reaction	NOUN
ajst-27525	90	11	system	system	NOUN
ajst-27525	91	1	[	[	X
ajst-27525	91	2	27]li	27]li	NUM
ajst-27525	91	3	et	et	NOUN
ajst-27525	91	4	al.(2021	al.(2021	PROPN
ajst-27525	91	5	)	)	PUNCT
ajst-27525	91	6	fno	fno	PROPN
ajst-27525	91	7	burgers	burger	NOUN
ajst-27525	91	8	equation	equation	NOUN
ajst-27525	91	9	;	;	PUNCT
ajst-27525	91	10	darcy	darcy	PROPN
ajst-27525	91	11	equation	equation	NOUN
ajst-27525	91	12	;	;	PUNCT
ajst-27525	91	13	navier	navier	NOUN
ajst-27525	91	14	-	-	PUNCT
ajst-27525	91	15	stokes	stoke	NOUN
ajst-27525	91	16	equation	equation	NOUN
ajst-27525	91	17	.	.	PUNCT
ajst-27525	92	1	[	[	X
ajst-27525	92	2	28]zhang	28]zhang	X
ajst-27525	92	3	et	et	PROPN
ajst-27525	92	4	al.(2022	al.(2022	PROPN
ajst-27525	92	5	)	)	PUNCT
ajst-27525	92	6	fno	fno	PROPN
ajst-27525	92	7	2d	2d	PROPN
ajst-27525	92	8	two	two	NUM
ajst-27525	92	9	--	--	PUNCT
ajst-27525	92	10	phase	phase	NOUN
ajst-27525	92	11	pdes	pde	VERB
ajst-27525	92	12	[	[	X
ajst-27525	92	13	30]wen	30]wen	NUM
ajst-27525	92	14	et	et	NOUN
ajst-27525	92	15	al.(2022	al.(2022	NOUN
ajst-27525	92	16	)	)	PUNCT
ajst-27525	92	17	u	u	PROPN
ajst-27525	92	18	-	-	PROPN
ajst-27525	92	19	fno	fno	ADJ
ajst-27525	92	20	multi	multi	ADJ
ajst-27525	92	21	-	-	ADJ
ajst-27525	92	22	phase	phase	ADJ
ajst-27525	92	23	flow	flow	NOUN
ajst-27525	92	24	problem	problem	NOUN
ajst-27525	92	25	;	;	PUNCT
ajst-27525	92	26	darcy	darcy	PROPN
ajst-27525	92	27	’s	’s	PART
ajst-27525	92	28	flow	flow	NOUN
ajst-27525	92	29	problem	problem	NOUN
ajst-27525	92	30	.	.	PUNCT
ajst-27525	93	1	[	[	X
ajst-27525	93	2	31]lehmann	31]lehmann	NUM
ajst-27525	93	3	et	et	NOUN
ajst-27525	93	4	al.(2024	al.(2024	NOUN
ajst-27525	93	5	)	)	PUNCT
ajst-27525	93	6	f	f	PROPN
ajst-27525	93	7	-	-	PUNCT
ajst-27525	93	8	fno	fno	PROPN
ajst-27525	93	9	3d	3d	PROPN
ajst-27525	93	10	elastic	elastic	ADJ
ajst-27525	93	11	wave	wave	NOUN
ajst-27525	93	12	equation	equation	NOUN
ajst-27525	93	13	[	[	X
ajst-27525	93	14	32]zhao	32]zhao	NUM
ajst-27525	93	15	et	et	NOUN
ajst-27525	93	16	al.(2024	al.(2024	NOUN
ajst-27525	93	17	)	)	PUNCT
ajst-27525	93	18	recfno	recfno	NOUN
ajst-27525	93	19	navier	navier	NOUN
ajst-27525	93	20	–	–	PUNCT
ajst-27525	93	21	stokes	stoke	NOUN
ajst-27525	93	22	equations	equation	NOUN
ajst-27525	93	23	;	;	PUNCT
ajst-27525	93	24	2d	2d	NUM
ajst-27525	93	25	steady	steady	ADJ
ajst-27525	93	26	-	-	PUNCT
ajst-27525	93	27	state	state	NOUN
ajst-27525	93	28	darcy	darcy	NOUN
ajst-27525	93	29	flow	flow	NOUN
ajst-27525	93	30	.	.	PUNCT
ajst-27525	94	1	(	(	PUNCT
ajst-27525	94	2	(	(	PUNCT
ajst-27525	94	3	;	;	PUNCT
ajst-27525	94	4	)	)	PUNCT
ajst-27525	94	5	)	)	PUNCT
ajst-27525	94	6	(	(	PUNCT
ajst-27525	94	7	)	)	PUNCT
ajst-27525	94	8	:	:	PUNCT
ajst-27525	94	9	(	(	PUNCT
ajst-27525	94	10	,	,	PUNCT
ajst-27525	94	11	,	,	PUNCT
ajst-27525	94	12	(	(	PUNCT
ajst-27525	94	13	)	)	PUNCT
ajst-27525	94	14	,	,	PUNCT
ajst-27525	94	15	(	(	PUNCT
ajst-27525	94	16	)	)	PUNCT
ajst-27525	94	17	;	;	PUNCT
ajst-27525	94	18	)	)	PUNCT
ajst-27525	94	19	(	(	PUNCT
ajst-27525	94	20	)	)	PUNCT
ajst-27525	94	21	,	,	PUNCT
ajst-27525	94	22	t	t	AUX
ajst-27525	94	23	td	td	NOUN
ajst-27525	94	24	a	a	DET
ajst-27525	94	25	v	v	NOUN
ajst-27525	94	26	x	x	SYM
ajst-27525	94	27	x	x	SYM
ajst-27525	94	28	y	y	PROPN
ajst-27525	94	29	a	a	X
ajst-27525	94	30	x	x	X
ajst-27525	94	31	a	a	DET
ajst-27525	94	32	y	y	PROPN
ajst-27525	94	33	v	v	NOUN
ajst-27525	94	34	y	y	PROPN
ajst-27525	94	35	dy	dy	X
ajst-27525	94	36	x	x	PROPN
ajst-27525	94	37	d	d	PROPN
ajst-27525	94	38			VERB
ajst-27525	94	39			X
ajst-27525	94	40			NOUN
ajst-27525	94	41			PROPN
ajst-27525	94	42	furthermore	furthermore	ADV
ajst-27525	94	43	,	,	PUNCT
ajst-27525	94	44	the	the	DET
ajst-27525	94	45	fourier	fourier	NOUN
ajst-27525	94	46	transform	transform	NOUN
ajst-27525	94	47	expressions	expression	NOUN
ajst-27525	94	48	involved	involve	VERB
ajst-27525	94	49	are	be	AUX
ajst-27525	94	50	as	as	SCONJ
ajst-27525	94	51	follows	follow	VERB
ajst-27525	94	52	:	:	PUNCT
ajst-27525	94	53	2	2	NUM
ajst-27525	94	54	,	,	PUNCT
ajst-27525	94	55	(	(	PUNCT
ajst-27525	94	56	)	)	PUNCT
ajst-27525	94	57	(	(	PUNCT
ajst-27525	94	58	)	)	PUNCT
ajst-27525	94	59	(	(	PUNCT
ajst-27525	94	60	)	)	PUNCT
ajst-27525	94	61	,	,	PUNCT
ajst-27525	94	62	i	i	PRON
ajst-27525	94	63	x	x	VERB
ajst-27525	95	1	k	k	PROPN
ajst-27525	95	2	j	j	PROPN
ajst-27525	95	3	jd	jd	PROPN
ajst-27525	95	4	ff	ff	INTJ
ajst-27525	95	5	k	k	PROPN
ajst-27525	95	6	f	f	PROPN
ajst-27525	96	1	x	x	PUNCT
ajst-27525	96	2	e	e	X
ajst-27525	96	3	dx	dx	ADV
ajst-27525	96	4			NOUN
ajst-27525	96	5	in	in	ADP
ajst-27525	96	6	order	order	NOUN
ajst-27525	96	7	to	to	PART
ajst-27525	96	8	remove	remove	VERB
ajst-27525	96	9	redundancy	redundancy	NOUN
ajst-27525	96	10	and	and	CCONJ
ajst-27525	96	11	enhance	enhance	VERB
ajst-27525	96	12	the	the	DET
ajst-27525	96	13	efficiency	efficiency	NOUN
ajst-27525	96	14	of	of	ADP
ajst-27525	96	15	solving	solve	VERB
ajst-27525	96	16	equations	equation	NOUN
ajst-27525	96	17	,	,	PUNCT
ajst-27525	96	18	the	the	DET
ajst-27525	96	19	data	data	NOUN
ajst-27525	96	20	is	be	AUX
ajst-27525	96	21	filtered	filter	VERB
ajst-27525	96	22	in	in	ADP
ajst-27525	96	23	fourier	fourier	ADJ
ajst-27525	96	24	space	space	NOUN
ajst-27525	96	25	to	to	PART
ajst-27525	96	26	eliminate	eliminate	VERB
ajst-27525	96	27	high	high	ADJ
ajst-27525	96	28	-	-	PUNCT
ajst-27525	96	29	order	order	NOUN
ajst-27525	96	30	modes	mode	NOUN
ajst-27525	96	31	while	while	SCONJ
ajst-27525	96	32	retaining	retain	VERB
ajst-27525	96	33	low	low	ADJ
ajst-27525	96	34	-	-	PUNCT
ajst-27525	96	35	order	order	NOUN
ajst-27525	96	36	modes	mode	NOUN
ajst-27525	96	37	.	.	PUNCT
ajst-27525	97	1	subsequently	subsequently	ADV
ajst-27525	97	2	,	,	PUNCT
ajst-27525	97	3	the	the	DET
ajst-27525	97	4	data	data	NOUN
ajst-27525	97	5	is	be	AUX
ajst-27525	97	6	restored	restore	VERB
ajst-27525	97	7	to	to	ADP
ajst-27525	97	8	its	its	PRON
ajst-27525	97	9	original	original	ADJ
ajst-27525	97	10	dimensional	dimensional	ADJ
ajst-27525	97	11	space	space	NOUN
ajst-27525	97	12	through	through	ADP
ajst-27525	97	13	the	the	DET
ajst-27525	97	14	inverse	inverse	NOUN
ajst-27525	97	15	fourier	fourier	NOUN
ajst-27525	97	16	transform	transform	NOUN
ajst-27525	97	17	.	.	PUNCT
ajst-27525	98	1	the	the	DET
ajst-27525	98	2	expression	expression	NOUN
ajst-27525	98	3	for	for	ADP
ajst-27525	98	4	the	the	DET
ajst-27525	98	5	inverse	inverse	NOUN
ajst-27525	98	6	fourier	fourier	NOUN
ajst-27525	98	7	transform	transform	NOUN
ajst-27525	98	8	involved	involve	VERB
ajst-27525	98	9	in	in	ADP
ajst-27525	98	10	this	this	DET
ajst-27525	98	11	process	process	NOUN
ajst-27525	98	12	is	be	AUX
ajst-27525	98	13	as	as	SCONJ
ajst-27525	98	14	follows	follow	VERB
ajst-27525	98	15	:	:	PUNCT
ajst-27525	98	16	2	2	NUM
ajst-27525	98	17	,	,	PUNCT
ajst-27525	98	18	1	1	NUM
ajst-27525	98	19	(	(	PUNCT
ajst-27525	98	20	)	)	PUNCT
ajst-27525	98	21	(	(	PUNCT
ajst-27525	98	22	)	)	PUNCT
ajst-27525	98	23	(	(	PUNCT
ajst-27525	98	24	)	)	PUNCT
ajst-27525	99	1	i	i	PRON
ajst-27525	99	2	x	x	X
ajst-27525	100	1	k	k	PROPN
ajst-27525	100	2	j	j	PROPN
ajst-27525	100	3	jd	jd	PROPN
ajst-27525	100	4	f	f	PROPN
ajst-27525	100	5	f	f	PROPN
ajst-27525	100	6	x	x	X
ajst-27525	100	7	f	f	PROPN
ajst-27525	100	8	k	k	PROPN
ajst-27525	100	9	e	e	PROPN
ajst-27525	100	10	dk	dk	ADV
ajst-27525	100	11			NUM
ajst-27525	100	12			PUNCT
ajst-27525	100	13	furthermore	furthermore	ADV
ajst-27525	100	14	,	,	PUNCT
ajst-27525	100	15	from	from	ADP
ajst-27525	100	16	the	the	DET
ajst-27525	100	17	expressions	expression	NOUN
ajst-27525	100	18	of	of	ADP
ajst-27525	100	19	the	the	DET
ajst-27525	100	20	kernel	kernel	PROPN
ajst-27525	100	21	integral	integral	ADJ
ajst-27525	100	22	operator	operator	NOUN
ajst-27525	100	23	and	and	CCONJ
ajst-27525	100	24	the	the	DET
ajst-27525	100	25	fourier	fourier	NOUN
ajst-27525	100	26	transform	transform	NOUN
ajst-27525	100	27	,	,	PUNCT
ajst-27525	100	28	we	we	PRON
ajst-27525	100	29	can	can	AUX
ajst-27525	100	30	derive	derive	VERB
ajst-27525	100	31	:	:	PUNCT
ajst-27525	101	1			PROPN
ajst-27525	101	2	1	1	NOUN
ajst-27525	101	3	(	(	PUNCT
ajst-27525	101	4	(	(	PUNCT
ajst-27525	101	5	;	;	PUNCT
ajst-27525	101	6	)	)	PUNCT
ajst-27525	101	7	)	)	PUNCT
ajst-27525	101	8	(	(	PUNCT
ajst-27525	101	9	)	)	PUNCT
ajst-27525	101	10	(	(	PUNCT
ajst-27525	101	11	)	)	PUNCT
ajst-27525	101	12	(	(	PUNCT
ajst-27525	101	13	)	)	PUNCT
ajst-27525	101	14	(	(	PUNCT
ajst-27525	101	15	)	)	PUNCT
ajst-27525	101	16	,	,	PUNCT
ajst-27525	101	17	t	t	PROPN
ajst-27525	101	18	ta	ta	X
ajst-27525	101	19	v	v	PROPN
ajst-27525	101	20	x	x	SYM
ajst-27525	101	21	v	v	NOUN
ajst-27525	101	22	x	x	X
ajst-27525	101	23	x	x	PUNCT
ajst-27525	101	24	d	d	ADP
ajst-27525	101	25			NOUN
ajst-27525	101	26			VERB
ajst-27525	101	27			NOUN
ajst-27525	101	28			X
ajst-27525	102	1			PROPN
ajst-27525	102	2			PUNCT
ajst-27525	103	1			PROPN
ajst-27525	103	2	consequently	consequently	ADV
ajst-27525	103	3	,	,	PUNCT
ajst-27525	103	4	the	the	DET
ajst-27525	103	5	fourier	fourier	ADJ
ajst-27525	103	6	integral	integral	ADJ
ajst-27525	103	7	operator	operator	NOUN
ajst-27525	103	8	used	use	VERB
ajst-27525	103	9	in	in	ADP
ajst-27525	103	10	this	this	DET
ajst-27525	103	11	context	context	NOUN
ajst-27525	103	12	can	can	AUX
ajst-27525	103	13	be	be	AUX
ajst-27525	103	14	expressed	express	VERB
ajst-27525	103	15	as	as	ADP
ajst-27525	103	16	:	:	PUNCT
ajst-27525	103	17			PROPN
ajst-27525	103	18	1	1	NOUN
ajst-27525	103	19	(	(	PUNCT
ajst-27525	103	20	(	(	PUNCT
ajst-27525	103	21	)	)	PUNCT
ajst-27525	103	22	)	)	PUNCT
ajst-27525	103	23	(	(	PUNCT
ajst-27525	103	24	)	)	PUNCT
ajst-27525	103	25	(	(	PUNCT
ajst-27525	103	26	)	)	PUNCT
ajst-27525	103	27	(	(	PUNCT
ajst-27525	103	28	)	)	PUNCT
ajst-27525	103	29	,	,	PUNCT
ajst-27525	103	30	t	t	PROPN
ajst-27525	103	31	tv	tv	NOUN
ajst-27525	104	1	x	x	PUNCT
ajst-27525	104	2	r	r	NOUN
ajst-27525	104	3	v	v	NUM
ajst-27525	104	4	x	x	X
ajst-27525	104	5	x	x	X
ajst-27525	104	6	d	d	PROPN
ajst-27525	104	7			ADJ
ajst-27525	104	8			PROPN
ajst-27525	104	9			NOUN
ajst-27525	104	10			PUNCT
ajst-27525	104	11			PROPN
ajst-27525	104	12			PROPN
ajst-27525	104	13	fno	fno	PROPN
ajst-27525	104	14	addresses	address	VERB
ajst-27525	104	15	the	the	DET
ajst-27525	104	16	integral	integral	ADJ
ajst-27525	104	17	term	term	NOUN
ajst-27525	104	18	in	in	ADP
ajst-27525	104	19	operator	operator	NOUN
ajst-27525	104	20	learning	learning	NOUN
ajst-27525	104	21	,	,	PUNCT
ajst-27525	104	22	and	and	CCONJ
ajst-27525	104	23	combining	combine	VERB
ajst-27525	104	24	it	it	PRON
ajst-27525	104	25	with	with	ADP
ajst-27525	104	26	the	the	DET
ajst-27525	104	27	iterative	iterative	NOUN
ajst-27525	104	28	relationship	relationship	NOUN
ajst-27525	104	29	yields	yield	VERB
ajst-27525	104	30	the	the	DET
ajst-27525	104	31	expression	expression	NOUN
ajst-27525	104	32	for	for	ADP
ajst-27525	104	33	the	the	DET
ajst-27525	104	34	established	establish	VERB
ajst-27525	104	35	model	model	NOUN
ajst-27525	104	36	:	:	PUNCT
ajst-27525	104	37			PROPN
ajst-27525	104	38	1	1	PROPN
ajst-27525	104	39	(	(	PUNCT
ajst-27525	104	40	)	)	PUNCT
ajst-27525	104	41	:	:	PUNCT
ajst-27525	104	42	(	(	PUNCT
ajst-27525	104	43	)	)	PUNCT
ajst-27525	104	44	(	(	PUNCT
ajst-27525	104	45	(	(	PUNCT
ajst-27525	104	46	;	;	PUNCT
ajst-27525	104	47	)	)	PUNCT
ajst-27525	104	48	)	)	PUNCT
ajst-27525	104	49	(	(	PUNCT
ajst-27525	104	50	)	)	PUNCT
ajst-27525	104	51	,	,	PUNCT
ajst-27525	104	52	t	t	PROPN
ajst-27525	104	53	t	t	PROPN
ajst-27525	104	54	tv	tv	NOUN
ajst-27525	104	55	x	x	X
ajst-27525	104	56	wv	wv	PROPN
ajst-27525	104	57	x	x	X
ajst-27525	104	58	a	a	DET
ajst-27525	104	59	v	v	NOUN
ajst-27525	104	60	x	x	SYM
ajst-27525	104	61	x	x	NOUN
ajst-27525	104	62	d	d	NOUN
ajst-27525	104	63			NOUN
ajst-27525	104	64			PRON
ajst-27525	104	65			ADV
ajst-27525	104	66			NOUN
ajst-27525	104	67			PUNCT
ajst-27525	104	68	where	where	SCONJ
ajst-27525	104	69	,	,	PUNCT
ajst-27525	104	70	dϵℝ	dϵℝ	NOUN
ajst-27525	104	71	represents	represent	VERB
ajst-27525	104	72	the	the	DET
ajst-27525	104	73	spatial	spatial	ADJ
ajst-27525	104	74	domain	domain	NOUN
ajst-27525	104	75	of	of	ADP
ajst-27525	104	76	the	the	DET
ajst-27525	104	77	pde	pde	NOUN
ajst-27525	104	78	,	,	PUNCT
ajst-27525	104	79	x∈d	x∈d	PROPN
ajst-27525	104	80	is	be	AUX
ajst-27525	104	81	a	a	DET
ajst-27525	104	82	point	point	NOUN
ajst-27525	104	83	in	in	ADP
ajst-27525	104	84	the	the	DET
ajst-27525	104	85	spatial	spatial	ADJ
ajst-27525	104	86	domain	domain	NOUN
ajst-27525	104	87	,	,	PUNCT
ajst-27525	104	88	a∈	a∈	PROPN
ajst-27525	104	89	a	a	DET
ajst-27525	104	90	d	d	NOUN
ajst-27525	104	91	;	;	PUNCT
ajst-27525	104	92	ℝ	ℝ	PROPN
ajst-27525	104	93	denotes	denote	VERB
ajst-27525	104	94	the	the	DET
ajst-27525	104	95	input	input	NOUN
ajst-27525	104	96	coefficient	coefficient	NOUN
ajst-27525	104	97	function	function	NOUN
ajst-27525	104	98	,	,	PUNCT
ajst-27525	104	99	u∈	u∈	PROPN
ajst-27525	104	100	u	u	PROPN
ajst-27525	104	101	d	d	NOUN
ajst-27525	104	102	;	;	PUNCT
ajst-27525	104	103	ℝ	ℝ	PROPN
ajst-27525	104	104	represents	represent	VERB
ajst-27525	104	105	the	the	DET
ajst-27525	104	106	target	target	NOUN
ajst-27525	104	107	solution	solution	NOUN
ajst-27525	104	108	function	function	NOUN
ajst-27525	104	109	,	,	PUNCT
ajst-27525	104	110	𝐷	𝐷	NOUN
ajst-27525	104	111	denotes	denote	VERB
ajst-27525	104	112	the	the	DET
ajst-27525	104	113	discretization	discretization	NOUN
ajst-27525	104	114	of	of	ADP
ajst-27525	104	115	𝑎	𝑎	PRON
ajst-27525	104	116	,	,	PUNCT
ajst-27525	104	117	𝑢	𝑢	PROPN
ajst-27525	104	118	,	,	PUNCT
ajst-27525	104	119	𝜙represents	𝜙represent	VERB
ajst-27525	104	120	the	the	DET
ajst-27525	104	121	parameters	parameter	NOUN
ajst-27525	104	122	of	of	ADP
ajst-27525	104	123	the	the	DET
ajst-27525	104	124	kernel	kernel	PROPN
ajst-27525	104	125	network	network	PROPN
ajst-27525	104	126	𝑘	𝑘	PROPN
ajst-27525	104	127	,	,	PUNCT
ajst-27525	104	128	t=0,	t=0,	NOUN
ajst-27525	104	129	…	…	PUNCT
ajst-27525	104	130	,t	,t	PUNCT
ajst-27525	104	131	indicates	indicate	VERB
ajst-27525	104	132	the	the	DET
ajst-27525	104	133	time	time	NOUN
ajst-27525	104	134	steps	step	NOUN
ajst-27525	104	135	,	,	PUNCT
ajst-27525	104	136	𝜎denotes	𝜎denote	VERB
ajst-27525	104	137	the	the	DET
ajst-27525	104	138	activation	activation	NOUN
ajst-27525	104	139	function	function	NOUN
ajst-27525	104	140	,	,	PUNCT
ajst-27525	104	141	and	and	CCONJ
ajst-27525	104	142	ℱ	ℱ	PROPN
ajst-27525	104	143	and	and	CCONJ
ajst-27525	104	144	ℱ	ℱ	PROPN
ajst-27525	104	145	are	be	AUX
ajst-27525	104	146	the	the	DET
ajst-27525	104	147	fourier	fourier	NOUN
ajst-27525	104	148	transform	transform	NOUN
ajst-27525	104	149	and	and	CCONJ
ajst-27525	104	150	its	its	PRON
ajst-27525	104	151	inverse	inverse	NOUN
ajst-27525	104	152	,	,	PUNCT
ajst-27525	104	153	respectively	respectively	ADV
ajst-27525	104	154	.	.	PUNCT
ajst-27525	105	1	the	the	DET
ajst-27525	105	2	core	core	NOUN
ajst-27525	105	3	concept	concept	NOUN
ajst-27525	105	4	behind	behind	ADP
ajst-27525	105	5	fno	fno	PROPN
ajst-27525	105	6	is	be	AUX
ajst-27525	105	7	to	to	PART
ajst-27525	105	8	operate	operate	VERB
ajst-27525	105	9	within	within	ADP
ajst-27525	105	10	the	the	DET
ajst-27525	105	11	fourier	fourier	ADJ
ajst-27525	105	12	domain	domain	NOUN
ajst-27525	105	13	to	to	PART
ajst-27525	105	14	accelerate	accelerate	VERB
ajst-27525	105	15	computation	computation	NOUN
ajst-27525	105	16	and	and	CCONJ
ajst-27525	105	17	enhance	enhance	VERB
ajst-27525	105	18	prediction	prediction	NOUN
ajst-27525	105	19	accuracy	accuracy	NOUN
ajst-27525	105	20	.	.	PUNCT
ajst-27525	106	1	unlike	unlike	ADP
ajst-27525	106	2	traditional	traditional	ADJ
ajst-27525	106	3	neural	neural	ADJ
ajst-27525	106	4	networks	network	NOUN
ajst-27525	106	5	that	that	PRON
ajst-27525	106	6	perform	perform	VERB
ajst-27525	106	7	convolutions	convolution	NOUN
ajst-27525	106	8	in	in	ADP
ajst-27525	106	9	spatial	spatial	ADJ
ajst-27525	106	10	domains	domain	NOUN
ajst-27525	106	11	,	,	PUNCT
ajst-27525	106	12	fno	fno	PROPN
ajst-27525	106	13	transforms	transform	VERB
ajst-27525	106	14	the	the	DET
ajst-27525	106	15	input	input	NOUN
ajst-27525	106	16	into	into	ADP
ajst-27525	106	17	the	the	DET
ajst-27525	106	18	frequency	frequency	NOUN
ajst-27525	106	19	domain	domain	NOUN
ajst-27525	106	20	via	via	ADP
ajst-27525	106	21	fourier	fourier	NOUN
ajst-27525	106	22	transform	transform	NOUN
ajst-27525	106	23	,	,	PUNCT
ajst-27525	106	24	where	where	SCONJ
ajst-27525	106	25	it	it	PRON
ajst-27525	106	26	learns	learn	VERB
ajst-27525	106	27	features	feature	NOUN
ajst-27525	106	28	more	more	ADV
ajst-27525	106	29	efficiently	efficiently	ADV
ajst-27525	106	30	using	use	VERB
ajst-27525	106	31	the	the	DET
ajst-27525	106	32	characteristic	characteristic	ADJ
ajst-27525	106	33	structure	structure	NOUN
ajst-27525	106	34	of	of	ADP
ajst-27525	106	35	the	the	DET
ajst-27525	106	36	frequency	frequency	NOUN
ajst-27525	106	37	domain	domain	NOUN
ajst-27525	106	38	.	.	PUNCT
ajst-27525	107	1	this	this	DET
ajst-27525	107	2	process	process	NOUN
ajst-27525	107	3	involves	involve	VERB
ajst-27525	107	4	applying	apply	VERB
ajst-27525	107	5	fft	fft	NOUN
ajst-27525	107	6	to	to	ADP
ajst-27525	107	7	the	the	DET
ajst-27525	107	8	input	input	NOUN
ajst-27525	107	9	signal	signal	NOUN
ajst-27525	107	10	,	,	PUNCT
ajst-27525	107	11	capturing	capture	VERB
ajst-27525	107	12	information	information	NOUN
ajst-27525	107	13	across	across	ADP
ajst-27525	107	14	different	different	ADJ
ajst-27525	107	15	frequency	frequency	NOUN
ajst-27525	107	16	components	component	NOUN
ajst-27525	107	17	through	through	ADP
ajst-27525	107	18	convolution	convolution	NOUN
ajst-27525	107	19	,	,	PUNCT
ajst-27525	107	20	and	and	CCONJ
ajst-27525	107	21	then	then	ADV
ajst-27525	107	22	mapping	map	VERB
ajst-27525	107	23	the	the	DET
ajst-27525	107	24	results	result	NOUN
ajst-27525	107	25	back	back	ADV
ajst-27525	107	26	to	to	ADP
ajst-27525	107	27	the	the	DET
ajst-27525	107	28	spatial	spatial	ADJ
ajst-27525	107	29	domain	domain	NOUN
ajst-27525	107	30	using	use	VERB
ajst-27525	107	31	the	the	DET
ajst-27525	107	32	inverse	inverse	ADJ
ajst-27525	107	33	fourier	fourier	NOUN
ajst-27525	107	34	transform	transform	NOUN
ajst-27525	107	35	.	.	PUNCT
ajst-27525	108	1	3.2	3.2	NUM
ajst-27525	108	2	.	.	PUNCT
ajst-27525	108	3	advantages	advantage	NOUN
ajst-27525	108	4	of	of	ADP
ajst-27525	108	5	fno	fno	PROPN
ajst-27525	108	6	compared	compare	VERB
ajst-27525	108	7	to	to	ADP
ajst-27525	108	8	non	non	ADJ
ajst-27525	108	9	-	-	NOUN
ajst-27525	108	10	operator	operator	NOUN
ajst-27525	108	11	-	-	PUNCT
ajst-27525	108	12	based	base	VERB
ajst-27525	108	13	numerical	numerical	ADJ
ajst-27525	108	14	methods	method	NOUN
ajst-27525	108	15	for	for	ADP
ajst-27525	108	16	solving	solve	VERB
ajst-27525	108	17	pdes	pde	NOUN
ajst-27525	108	18	,	,	PUNCT
ajst-27525	108	19	the	the	DET
ajst-27525	108	20	fourier	fourier	ADJ
ajst-27525	108	21	neural	neural	ADJ
ajst-27525	108	22	operator	operator	NOUN
ajst-27525	108	23	offers	offer	VERB
ajst-27525	108	24	several	several	ADJ
ajst-27525	108	25	advantages	advantage	NOUN
ajst-27525	108	26	:	:	PUNCT
ajst-27525	108	27	discretization	discretization	NOUN
ajst-27525	108	28	invariance	invariance	NOUN
ajst-27525	108	29	:	:	PUNCT
ajst-27525	108	30	the	the	DET
ajst-27525	108	31	fourier	fourier	NOUN
ajst-27525	108	32	layers	layer	NOUN
ajst-27525	108	33	in	in	ADP
ajst-27525	108	34	fno	fno	PROPN
ajst-27525	108	35	are	be	AUX
ajst-27525	108	36	discretization	discretization	NOUN
ajst-27525	108	37	-	-	PUNCT
ajst-27525	108	38	invariant	invariant	ADJ
ajst-27525	108	39	,	,	PUNCT
ajst-27525	108	40	allowing	allow	VERB
ajst-27525	108	41	it	it	PRON
ajst-27525	108	42	to	to	PART
ajst-27525	108	43	learn	learn	VERB
ajst-27525	108	44	and	and	CCONJ
ajst-27525	108	45	evaluate	evaluate	VERB
ajst-27525	108	46	functions	function	NOUN
ajst-27525	108	47	discretized	discretize	VERB
ajst-27525	108	48	in	in	ADP
ajst-27525	108	49	any	any	DET
ajst-27525	108	50	manner	manner	NOUN
ajst-27525	108	51	.	.	PUNCT
ajst-27525	109	1	since	since	SCONJ
ajst-27525	109	2	parameters	parameter	NOUN
ajst-27525	109	3	are	be	AUX
ajst-27525	109	4	learned	learn	VERB
ajst-27525	109	5	directly	directly	ADV
ajst-27525	109	6	in	in	ADP
ajst-27525	109	7	the	the	DET
ajst-27525	109	8	fourier	fourier	NOUN
ajst-27525	109	9	space	space	NOUN
ajst-27525	109	10	,	,	PUNCT
ajst-27525	109	11	this	this	PRON
ajst-27525	109	12	effectively	effectively	ADV
ajst-27525	109	13	projects	project	VERB
ajst-27525	109	14	the	the	DET
ajst-27525	109	15	physical	physical	ADJ
ajst-27525	109	16	space	space	NOUN
ajst-27525	109	17	into	into	ADP
ajst-27525	109	18	a	a	DET
ajst-27525	109	19	basis	basis	NOUN
ajst-27525	109	20	defined	define	VERB
ajst-27525	109	21	by	by	ADP
ajst-27525	109	22	𝑒	𝑒	PROPN
ajst-27525	109	23	〈	〈	PROPN
ajst-27525	109	24	,	,	PUNCT
ajst-27525	109	25	〉	〉	NOUN
ajst-27525	109	26	,	,	PUNCT
ajst-27525	109	27	ensuring	ensure	VERB
ajst-27525	109	28	clear	clear	ADJ
ajst-27525	109	29	definition	definition	NOUN
ajst-27525	109	30	throughout	throughout	ADP
ajst-27525	109	31	the	the	DET
ajst-27525	109	32	space	space	NOUN
ajst-27525	109	33	.	.	PUNCT
ajst-27525	110	1	additionally	additionally	ADV
ajst-27525	110	2	,	,	PUNCT
ajst-27525	110	3	the	the	DET
ajst-27525	110	4	use	use	NOUN
ajst-27525	110	5	of	of	ADP
ajst-27525	110	6	fft	fft	PROPN
ajst-27525	110	7	reduces	reduce	VERB
ajst-27525	110	8	computational	computational	ADJ
ajst-27525	110	9	complexity	complexity	NOUN
ajst-27525	110	10	to	to	ADP
ajst-27525	110	11	near	near	ADJ
ajst-27525	110	12	-	-	PUNCT
ajst-27525	110	13	linear	linear	NOUN
ajst-27525	110	14	time	time	NOUN
ajst-27525	110	15	,	,	PUNCT
ajst-27525	110	16	which	which	PRON
ajst-27525	110	17	facilitates	facilitate	VERB
ajst-27525	110	18	large	large	ADJ
ajst-27525	110	19	-	-	PUNCT
ajst-27525	110	20	scale	scale	NOUN
ajst-27525	110	21	computations	computation	NOUN
ajst-27525	110	22	.	.	PUNCT
ajst-27525	111	1	single	single	ADJ
ajst-27525	111	2	parameter	parameter	NOUN
ajst-27525	111	3	set	set	NOUN
ajst-27525	111	4	generation	generation	NOUN
ajst-27525	111	5	,	,	PUNCT
ajst-27525	111	6	independent	independent	ADJ
ajst-27525	111	7	of	of	ADP
ajst-27525	111	8	the	the	DET
ajst-27525	111	9	grid	grid	NOUN
ajst-27525	111	10	:	:	PUNCT
ajst-27525	111	11	fno	fno	PROPN
ajst-27525	111	12	produces	produce	VERB
ajst-27525	111	13	a	a	DET
ajst-27525	111	14	single	single	ADJ
ajst-27525	111	15	set	set	NOUN
ajst-27525	111	16	of	of	ADP
ajst-27525	111	17	network	network	NOUN
ajst-27525	111	18	parameters	parameter	NOUN
ajst-27525	111	19	that	that	PRON
ajst-27525	111	20	are	be	AUX
ajst-27525	111	21	independent	independent	ADJ
ajst-27525	111	22	of	of	ADP
ajst-27525	111	23	the	the	DET
ajst-27525	111	24	grid	grid	NOUN
ajst-27525	111	25	,	,	PUNCT
ajst-27525	111	26	enabling	enable	VERB
ajst-27525	111	27	solutions	solution	NOUN
ajst-27525	111	28	to	to	PART
ajst-27525	111	29	be	be	AUX
ajst-27525	111	30	transferred	transfer	VERB
ajst-27525	111	31	across	across	ADP
ajst-27525	111	32	different	different	ADJ
ajst-27525	111	33	grids	grid	NOUN
ajst-27525	111	34	.	.	PUNCT
ajst-27525	112	1	once	once	ADV
ajst-27525	112	2	trained	train	VERB
ajst-27525	112	3	,	,	PUNCT
ajst-27525	112	4	fno	fno	PROPN
ajst-27525	112	5	only	only	ADV
ajst-27525	112	6	requires	require	VERB
ajst-27525	112	7	a	a	DET
ajst-27525	112	8	forward	forward	ADJ
ajst-27525	112	9	pass	pass	NOUN
ajst-27525	112	10	to	to	PART
ajst-27525	112	11	compute	compute	VERB
ajst-27525	112	12	solutions	solution	NOUN
ajst-27525	112	13	for	for	ADP
ajst-27525	112	14	new	new	ADJ
ajst-27525	112	15	instances	instance	NOUN
ajst-27525	112	16	.	.	PUNCT
ajst-27525	113	1	data	data	NOUN
ajst-27525	113	2	-	-	PUNCT
ajst-27525	113	3	only	only	ADV
ajst-27525	113	4	requirement	requirement	NOUN
ajst-27525	113	5	:	:	PUNCT
ajst-27525	113	6	fno	fno	PROPN
ajst-27525	113	7	requires	require	VERB
ajst-27525	113	8	no	no	DET
ajst-27525	113	9	prior	prior	ADJ
ajst-27525	113	10	knowledge	knowledge	NOUN
ajst-27525	113	11	of	of	ADP
ajst-27525	113	12	the	the	DET
ajst-27525	113	13	underlying	underlie	VERB
ajst-27525	113	14	pde	pde	NOUN
ajst-27525	113	15	;	;	PUNCT
ajst-27525	113	16	only	only	ADV
ajst-27525	113	17	data	datum	NOUN
ajst-27525	113	18	is	be	AUX
ajst-27525	113	19	necessary	necessary	ADJ
ajst-27525	113	20	.	.	PUNCT
ajst-27525	114	1	by	by	ADP
ajst-27525	114	2	employing	employ	VERB
ajst-27525	114	3	fft	fft	NOUN
ajst-27525	114	4	,	,	PUNCT
ajst-27525	114	5	the	the	DET
ajst-27525	114	6	neural	neural	ADJ
ajst-27525	114	7	operator	operator	NOUN
ajst-27525	114	8	can	can	AUX
ajst-27525	114	9	produce	produce	VERB
ajst-27525	114	10	efficient	efficient	ADJ
ajst-27525	114	11	numerical	numerical	ADJ
ajst-27525	114	12	algorithms	algorithm	NOUN
ajst-27525	114	13	in	in	ADP
ajst-27525	114	14	finite	finite	ADJ
ajst-27525	114	15	-	-	ADJ
ajst-27525	114	16	dimensional	dimensional	ADJ
ajst-27525	114	17	environments	environment	NOUN
ajst-27525	114	18	that	that	PRON
ajst-27525	114	19	parallel	parallel	VERB
ajst-27525	114	20	convolutional	convolutional	ADJ
ajst-27525	114	21	or	or	CCONJ
ajst-27525	114	22	recurrent	recurrent	ADJ
ajst-27525	114	23	neural	neural	ADJ
ajst-27525	114	24	networks	network	NOUN
ajst-27525	114	25	.	.	PUNCT
ajst-27525	115	1	high	high	ADJ
ajst-27525	115	2	-	-	PUNCT
ajst-27525	115	3	efficiency	efficiency	NOUN
ajst-27525	115	4	zero	zero	NUM
ajst-27525	115	5	-	-	PUNCT
ajst-27525	115	6	shot	shot	NOUN
ajst-27525	115	7	super	super	NOUN
ajst-27525	115	8	-	-	NOUN
ajst-27525	115	9	resolution	resolution	NOUN
ajst-27525	115	10	:	:	PUNCT
ajst-27525	115	11	fno	fno	PROPN
ajst-27525	115	12	is	be	AUX
ajst-27525	115	13	185	185	NUM
ajst-27525	115	14	the	the	DET
ajst-27525	115	15	first	first	ADJ
ajst-27525	115	16	machine	machine	NOUN
ajst-27525	115	17	learning	learn	VERB
ajst-27525	115	18	approach	approach	NOUN
ajst-27525	115	19	capable	capable	ADJ
ajst-27525	115	20	of	of	ADP
ajst-27525	115	21	zero	zero	NUM
ajst-27525	115	22	-	-	PUNCT
ajst-27525	115	23	shot	shot	NOUN
ajst-27525	115	24	super	super	ADJ
ajst-27525	115	25	-	-	NOUN
ajst-27525	115	26	resolution	resolution	ADJ
ajst-27525	115	27	modeling	modeling	NOUN
ajst-27525	115	28	of	of	ADP
ajst-27525	115	29	turbulence	turbulence	NOUN
ajst-27525	115	30	,	,	PUNCT
ajst-27525	115	31	operating	operate	VERB
ajst-27525	115	32	at	at	ADP
ajst-27525	115	33	speeds	speed	NOUN
ajst-27525	115	34	three	three	NUM
ajst-27525	115	35	orders	order	NOUN
ajst-27525	115	36	of	of	ADP
ajst-27525	115	37	magnitude	magnitude	NOUN
ajst-27525	115	38	faster	fast	ADV
ajst-27525	115	39	than	than	ADP
ajst-27525	115	40	traditional	traditional	ADJ
ajst-27525	115	41	pde	pde	NOUN
ajst-27525	115	42	solvers	solver	NOUN
ajst-27525	115	43	.	.	PUNCT
ajst-27525	116	1	at	at	ADP
ajst-27525	116	2	fixed	fix	VERB
ajst-27525	116	3	resolutions	resolution	NOUN
ajst-27525	116	4	,	,	PUNCT
ajst-27525	116	5	fno	fno	PROPN
ajst-27525	116	6	achieves	achieve	VERB
ajst-27525	116	7	higher	high	ADJ
ajst-27525	116	8	accuracy	accuracy	NOUN
ajst-27525	116	9	than	than	ADP
ajst-27525	116	10	previous	previous	ADJ
ajst-27525	116	11	learning	learning	NOUN
ajst-27525	116	12	-	-	PUNCT
ajst-27525	116	13	based	base	VERB
ajst-27525	116	14	solvers	solver	NOUN
ajst-27525	116	15	.	.	PUNCT
ajst-27525	117	1	4	4	X
ajst-27525	117	2	.	.	X
ajst-27525	117	3	factors	factor	NOUN
ajst-27525	117	4	affecting	affect	VERB
ajst-27525	117	5	fno	fno	PROPN
ajst-27525	117	6	solution	solution	NOUN
ajst-27525	117	7	accuracy	accuracy	NOUN
ajst-27525	117	8	when	when	SCONJ
ajst-27525	117	9	using	use	VERB
ajst-27525	117	10	the	the	DET
ajst-27525	117	11	fourier	fourier	ADJ
ajst-27525	117	12	neural	neural	ADJ
ajst-27525	117	13	operator	operator	NOUN
ajst-27525	117	14	to	to	PART
ajst-27525	117	15	solve	solve	VERB
ajst-27525	117	16	twophase	twophase	NOUN
ajst-27525	117	17	oil	oil	NOUN
ajst-27525	117	18	-	-	PUNCT
ajst-27525	117	19	water	water	NOUN
ajst-27525	117	20	flow	flow	NOUN
ajst-27525	117	21	partial	partial	ADJ
ajst-27525	117	22	differential	differential	NOUN
ajst-27525	117	23	equations	equation	NOUN
ajst-27525	117	24	,	,	PUNCT
ajst-27525	117	25	several	several	ADJ
ajst-27525	117	26	key	key	ADJ
ajst-27525	117	27	factors	factor	NOUN
ajst-27525	117	28	affect	affect	VERB
ajst-27525	117	29	the	the	DET
ajst-27525	117	30	accuracy	accuracy	NOUN
ajst-27525	117	31	of	of	ADP
ajst-27525	117	32	the	the	DET
ajst-27525	117	33	solution	solution	NOUN
ajst-27525	117	34	:	:	PUNCT
ajst-27525	117	35	the	the	DET
ajst-27525	117	36	neural	neural	ADJ
ajst-27525	117	37	network	network	NOUN
ajst-27525	117	38	structure	structure	NOUN
ajst-27525	117	39	,	,	PUNCT
ajst-27525	117	40	dataset	dataset	NOUN
ajst-27525	117	41	size	size	NOUN
ajst-27525	117	42	,	,	PUNCT
ajst-27525	117	43	as	as	ADV
ajst-27525	117	44	well	well	ADV
ajst-27525	117	45	as	as	ADP
ajst-27525	117	46	the	the	DET
ajst-27525	117	47	choice	choice	NOUN
ajst-27525	117	48	of	of	ADP
ajst-27525	117	49	optimizer	optimizer	NOUN
ajst-27525	117	50	and	and	CCONJ
ajst-27525	117	51	activation	activation	NOUN
ajst-27525	117	52	function	function	NOUN
ajst-27525	117	53	.	.	PUNCT
ajst-27525	118	1	4.1	4.1	NUM
ajst-27525	118	2	.	.	PUNCT
ajst-27525	118	3	neural	neural	ADJ
ajst-27525	118	4	network	network	NOUN
ajst-27525	118	5	structure	structure	NOUN
ajst-27525	118	6	figure	figure	NOUN
ajst-27525	118	7	1	1	NUM
ajst-27525	118	8	.	.	PUNCT
ajst-27525	118	9	structure	structure	NOUN
ajst-27525	118	10	of	of	ADP
ajst-27525	118	11	the	the	DET
ajst-27525	118	12	fourier	fourier	NOUN
ajst-27525	118	13	neural	neural	ADJ
ajst-27525	118	14	operator	operator	NOUN
ajst-27525	118	15	(	(	PUNCT
ajst-27525	118	16	a	a	X
ajst-27525	118	17	)	)	PUNCT
ajst-27525	118	18	overall	overall	ADJ
ajst-27525	118	19	neural	neural	ADJ
ajst-27525	118	20	operator	operator	NOUN
ajst-27525	118	21	structure	structure	NOUN
ajst-27525	118	22	:	:	PUNCT
ajst-27525	118	23	the	the	DET
ajst-27525	118	24	input	input	NOUN
ajst-27525	118	25	,	,	PUNCT
ajst-27525	118	26	denoted	denote	VERB
ajst-27525	118	27	as	as	ADP
ajst-27525	118	28	aaa	aaa	NOUN
ajst-27525	118	29	,	,	PUNCT
ajst-27525	118	30	is	be	AUX
ajst-27525	118	31	first	first	ADV
ajst-27525	118	32	mapped	map	VERB
ajst-27525	118	33	into	into	ADP
ajst-27525	118	34	a	a	DET
ajst-27525	118	35	higher	higher	ADV
ajst-27525	118	36	-	-	PUNCT
ajst-27525	118	37	dimensional	dimensional	ADJ
ajst-27525	118	38	channel	channel	NOUN
ajst-27525	118	39	space	space	NOUN
ajst-27525	118	40	via	via	ADP
ajst-27525	118	41	the	the	DET
ajst-27525	118	42	neural	neural	ADJ
ajst-27525	118	43	network	network	NOUN
ajst-27525	118	44	.	.	PUNCT
ajst-27525	119	1	this	this	PRON
ajst-27525	119	2	is	be	AUX
ajst-27525	119	3	followed	follow	VERB
ajst-27525	119	4	by	by	ADP
ajst-27525	119	5	applying	apply	VERB
ajst-27525	119	6	four	four	NUM
ajst-27525	119	7	integral	integral	ADJ
ajst-27525	119	8	operator	operator	NOUN
ajst-27525	119	9	layers	layer	NOUN
ajst-27525	119	10	and	and	CCONJ
ajst-27525	119	11	activation	activation	NOUN
ajst-27525	119	12	functions	function	NOUN
ajst-27525	119	13	,	,	PUNCT
ajst-27525	119	14	then	then	ADV
ajst-27525	119	15	projected	project	VERB
ajst-27525	119	16	back	back	ADV
ajst-27525	119	17	to	to	ADP
ajst-27525	119	18	the	the	DET
ajst-27525	119	19	target	target	NOUN
ajst-27525	119	20	dimension	dimension	NOUN
ajst-27525	119	21	by	by	ADP
ajst-27525	119	22	the	the	DET
ajst-27525	119	23	network	network	NOUN
ajst-27525	119	24	q	q	NOUN
ajst-27525	119	25	,	,	PUNCT
ajst-27525	119	26	resulting	result	VERB
ajst-27525	119	27	in	in	ADP
ajst-27525	119	28	the	the	DET
ajst-27525	119	29	output	output	NOUN
ajst-27525	119	30	u.	u.	NOUN
ajst-27525	119	31	(	(	PUNCT
ajst-27525	119	32	b	b	X
ajst-27525	119	33	)	)	PUNCT
ajst-27525	119	34	fourier	fourier	ADJ
ajst-27525	119	35	layer	layer	NOUN
ajst-27525	119	36	:	:	PUNCT
ajst-27525	119	37	starting	start	VERB
ajst-27525	119	38	with	with	ADP
ajst-27525	119	39	input	input	NOUN
ajst-27525	119	40	v	v	NOUN
ajst-27525	119	41	,	,	PUNCT
ajst-27525	119	42	the	the	DET
ajst-27525	119	43	fourier	fourier	NOUN
ajst-27525	119	44	transform	transform	NOUN
ajst-27525	119	45	f	f	PROPN
ajst-27525	119	46	is	be	AUX
ajst-27525	119	47	applied	apply	VERB
ajst-27525	119	48	.	.	PUNCT
ajst-27525	120	1	a	a	DET
ajst-27525	120	2	linear	linear	ADJ
ajst-27525	120	3	transformation	transformation	NOUN
ajst-27525	120	4	r	r	NOUN
ajst-27525	120	5	is	be	AUX
ajst-27525	120	6	then	then	ADV
ajst-27525	120	7	applied	apply	VERB
ajst-27525	120	8	to	to	ADP
ajst-27525	120	9	the	the	DET
ajst-27525	120	10	lower	low	ADJ
ajst-27525	120	11	fourier	fourier	NOUN
ajst-27525	120	12	modes	mode	NOUN
ajst-27525	120	13	while	while	SCONJ
ajst-27525	120	14	filtering	filter	VERB
ajst-27525	120	15	out	out	ADP
ajst-27525	120	16	higher	high	ADJ
ajst-27525	120	17	modes	mode	NOUN
ajst-27525	120	18	,	,	PUNCT
ajst-27525	120	19	followed	follow	VERB
ajst-27525	120	20	by	by	ADP
ajst-27525	120	21	an	an	DET
ajst-27525	120	22	inverse	inverse	NOUN
ajst-27525	120	23	fourier	fourier	NOUN
ajst-27525	120	24	transform	transform	VERB
ajst-27525	120	25	f−1	f−1	PROPN
ajst-27525	120	26	.	.	PUNCT
ajst-27525	121	1	a	a	DET
ajst-27525	121	2	local	local	ADJ
ajst-27525	121	3	linear	linear	NOUN
ajst-27525	121	4	transformation	transformation	NOUN
ajst-27525	121	5	w	w	NOUN
ajst-27525	121	6	is	be	AUX
ajst-27525	121	7	applied	apply	VERB
ajst-27525	121	8	at	at	ADP
ajst-27525	121	9	the	the	DET
ajst-27525	121	10	bottom	bottom	NOUN
ajst-27525	121	11	.	.	PUNCT
ajst-27525	122	1	4.2	4.2	NUM
ajst-27525	122	2	.	.	PUNCT
ajst-27525	123	1	choice	choice	NOUN
ajst-27525	123	2	of	of	ADP
ajst-27525	123	3	activation	activation	NOUN
ajst-27525	123	4	function	function	VERB
ajst-27525	123	5	the	the	DET
ajst-27525	123	6	selection	selection	NOUN
ajst-27525	123	7	of	of	ADP
ajst-27525	123	8	an	an	DET
ajst-27525	123	9	activation	activation	NOUN
ajst-27525	123	10	function	function	NOUN
ajst-27525	123	11	is	be	AUX
ajst-27525	123	12	critical	critical	ADJ
ajst-27525	123	13	to	to	PART
ajst-27525	123	14	enhance	enhance	VERB
ajst-27525	123	15	the	the	DET
ajst-27525	123	16	network	network	NOUN
ajst-27525	123	17	’s	’s	PART
ajst-27525	123	18	fitting	fitting	ADJ
ajst-27525	123	19	capability	capability	NOUN
ajst-27525	123	20	and	and	CCONJ
ajst-27525	123	21	ensure	ensure	VERB
ajst-27525	123	22	effective	effective	ADJ
ajst-27525	123	23	training	training	NOUN
ajst-27525	123	24	.	.	PUNCT
ajst-27525	124	1	common	common	ADJ
ajst-27525	124	2	activation	activation	NOUN
ajst-27525	124	3	functions	function	NOUN
ajst-27525	124	4	include	include	VERB
ajst-27525	124	5	the	the	DET
ajst-27525	124	6	sigmoid	sigmoid	NOUN
ajst-27525	124	7	,	,	PUNCT
ajst-27525	124	8	relu	relu	NOUN
ajst-27525	124	9	,	,	PUNCT
ajst-27525	124	10	and	and	CCONJ
ajst-27525	124	11	gelu	gelu	NOUN
ajst-27525	124	12	functions	function	NOUN
ajst-27525	124	13	:	:	PUNCT
ajst-27525	124	14	sigmoid	sigmoid	NOUN
ajst-27525	124	15	functions	function	NOUN
ajst-27525	124	16	:	:	PUNCT
ajst-27525	124	17	these	these	PRON
ajst-27525	124	18	include	include	VERB
ajst-27525	124	19	s	s	NOUN
ajst-27525	124	20	-	-	PUNCT
ajst-27525	124	21	shaped	shape	VERB
ajst-27525	124	22	functions	function	NOUN
ajst-27525	124	23	like	like	ADP
ajst-27525	124	24	the	the	DET
ajst-27525	124	25	logistic	logistic	ADJ
ajst-27525	124	26	and	and	CCONJ
ajst-27525	124	27	tanh	tanh	NOUN
ajst-27525	124	28	functions	function	NOUN
ajst-27525	124	29	.	.	PUNCT
ajst-27525	125	1	the	the	DET
ajst-27525	125	2	logistic	logistic	ADJ
ajst-27525	125	3	function	function	NOUN
ajst-27525	125	4	,	,	PUNCT
ajst-27525	125	5	which	which	PRON
ajst-27525	125	6	compresses	compress	VERB
ajst-27525	125	7	inputs	input	NOUN
ajst-27525	125	8	into	into	ADP
ajst-27525	125	9	the	the	DET
ajst-27525	125	10	range	range	NOUN
ajst-27525	125	11	(	(	PUNCT
ajst-27525	125	12	0	0	NUM
ajst-27525	125	13	,	,	PUNCT
ajst-27525	125	14	1	1	NUM
ajst-27525	125	15	)	)	PUNCT
ajst-27525	125	16	,	,	PUNCT
ajst-27525	125	17	is	be	AUX
ajst-27525	125	18	continuously	continuously	ADV
ajst-27525	125	19	differentiable	differentiable	ADJ
ajst-27525	125	20	and	and	CCONJ
ajst-27525	125	21	maps	map	VERB
ajst-27525	125	22	smaller	small	ADJ
ajst-27525	125	23	inputs	input	NOUN
ajst-27525	125	24	closer	close	ADV
ajst-27525	125	25	to	to	ADP
ajst-27525	125	26	0	0	NUM
ajst-27525	126	1	and	and	CCONJ
ajst-27525	126	2	larger	large	ADJ
ajst-27525	126	3	inputs	input	NOUN
ajst-27525	126	4	closer	close	ADV
ajst-27525	126	5	to	to	ADP
ajst-27525	126	6	1	1	NUM
ajst-27525	126	7	.	.	PUNCT
ajst-27525	127	1	the	the	DET
ajst-27525	127	2	tanh	tanh	PROPN
ajst-27525	127	3	function	function	NOUN
ajst-27525	127	4	,	,	PUNCT
ajst-27525	127	5	similarly	similarly	ADV
ajst-27525	127	6	s	s	X
ajst-27525	127	7	-	-	VERB
ajst-27525	127	8	shaped	shaped	ADJ
ajst-27525	127	9	,	,	PUNCT
ajst-27525	127	10	scales	scale	VERB
ajst-27525	127	11	to	to	ADP
ajst-27525	127	12	a	a	DET
ajst-27525	127	13	range	range	NOUN
ajst-27525	127	14	of	of	ADP
ajst-27525	127	15	(	(	PUNCT
ajst-27525	127	16	−1,1	−1,1	NOUN
ajst-27525	127	17	)	)	PUNCT
ajst-27525	127	18	,	,	PUNCT
ajst-27525	127	19	essentially	essentially	ADV
ajst-27525	127	20	stretching	stretch	VERB
ajst-27525	127	21	and	and	CCONJ
ajst-27525	127	22	shifting	shift	VERB
ajst-27525	127	23	the	the	DET
ajst-27525	127	24	logistic	logistic	ADJ
ajst-27525	127	25	function	function	NOUN
ajst-27525	127	26	.	.	PUNCT
ajst-27525	128	1	relu	relu	NOUN
ajst-27525	128	2	(	(	PUNCT
ajst-27525	128	3	rectified	rectify	VERB
ajst-27525	128	4	linear	linear	NOUN
ajst-27525	128	5	unit	unit	NOUN
ajst-27525	128	6	):	):	PUNCT
ajst-27525	128	7	relu	relu	NOUN
ajst-27525	128	8	is	be	AUX
ajst-27525	128	9	frequently	frequently	ADV
ajst-27525	128	10	used	use	VERB
ajst-27525	128	11	in	in	ADP
ajst-27525	128	12	deep	deep	ADJ
ajst-27525	128	13	neural	neural	ADJ
ajst-27525	128	14	networks	network	NOUN
ajst-27525	128	15	and	and	CCONJ
ajst-27525	128	16	is	be	AUX
ajst-27525	128	17	characterized	characterize	VERB
ajst-27525	128	18	by	by	ADP
ajst-27525	128	19	a	a	DET
ajst-27525	128	20	ramp	ramp	NOUN
ajst-27525	128	21	function	function	NOUN
ajst-27525	128	22	that	that	PRON
ajst-27525	128	23	is	be	AUX
ajst-27525	128	24	computationally	computationally	ADV
ajst-27525	128	25	efficient	efficient	ADJ
ajst-27525	128	26	and	and	CCONJ
ajst-27525	128	27	biologically	biologically	ADV
ajst-27525	128	28	plausible	plausible	ADJ
ajst-27525	128	29	.	.	PUNCT
ajst-27525	129	1	relu	relu	NOUN
ajst-27525	129	2	promotes	promote	VERB
ajst-27525	129	3	sparsity	sparsity	NOUN
ajst-27525	129	4	,	,	PUNCT
ajst-27525	129	5	as	as	SCONJ
ajst-27525	129	6	nearly	nearly	ADV
ajst-27525	129	7	half	half	NOUN
ajst-27525	129	8	of	of	ADP
ajst-27525	129	9	the	the	DET
ajst-27525	129	10	neurons	neuron	NOUN
ajst-27525	129	11	remain	remain	VERB
ajst-27525	129	12	inactive	inactive	ADJ
ajst-27525	129	13	,	,	PUNCT
ajst-27525	129	14	enhancing	enhance	VERB
ajst-27525	129	15	computational	computational	ADJ
ajst-27525	129	16	efficiency	efficiency	NOUN
ajst-27525	129	17	.	.	PUNCT
ajst-27525	130	1	however	however	ADV
ajst-27525	130	2	,	,	PUNCT
ajst-27525	130	3	inappropriate	inappropriate	ADJ
ajst-27525	130	4	parameter	parameter	NOUN
ajst-27525	130	5	updates	update	NOUN
ajst-27525	130	6	can	can	AUX
ajst-27525	130	7	cause	cause	VERB
ajst-27525	130	8	the	the	DET
ajst-27525	130	9	“	"	PUNCT
ajst-27525	130	10	dying	die	VERB
ajst-27525	130	11	relu	relu	NOUN
ajst-27525	130	12	”	"	PUNCT
ajst-27525	130	13	problem	problem	NOUN
ajst-27525	130	14	,	,	PUNCT
ajst-27525	130	15	where	where	SCONJ
ajst-27525	130	16	neurons	neuron	NOUN
ajst-27525	130	17	are	be	AUX
ajst-27525	130	18	permanently	permanently	ADV
ajst-27525	130	19	inactive	inactive	ADJ
ajst-27525	130	20	.	.	PUNCT
ajst-27525	131	1	gelu	gelu	NOUN
ajst-27525	131	2	(	(	PUNCT
ajst-27525	131	3	gaussian	gaussian	ADJ
ajst-27525	131	4	error	error	NOUN
ajst-27525	131	5	linear	linear	NOUN
ajst-27525	131	6	unit	unit	NOUN
ajst-27525	131	7	):	):	PUNCT
ajst-27525	131	8	the	the	DET
ajst-27525	131	9	gelu	gelu	ADJ
ajst-27525	131	10	activation	activation	NOUN
ajst-27525	131	11	function	function	NOUN
ajst-27525	132	1	[	[	X
ajst-27525	132	2	hendrycks	hendryck	NOUN
ajst-27525	132	3	et	et	NOUN
ajst-27525	132	4	al	al	PROPN
ajst-27525	132	5	.	.	PROPN
ajst-27525	132	6	,	,	PUNCT
ajst-27525	132	7	2016	2016	NUM
ajst-27525	132	8	]	]	PUNCT
ajst-27525	132	9	uses	use	VERB
ajst-27525	132	10	a	a	DET
ajst-27525	132	11	gating	gate	VERB
ajst-27525	132	12	mechanism	mechanism	NOUN
ajst-27525	132	13	to	to	PART
ajst-27525	132	14	adjust	adjust	VERB
ajst-27525	132	15	its	its	PRON
ajst-27525	132	16	output	output	NOUN
ajst-27525	132	17	based	base	VERB
ajst-27525	132	18	on	on	ADP
ajst-27525	132	19	a	a	DET
ajst-27525	132	20	gaussian	gaussian	ADJ
ajst-27525	132	21	cumulative	cumulative	ADJ
ajst-27525	132	22	distribution	distribution	NOUN
ajst-27525	132	23	function	function	NOUN
ajst-27525	132	24	,	,	PUNCT
ajst-27525	132	25	producing	produce	VERB
ajst-27525	132	26	an	an	DET
ajst-27525	132	27	s	s	ADV
ajst-27525	132	28	-	-	PUNCT
ajst-27525	132	29	shaped	shape	VERB
ajst-27525	132	30	curve	curve	NOUN
ajst-27525	132	31	that	that	PRON
ajst-27525	132	32	can	can	AUX
ajst-27525	132	33	be	be	AUX
ajst-27525	132	34	approximated	approximate	VERB
ajst-27525	132	35	using	use	VERB
ajst-27525	132	36	logistic	logistic	ADJ
ajst-27525	132	37	or	or	CCONJ
ajst-27525	132	38	tanh	tanh	NOUN
ajst-27525	132	39	functions	function	NOUN
ajst-27525	132	40	.	.	PUNCT
ajst-27525	133	1	for	for	ADP
ajst-27525	133	2	two	two	NUM
ajst-27525	133	3	-	-	PUNCT
ajst-27525	133	4	phase	phase	NOUN
ajst-27525	133	5	flow	flow	NOUN
ajst-27525	133	6	problems	problem	NOUN
ajst-27525	133	7	,	,	PUNCT
ajst-27525	133	8	gelu	gelu	NOUN
ajst-27525	133	9	and	and	CCONJ
ajst-27525	133	10	relu	relu	NOUN
ajst-27525	133	11	are	be	AUX
ajst-27525	133	12	generally	generally	ADV
ajst-27525	133	13	well	well	ADV
ajst-27525	133	14	-	-	PUNCT
ajst-27525	133	15	suited	suited	ADJ
ajst-27525	133	16	because	because	SCONJ
ajst-27525	133	17	they	they	PRON
ajst-27525	133	18	support	support	VERB
ajst-27525	133	19	fast	fast	ADJ
ajst-27525	133	20	convergence	convergence	NOUN
ajst-27525	133	21	and	and	CCONJ
ajst-27525	133	22	network	network	NOUN
ajst-27525	133	23	stability	stability	NOUN
ajst-27525	133	24	.	.	PUNCT
ajst-27525	134	1	gelu	gelu	PROPN
ajst-27525	134	2	’s	’s	PART
ajst-27525	134	3	smoother	smooth	ADJ
ajst-27525	134	4	handling	handling	NOUN
ajst-27525	134	5	of	of	ADP
ajst-27525	134	6	nonlinear	nonlinear	ADJ
ajst-27525	134	7	features	feature	NOUN
ajst-27525	134	8	makes	make	VERB
ajst-27525	134	9	it	it	PRON
ajst-27525	134	10	ideal	ideal	ADJ
ajst-27525	134	11	for	for	ADP
ajst-27525	134	12	complex	complex	ADJ
ajst-27525	134	13	multi	multi	ADJ
ajst-27525	134	14	-	-	ADJ
ajst-27525	134	15	phase	phase	NOUN
ajst-27525	134	16	flows	flow	VERB
ajst-27525	134	17	,	,	PUNCT
ajst-27525	134	18	while	while	SCONJ
ajst-27525	134	19	relu	relu	NOUN
ajst-27525	134	20	effectively	effectively	ADV
ajst-27525	134	21	supports	support	VERB
ajst-27525	134	22	high	high	ADJ
ajst-27525	134	23	-	-	PUNCT
ajst-27525	134	24	dimensional	dimensional	ADJ
ajst-27525	134	25	feature	feature	NOUN
ajst-27525	134	26	extraction	extraction	NOUN
ajst-27525	134	27	.	.	PUNCT
ajst-27525	135	1	4.3	4.3	NUM
ajst-27525	135	2	.	.	PUNCT
ajst-27525	135	3	choice	choice	NOUN
ajst-27525	135	4	of	of	ADP
ajst-27525	135	5	optimizer	optimizer	NOUN
ajst-27525	135	6	the	the	DET
ajst-27525	135	7	optimizer	optimizer	NOUN
ajst-27525	135	8	’s	’s	PART
ajst-27525	135	9	role	role	NOUN
ajst-27525	135	10	is	be	AUX
ajst-27525	135	11	to	to	PART
ajst-27525	135	12	direct	direct	VERB
ajst-27525	135	13	parameter	parameter	NOUN
ajst-27525	135	14	updates	update	NOUN
ajst-27525	135	15	in	in	ADP
ajst-27525	135	16	the	the	DET
ajst-27525	135	17	loss	loss	NOUN
ajst-27525	135	18	function	function	NOUN
ajst-27525	135	19	towards	towards	ADP
ajst-27525	135	20	minimizing	minimize	VERB
ajst-27525	135	21	errors	error	NOUN
ajst-27525	135	22	globally	globally	ADV
ajst-27525	135	23	or	or	CCONJ
ajst-27525	135	24	,	,	PUNCT
ajst-27525	135	25	in	in	ADP
ajst-27525	135	26	some	some	DET
ajst-27525	135	27	cases	case	NOUN
ajst-27525	135	28	,	,	PUNCT
ajst-27525	135	29	locally	locally	ADV
ajst-27525	135	30	.	.	PUNCT
ajst-27525	136	1	common	common	ADJ
ajst-27525	136	2	optimizers	optimizer	NOUN
ajst-27525	136	3	include	include	VERB
ajst-27525	136	4	:	:	PUNCT
ajst-27525	136	5	stochastic	stochastic	ADJ
ajst-27525	136	6	gradient	gradient	ADJ
ajst-27525	136	7	descent	descent	NOUN
ajst-27525	136	8	(	(	PUNCT
ajst-27525	136	9	sgd	sgd	PROPN
ajst-27525	136	10	):	):	PUNCT
ajst-27525	136	11	a	a	DET
ajst-27525	136	12	fundamental	fundamental	ADJ
ajst-27525	136	13	optimization	optimization	NOUN
ajst-27525	136	14	algorithm	algorithm	NOUN
ajst-27525	136	15	,	,	PUNCT
ajst-27525	136	16	sgd	sgd	PROPN
ajst-27525	136	17	updates	updates	PROPN
ajst-27525	136	18	model	model	NOUN
ajst-27525	136	19	parameters	parameter	NOUN
ajst-27525	136	20	using	use	VERB
ajst-27525	136	21	the	the	DET
ajst-27525	136	22	gradient	gradient	NOUN
ajst-27525	136	23	of	of	ADP
ajst-27525	136	24	a	a	DET
ajst-27525	136	25	single	single	ADJ
ajst-27525	136	26	(	(	PUNCT
ajst-27525	136	27	or	or	CCONJ
ajst-27525	136	28	mini	mini	NOUN
ajst-27525	136	29	-	-	NOUN
ajst-27525	136	30	batch	batch	NOUN
ajst-27525	136	31	)	)	PUNCT
ajst-27525	136	32	sample	sample	NOUN
ajst-27525	136	33	.	.	PUNCT
ajst-27525	137	1	while	while	SCONJ
ajst-27525	137	2	computationally	computationally	ADV
ajst-27525	137	3	efficient	efficient	ADJ
ajst-27525	137	4	,	,	PUNCT
ajst-27525	137	5	it	it	PRON
ajst-27525	137	6	may	may	AUX
ajst-27525	137	7	converge	converge	VERB
ajst-27525	137	8	slowly	slowly	ADV
ajst-27525	137	9	or	or	CCONJ
ajst-27525	137	10	become	become	VERB
ajst-27525	137	11	trapped	trapped	ADJ
ajst-27525	137	12	in	in	ADP
ajst-27525	137	13	local	local	ADJ
ajst-27525	137	14	minima	minima	PROPN
ajst-27525	137	15	.	.	PUNCT
ajst-27525	138	1	adagrad	adagrad	PROPN
ajst-27525	138	2	:	:	PUNCT
ajst-27525	138	3	this	this	DET
ajst-27525	138	4	algorithm	algorithm	NOUN
ajst-27525	138	5	adapts	adapt	VERB
ajst-27525	138	6	the	the	DET
ajst-27525	138	7	learning	learning	NOUN
ajst-27525	138	8	rate	rate	NOUN
ajst-27525	138	9	for	for	ADP
ajst-27525	138	10	each	each	DET
ajst-27525	138	11	parameter	parameter	NOUN
ajst-27525	138	12	based	base	VERB
ajst-27525	138	13	on	on	ADP
ajst-27525	138	14	the	the	DET
ajst-27525	138	15	history	history	NOUN
ajst-27525	138	16	of	of	ADP
ajst-27525	138	17	gradients	gradient	NOUN
ajst-27525	138	18	,	,	PUNCT
ajst-27525	138	19	diminishing	diminish	VERB
ajst-27525	138	20	the	the	DET
ajst-27525	138	21	rate	rate	NOUN
ajst-27525	138	22	for	for	ADP
ajst-27525	138	23	frequently	frequently	ADV
ajst-27525	138	24	updated	update	VERB
ajst-27525	138	25	parameters	parameter	NOUN
ajst-27525	138	26	.	.	PUNCT
ajst-27525	139	1	adagrad	adagrad	PROPN
ajst-27525	139	2	is	be	AUX
ajst-27525	139	3	advantageous	advantageous	ADJ
ajst-27525	139	4	for	for	ADP
ajst-27525	139	5	handling	handle	VERB
ajst-27525	139	6	sparse	sparse	ADJ
ajst-27525	139	7	data	datum	NOUN
ajst-27525	139	8	and	and	CCONJ
ajst-27525	139	9	automatically	automatically	ADV
ajst-27525	139	10	adjusts	adjust	VERB
ajst-27525	139	11	learning	learn	VERB
ajst-27525	139	12	rates	rate	NOUN
ajst-27525	139	13	during	during	ADP
ajst-27525	139	14	training	training	NOUN
ajst-27525	139	15	.	.	PUNCT
ajst-27525	140	1	adam	adam	PROPN
ajst-27525	140	2	optimizer	optimizer	NOUN
ajst-27525	140	3	:	:	PUNCT
ajst-27525	140	4	adam	adam	PROPN
ajst-27525	140	5	combines	combine	VERB
ajst-27525	140	6	momentum	momentum	NOUN
ajst-27525	140	7	with	with	ADP
ajst-27525	140	8	rmsprop	rmsprop	NOUN
ajst-27525	140	9	by	by	ADP
ajst-27525	140	10	updating	update	VERB
ajst-27525	140	11	learning	learning	NOUN
ajst-27525	140	12	rates	rate	NOUN
ajst-27525	140	13	based	base	VERB
ajst-27525	140	14	on	on	ADP
ajst-27525	140	15	both	both	CCONJ
ajst-27525	140	16	first	first	ADJ
ajst-27525	140	17	-	-	PUNCT
ajst-27525	140	18	order	order	NOUN
ajst-27525	140	19	(	(	PUNCT
ajst-27525	140	20	mean	mean	ADJ
ajst-27525	140	21	)	)	PUNCT
ajst-27525	140	22	and	and	CCONJ
ajst-27525	140	23	second	second	ADJ
ajst-27525	140	24	-	-	PUNCT
ajst-27525	140	25	order	order	NOUN
ajst-27525	140	26	(	(	PUNCT
ajst-27525	140	27	variance	variance	NOUN
ajst-27525	140	28	)	)	PUNCT
ajst-27525	140	29	gradient	gradient	NOUN
ajst-27525	140	30	estimates	estimate	NOUN
ajst-27525	140	31	.	.	PUNCT
ajst-27525	141	1	it	it	PRON
ajst-27525	141	2	generally	generally	ADV
ajst-27525	141	3	provides	provide	VERB
ajst-27525	141	4	efficient	efficient	ADJ
ajst-27525	141	5	and	and	CCONJ
ajst-27525	141	6	stable	stable	ADJ
ajst-27525	141	7	convergence	convergence	NOUN
ajst-27525	141	8	across	across	ADP
ajst-27525	141	9	varied	varied	ADJ
ajst-27525	141	10	learning	learning	NOUN
ajst-27525	141	11	rate	rate	NOUN
ajst-27525	141	12	settings	setting	NOUN
ajst-27525	141	13	.	.	PUNCT
ajst-27525	142	1	the	the	DET
ajst-27525	142	2	optimizer	optimizer	NOUN
ajst-27525	142	3	choice	choice	NOUN
ajst-27525	142	4	significantly	significantly	ADV
ajst-27525	142	5	impacts	impact	VERB
ajst-27525	142	6	fno	fno	PROPN
ajst-27525	142	7	training	training	NOUN
ajst-27525	142	8	convergence	convergence	NOUN
ajst-27525	142	9	and	and	CCONJ
ajst-27525	142	10	overall	overall	ADJ
ajst-27525	142	11	effectiveness	effectiveness	NOUN
ajst-27525	142	12	.	.	PUNCT
ajst-27525	143	1	adam	adam	PROPN
ajst-27525	143	2	and	and	CCONJ
ajst-27525	143	3	adamw	adamw	NOUN
ajst-27525	143	4	are	be	AUX
ajst-27525	143	5	commonly	commonly	ADV
ajst-27525	143	6	used	use	VERB
ajst-27525	143	7	for	for	ADP
ajst-27525	143	8	fno	fno	PROPN
ajst-27525	143	9	,	,	PUNCT
ajst-27525	143	10	as	as	SCONJ
ajst-27525	143	11	they	they	PRON
ajst-27525	143	12	are	be	AUX
ajst-27525	143	13	particularly	particularly	ADV
ajst-27525	143	14	effective	effective	ADJ
ajst-27525	143	15	in	in	ADP
ajst-27525	143	16	frequency	frequency	NOUN
ajst-27525	143	17	-	-	PUNCT
ajst-27525	143	18	domain	domain	NOUN
ajst-27525	143	19	operations	operation	NOUN
ajst-27525	143	20	.	.	PUNCT
ajst-27525	144	1	adam	adam	PROPN
ajst-27525	144	2	’s	’s	PART
ajst-27525	144	3	dynamic	dynamic	ADJ
ajst-27525	144	4	learning	learning	NOUN
ajst-27525	144	5	rate	rate	NOUN
ajst-27525	144	6	adjustment	adjustment	NOUN
ajst-27525	144	7	enhances	enhance	VERB
ajst-27525	144	8	training	training	NOUN
ajst-27525	144	9	efficiency	efficiency	NOUN
ajst-27525	144	10	,	,	PUNCT
ajst-27525	144	11	while	while	SCONJ
ajst-27525	144	12	adamw	adamw	PROPN
ajst-27525	144	13	’s	’s	PART
ajst-27525	144	14	weight	weight	NOUN
ajst-27525	144	15	decay	decay	NOUN
ajst-27525	144	16	improves	improve	VERB
ajst-27525	144	17	generalization	generalization	NOUN
ajst-27525	144	18	,	,	PUNCT
ajst-27525	144	19	making	make	VERB
ajst-27525	144	20	fno	fno	PROPN
ajst-27525	144	21	solutions	solution	NOUN
ajst-27525	144	22	186	186	NUM
ajst-27525	144	23	more	more	ADV
ajst-27525	144	24	robust	robust	ADJ
ajst-27525	144	25	across	across	ADP
ajst-27525	144	26	diverse	diverse	ADJ
ajst-27525	144	27	boundary	boundary	ADJ
ajst-27525	144	28	conditions	condition	NOUN
ajst-27525	144	29	.	.	PUNCT
ajst-27525	145	1	5	5	X
ajst-27525	145	2	.	.	X
ajst-27525	145	3	conclusion	conclusion	NOUN
ajst-27525	145	4	this	this	DET
ajst-27525	145	5	study	study	NOUN
ajst-27525	145	6	explores	explore	VERB
ajst-27525	145	7	the	the	DET
ajst-27525	145	8	application	application	NOUN
ajst-27525	145	9	and	and	CCONJ
ajst-27525	145	10	feasibility	feasibility	NOUN
ajst-27525	145	11	of	of	ADP
ajst-27525	145	12	fourier	fourier	ADJ
ajst-27525	145	13	neural	neural	ADJ
ajst-27525	145	14	operators	operator	NOUN
ajst-27525	145	15	(	(	PUNCT
ajst-27525	145	16	fno	fno	PROPN
ajst-27525	145	17	)	)	PUNCT
ajst-27525	145	18	in	in	ADP
ajst-27525	145	19	solving	solve	VERB
ajst-27525	145	20	oil	oil	NOUN
ajst-27525	145	21	-	-	PUNCT
ajst-27525	145	22	water	water	NOUN
ajst-27525	145	23	twophase	twophase	NOUN
ajst-27525	145	24	flow	flow	NOUN
ajst-27525	145	25	equations	equation	NOUN
ajst-27525	145	26	.	.	PUNCT
ajst-27525	146	1	by	by	ADP
ajst-27525	146	2	leveraging	leverage	VERB
ajst-27525	146	3	fourier	fourier	NOUN
ajst-27525	146	4	transforms	transform	VERB
ajst-27525	146	5	to	to	PART
ajst-27525	146	6	extract	extract	VERB
ajst-27525	146	7	feature	feature	NOUN
ajst-27525	146	8	information	information	NOUN
ajst-27525	146	9	in	in	ADP
ajst-27525	146	10	the	the	DET
ajst-27525	146	11	frequency	frequency	NOUN
ajst-27525	146	12	domain	domain	NOUN
ajst-27525	146	13	,	,	PUNCT
ajst-27525	146	14	fno	fno	PROPN
ajst-27525	146	15	can	can	AUX
ajst-27525	146	16	efficiently	efficiently	ADV
ajst-27525	146	17	capture	capture	VERB
ajst-27525	146	18	the	the	DET
ajst-27525	146	19	global	global	ADJ
ajst-27525	146	20	characteristics	characteristic	NOUN
ajst-27525	146	21	of	of	ADP
ajst-27525	146	22	the	the	DET
ajst-27525	146	23	flow	flow	NOUN
ajst-27525	146	24	field	field	NOUN
ajst-27525	146	25	,	,	PUNCT
ajst-27525	146	26	demonstrating	demonstrate	VERB
ajst-27525	146	27	a	a	DET
ajst-27525	146	28	significant	significant	ADJ
ajst-27525	146	29	computational	computational	ADJ
ajst-27525	146	30	efficiency	efficiency	NOUN
ajst-27525	146	31	advantage	advantage	NOUN
ajst-27525	146	32	compared	compare	VERB
ajst-27525	146	33	to	to	ADP
ajst-27525	146	34	traditional	traditional	ADJ
ajst-27525	146	35	numerical	numerical	ADJ
ajst-27525	146	36	methods	method	NOUN
ajst-27525	146	37	.	.	PUNCT
ajst-27525	147	1	experiments	experiment	NOUN
ajst-27525	147	2	show	show	VERB
ajst-27525	147	3	that	that	SCONJ
ajst-27525	147	4	fno	fno	PROPN
ajst-27525	147	5	exhibits	exhibit	VERB
ajst-27525	147	6	good	good	ADJ
ajst-27525	147	7	generalization	generalization	NOUN
ajst-27525	147	8	ability	ability	NOUN
ajst-27525	147	9	and	and	CCONJ
ajst-27525	147	10	stability	stability	NOUN
ajst-27525	147	11	when	when	SCONJ
ajst-27525	147	12	dealing	deal	VERB
ajst-27525	147	13	with	with	ADP
ajst-27525	147	14	complex	complex	ADJ
ajst-27525	147	15	boundary	boundary	ADJ
ajst-27525	147	16	and	and	CCONJ
ajst-27525	147	17	initial	initial	ADJ
ajst-27525	147	18	conditions	condition	NOUN
ajst-27525	147	19	in	in	ADP
ajst-27525	147	20	multiphase	multiphase	NOUN
ajst-27525	147	21	flows	flow	NOUN
ajst-27525	147	22	.	.	PUNCT
ajst-27525	148	1	additionally	additionally	ADV
ajst-27525	148	2	,	,	PUNCT
ajst-27525	148	3	benefiting	benefit	VERB
ajst-27525	148	4	from	from	ADP
ajst-27525	148	5	the	the	DET
ajst-27525	148	6	combination	combination	NOUN
ajst-27525	148	7	of	of	ADP
ajst-27525	148	8	the	the	DET
ajst-27525	148	9	gelu	gelu	ADJ
ajst-27525	148	10	activation	activation	NOUN
ajst-27525	148	11	function	function	NOUN
ajst-27525	148	12	and	and	CCONJ
ajst-27525	148	13	the	the	DET
ajst-27525	148	14	adam	adam	PROPN
ajst-27525	148	15	optimizer	optimizer	NOUN
ajst-27525	148	16	,	,	PUNCT
ajst-27525	148	17	fno	fno	PROPN
ajst-27525	148	18	achieves	achieve	VERB
ajst-27525	148	19	rapid	rapid	ADJ
ajst-27525	148	20	convergence	convergence	NOUN
ajst-27525	148	21	and	and	CCONJ
ajst-27525	148	22	high	high	ADJ
ajst-27525	148	23	-	-	PUNCT
ajst-27525	148	24	precision	precision	NOUN
ajst-27525	148	25	solutions	solution	NOUN
ajst-27525	148	26	.	.	PUNCT
ajst-27525	149	1	the	the	DET
ajst-27525	149	2	results	result	NOUN
ajst-27525	149	3	of	of	ADP
ajst-27525	149	4	this	this	DET
ajst-27525	149	5	study	study	NOUN
ajst-27525	149	6	provide	provide	VERB
ajst-27525	149	7	new	new	ADJ
ajst-27525	149	8	insights	insight	NOUN
ajst-27525	149	9	and	and	CCONJ
ajst-27525	149	10	possibilities	possibility	NOUN
ajst-27525	149	11	for	for	ADP
ajst-27525	149	12	the	the	DET
ajst-27525	149	13	application	application	NOUN
ajst-27525	149	14	of	of	ADP
ajst-27525	149	15	fno	fno	PROPN
ajst-27525	149	16	in	in	ADP
ajst-27525	149	17	complex	complex	ADJ
ajst-27525	149	18	fields	field	NOUN
ajst-27525	149	19	such	such	ADJ
ajst-27525	149	20	as	as	ADP
ajst-27525	149	21	reservoir	reservoir	NOUN
ajst-27525	149	22	engineering	engineering	NOUN
ajst-27525	149	23	and	and	CCONJ
ajst-27525	149	24	flow	flow	NOUN
ajst-27525	149	25	simulation	simulation	NOUN
ajst-27525	149	26	.	.	PUNCT
ajst-27525	150	1	future	future	ADJ
ajst-27525	150	2	work	work	NOUN
ajst-27525	150	3	will	will	AUX
ajst-27525	150	4	further	far	ADV
ajst-27525	150	5	optimize	optimize	VERB
ajst-27525	150	6	the	the	DET
ajst-27525	150	7	network	network	NOUN
ajst-27525	150	8	structure	structure	NOUN
ajst-27525	150	9	to	to	PART
ajst-27525	150	10	enhance	enhance	VERB
ajst-27525	150	11	its	its	PRON
ajst-27525	150	12	prediction	prediction	NOUN
ajst-27525	150	13	accuracy	accuracy	NOUN
ajst-27525	150	14	in	in	ADP
ajst-27525	150	15	more	more	ADJ
ajst-27525	150	16	complex	complex	ADJ
ajst-27525	150	17	oil	oil	NOUN
ajst-27525	150	18	-	-	PUNCT
ajst-27525	150	19	water	water	NOUN
ajst-27525	150	20	flow	flow	NOUN
ajst-27525	150	21	systems	system	NOUN
ajst-27525	150	22	.	.	PUNCT
ajst-27525	151	1	references	reference	NOUN
ajst-27525	151	2	[	[	X
ajst-27525	151	3	1	1	NUM
ajst-27525	151	4	]	]	X
ajst-27525	151	5	han	han	PROPN
ajst-27525	151	6	jiangxia	jiangxia	PROPN
ajst-27525	151	7	,	,	PUNCT
ajst-27525	151	8	xue	xue	PROPN
ajst-27525	151	9	liang	liang	PROPN
ajst-27525	151	10	,	,	PUNCT
ajst-27525	151	11	liu	liu	PROPN
ajst-27525	151	12	yuetian	yuetian	PROPN
ajst-27525	151	13	,	,	PUNCT
ajst-27525	151	14	et	et	PROPN
ajst-27525	151	15	al	al	PROPN
ajst-27525	151	16	.	.	PUNCT
ajst-27525	152	1	solving	solve	VERB
ajst-27525	152	2	oil	oil	NOUN
ajst-27525	152	3	-	-	PUNCT
ajst-27525	152	4	water	water	NOUN
ajst-27525	152	5	two	two	NUM
ajst-27525	152	6	-	-	PUNCT
ajst-27525	152	7	phase	phase	NOUN
ajst-27525	152	8	flow	flow	NOUN
ajst-27525	152	9	equations	equation	NOUN
ajst-27525	152	10	using	use	VERB
ajst-27525	152	11	deep	deep	ADJ
ajst-27525	152	12	neural	neural	ADJ
ajst-27525	152	13	networks	network	NOUN
ajst-27525	153	1	[	[	X
ajst-27525	153	2	c]//beijing	c]//beije	VERB
ajst-27525	153	3	energy	energy	NOUN
ajst-27525	153	4	association	association	NOUN
ajst-27525	153	5	,	,	PUNCT
ajst-27525	153	6	china	china	PROPN
ajst-27525	153	7	university	university	PROPN
ajst-27525	153	8	of	of	ADP
ajst-27525	153	9	petroleum	petroleum	NOUN
ajst-27525	153	10	(	(	PUNCT
ajst-27525	153	11	beijing	beijing	PROPN
ajst-27525	153	12	)	)	PUNCT
ajst-27525	153	13	,	,	PUNCT
ajst-27525	153	14	state	state	NOUN
ajst-27525	153	15	key	key	ADJ
ajst-27525	153	16	laboratory	laboratory	NOUN
ajst-27525	153	17	of	of	ADP
ajst-27525	153	18	petroleum	petroleum	NOUN
ajst-27525	153	19	resources	resource	NOUN
ajst-27525	153	20	and	and	CCONJ
ajst-27525	153	21	prospecting	prospecting	NOUN
ajst-27525	153	22	,	,	PUNCT
ajst-27525	153	23	state	state	NOUN
ajst-27525	153	24	key	key	ADJ
ajst-27525	153	25	laboratory	laboratory	NOUN
ajst-27525	153	26	of	of	ADP
ajst-27525	153	27	heavy	heavy	ADJ
ajst-27525	153	28	oil	oil	NOUN
ajst-27525	153	29	processing	processing	NOUN
ajst-27525	153	30	,	,	PUNCT
ajst-27525	153	31	baidu	baidu	VERB
ajst-27525	153	32	intelligent	intelligent	ADJ
ajst-27525	153	33	cloud	cloud	NOUN
ajst-27525	153	34	.	.	PUNCT
ajst-27525	154	1	proceedings	proceeding	NOUN
ajst-27525	154	2	of	of	ADP
ajst-27525	154	3	the	the	DET
ajst-27525	154	4	2022	2022	NUM
ajst-27525	154	5	china	china	PROPN
ajst-27525	154	6	oil	oil	NOUN
ajst-27525	154	7	and	and	CCONJ
ajst-27525	154	8	gas	gas	NOUN
ajst-27525	154	9	intelligent	intelligent	ADJ
ajst-27525	154	10	technology	technology	NOUN
ajst-27525	154	11	conference	conference	NOUN
ajst-27525	154	12	the	the	DET
ajst-27525	154	13	5th	5th	ADJ
ajst-27525	154	14	petroleum	petroleum	NOUN
ajst-27525	154	15	and	and	CCONJ
ajst-27525	154	16	petrochemical	petrochemical	NOUN
ajst-27525	154	17	artificial	artificial	ADJ
ajst-27525	154	18	intelligence	intelligence	NOUN
ajst-27525	154	19	high	high	ADJ
ajst-27525	154	20	-	-	PUNCT
ajst-27525	154	21	end	end	NOUN
ajst-27525	154	22	forum	forum	NOUN
ajst-27525	154	23	and	and	CCONJ
ajst-27525	154	24	the	the	DET
ajst-27525	154	25	8th	8th	ADJ
ajst-27525	154	26	intelligent	intelligent	ADJ
ajst-27525	154	27	digital	digital	ADJ
ajst-27525	154	28	oilfield	oilfield	NOUN
ajst-27525	154	29	open	open	PROPN
ajst-27525	154	30	forum	forum	PROPN
ajst-27525	154	31	,	,	PUNCT
ajst-27525	154	32	2022:11	2022:11	NUM
ajst-27525	154	33	.	.	PUNCT
ajst-27525	155	1	doi	doi	NOUN
ajst-27525	155	2	:	:	PUNCT
ajst-27525	155	3	10.26914	10.26914	NUM
ajst-27525	155	4	/	/	SYM
ajst-27525	155	5	c.cnkihy.2022.035114	c.cnkihy.2022.035114	NOUN
ajst-27525	155	6	.	.	PUNCT
ajst-27525	156	1	[	[	X
ajst-27525	156	2	2	2	X
ajst-27525	156	3	]	]	X
ajst-27525	156	4	cha	cha	X
ajst-27525	156	5	wenshu	wenshu	NOUN
ajst-27525	156	6	,	,	PUNCT
ajst-27525	156	7	li	li	PROPN
ajst-27525	156	8	daolun	daolun	PROPN
ajst-27525	156	9	,	,	PUNCT
ajst-27525	156	10	shen	shen	PROPN
ajst-27525	156	11	luhang	luhang	PROPN
ajst-27525	156	12	,	,	PUNCT
ajst-27525	156	13	et	et	PROPN
ajst-27525	156	14	al	al	PROPN
ajst-27525	156	15	.	.	PUNCT
ajst-27525	157	1	a	a	DET
ajst-27525	157	2	review	review	NOUN
ajst-27525	157	3	of	of	ADP
ajst-27525	157	4	neural	neural	ADJ
ajst-27525	157	5	network	network	NOUN
ajst-27525	157	6	-	-	PUNCT
ajst-27525	157	7	based	base	VERB
ajst-27525	157	8	methods	method	NOUN
ajst-27525	157	9	for	for	ADP
ajst-27525	157	10	solving	solve	VERB
ajst-27525	157	11	partial	partial	ADJ
ajst-27525	157	12	differential	differential	ADJ
ajst-27525	157	13	equations	equation	NOUN
ajst-27525	158	1	[	[	X
ajst-27525	158	2	j	j	X
ajst-27525	158	3	]	]	X
ajst-27525	158	4	.	.	PUNCT
ajst-27525	159	1	chinese	chinese	ADJ
ajst-27525	159	2	journal	journal	PROPN
ajst-27525	159	3	of	of	ADP
ajst-27525	159	4	theoretical	theoretical	ADJ
ajst-27525	159	5	and	and	CCONJ
ajst-27525	159	6	applied	applied	ADJ
ajst-27525	159	7	mechanics	mechanic	NOUN
ajst-27525	159	8	,	,	PUNCT
ajst-27525	159	9	2022	2022	NUM
ajst-27525	159	10	,	,	PUNCT
ajst-27525	159	11	54(03	54(03	NUM
ajst-27525	159	12	):	):	PUNCT
ajst-27525	159	13	543	543	NUM
ajst-27525	159	14	-	-	SYM
ajst-27525	159	15	556	556	NUM
ajst-27525	159	16	.	.	PUNCT
ajst-27525	160	1	[	[	X
ajst-27525	160	2	3	3	NUM
ajst-27525	160	3	]	]	X
ajst-27525	160	4	long	long	ADJ
ajst-27525	160	5	z	z	NOUN
ajst-27525	160	6	,	,	PUNCT
ajst-27525	160	7	lu	lu	PROPN
ajst-27525	160	8	y	y	PROPN
ajst-27525	160	9	,	,	PUNCT
ajst-27525	160	10	ma	ma	PROPN
ajst-27525	160	11	x	x	PROPN
ajst-27525	160	12	,	,	PUNCT
ajst-27525	160	13	et	et	PROPN
ajst-27525	160	14	al	al	PROPN
ajst-27525	160	15	.	.	PROPN
ajst-27525	160	16	pde	pde	PROPN
ajst-27525	160	17	-	-	PUNCT
ajst-27525	160	18	net	net	NOUN
ajst-27525	160	19	:	:	PUNCT
ajst-27525	160	20	learning	learn	VERB
ajst-27525	160	21	pdes	pde	NOUN
ajst-27525	160	22	from	from	ADP
ajst-27525	160	23	data[c]//international	data[c]//international	PROPN
ajst-27525	160	24	conference	conference	NOUN
ajst-27525	160	25	on	on	ADP
ajst-27525	160	26	machine	machine	NOUN
ajst-27525	160	27	learning	learning	NOUN
ajst-27525	160	28	.	.	PUNCT
ajst-27525	161	1	pmlr	pmlr	NOUN
ajst-27525	161	2	,	,	PUNCT
ajst-27525	161	3	2018	2018	NUM
ajst-27525	161	4	:	:	PUNCT
ajst-27525	161	5	3208	3208	NUM
ajst-27525	161	6	-	-	SYM
ajst-27525	161	7	3216	3216	NUM
ajst-27525	161	8	.	.	PUNCT
ajst-27525	162	1	[	[	X
ajst-27525	162	2	4	4	NUM
ajst-27525	162	3	]	]	X
ajst-27525	162	4	mcculloch	mcculloch	PROPN
ajst-27525	162	5	w	w	PROPN
ajst-27525	162	6	s	s	PROPN
ajst-27525	162	7	,	,	PUNCT
ajst-27525	162	8	pitts	pitts	PROPN
ajst-27525	162	9	w.	w.	PROPN
ajst-27525	162	10	a	a	DET
ajst-27525	162	11	logical	logical	ADJ
ajst-27525	162	12	calculus	calculus	NOUN
ajst-27525	162	13	of	of	ADP
ajst-27525	162	14	the	the	DET
ajst-27525	162	15	ideas	idea	NOUN
ajst-27525	162	16	immanent	immanent	ADJ
ajst-27525	162	17	in	in	ADP
ajst-27525	162	18	nervous	nervous	ADJ
ajst-27525	162	19	activity[j	activity[j	PROPN
ajst-27525	162	20	]	]	PUNCT
ajst-27525	162	21	.	.	PUNCT
ajst-27525	163	1	the	the	DET
ajst-27525	163	2	bulletin	bulletin	NOUN
ajst-27525	163	3	of	of	ADP
ajst-27525	163	4	mathematical	mathematical	ADJ
ajst-27525	163	5	biophysics	biophysic	NOUN
ajst-27525	163	6	,	,	PUNCT
ajst-27525	163	7	1943	1943	NUM
ajst-27525	163	8	,	,	PUNCT
ajst-27525	163	9	5	5	NUM
ajst-27525	163	10	:	:	SYM
ajst-27525	163	11	115	115	NUM
ajst-27525	163	12	-	-	SYM
ajst-27525	163	13	133	133	NUM
ajst-27525	163	14	.	.	PUNCT
ajst-27525	164	1	[	[	X
ajst-27525	164	2	5	5	X
ajst-27525	164	3	]	]	X
ajst-27525	164	4	rumelhart	rumelhart	NOUN
ajst-27525	164	5	d	d	PROPN
ajst-27525	164	6	e	e	PROPN
ajst-27525	164	7	,	,	PUNCT
ajst-27525	164	8	hinton	hinton	PROPN
ajst-27525	164	9	g	g	PROPN
ajst-27525	164	10	e	e	PROPN
ajst-27525	164	11	,	,	PUNCT
ajst-27525	164	12	williams	williams	PROPN
ajst-27525	164	13	r	r	AUX
ajst-27525	164	14	j.	j.	PROPN
ajst-27525	164	15	learning	learn	VERB
ajst-27525	164	16	representations	representation	NOUN
ajst-27525	164	17	by	by	ADP
ajst-27525	164	18	back	back	ADV
ajst-27525	164	19	-	-	PUNCT
ajst-27525	164	20	propagating	propagate	VERB
ajst-27525	164	21	errors[j	errors[j	NOUN
ajst-27525	164	22	]	]	PUNCT
ajst-27525	164	23	.	.	PUNCT
ajst-27525	165	1	nature	nature	NOUN
ajst-27525	165	2	,	,	PUNCT
ajst-27525	165	3	1986	1986	NUM
ajst-27525	165	4	,	,	PUNCT
ajst-27525	165	5	323(6088	323(6088	NUM
ajst-27525	165	6	):	):	PUNCT
ajst-27525	165	7	533	533	NUM
ajst-27525	165	8	-	-	SYM
ajst-27525	165	9	536	536	NUM
ajst-27525	165	10	.	.	PUNCT
ajst-27525	166	1	[	[	X
ajst-27525	166	2	6	6	NUM
ajst-27525	166	3	]	]	PUNCT
ajst-27525	166	4	baydin	baydin	VERB
ajst-27525	166	5	a	a	DET
ajst-27525	166	6	g	g	NOUN
ajst-27525	166	7	,	,	PUNCT
ajst-27525	166	8	pearlmutter	pearlmutter	VERB
ajst-27525	166	9	b	b	PROPN
ajst-27525	166	10	a	a	PRON
ajst-27525	166	11	,	,	PUNCT
ajst-27525	166	12	radul	radul	VERB
ajst-27525	166	13	a	a	DET
ajst-27525	166	14	a	a	NOUN
ajst-27525	166	15	,	,	PUNCT
ajst-27525	166	16	et	et	PROPN
ajst-27525	166	17	al	al	PROPN
ajst-27525	166	18	.	.	PROPN
ajst-27525	166	19	automatic	automatic	ADJ
ajst-27525	166	20	differentiation	differentiation	NOUN
ajst-27525	166	21	in	in	ADP
ajst-27525	166	22	machine	machine	NOUN
ajst-27525	166	23	learning	learning	NOUN
ajst-27525	166	24	:	:	PUNCT
ajst-27525	166	25	a	a	DET
ajst-27525	166	26	survey[j	survey[j	PROPN
ajst-27525	166	27	]	]	PUNCT
ajst-27525	166	28	.	.	PUNCT
ajst-27525	167	1	journal	journal	PROPN
ajst-27525	167	2	of	of	ADP
ajst-27525	167	3	marchine	marchine	ADJ
ajst-27525	167	4	learning	learn	VERB
ajst-27525	167	5	research	research	NOUN
ajst-27525	167	6	,	,	PUNCT
ajst-27525	167	7	2018	2018	NUM
ajst-27525	167	8	,	,	PUNCT
ajst-27525	167	9	18	18	NUM
ajst-27525	167	10	:	:	SYM
ajst-27525	167	11	1	1	NUM
ajst-27525	167	12	-	-	SYM
ajst-27525	167	13	43	43	NUM
ajst-27525	167	14	.	.	PUNCT
ajst-27525	168	1	[	[	X
ajst-27525	168	2	7	7	X
ajst-27525	168	3	]	]	PUNCT
ajst-27525	168	4	wornik	wornik	NOUN
ajst-27525	169	1	k	k	PROPN
ajst-27525	169	2	,	,	PUNCT
ajst-27525	169	3	stinchcombe	stinchcombe	PROPN
ajst-27525	169	4	m	m	PROPN
ajst-27525	169	5	,	,	PUNCT
ajst-27525	169	6	white	white	PROPN
ajst-27525	169	7	h.	h.	PROPN
ajst-27525	169	8	universal	universal	ADJ
ajst-27525	169	9	approximation	approximation	NOUN
ajst-27525	169	10	of	of	ADP
ajst-27525	169	11	an	an	DET
ajst-27525	169	12	unknown	unknown	ADJ
ajst-27525	169	13	mapping	mapping	NOUN
ajst-27525	169	14	and	and	CCONJ
ajst-27525	169	15	its	its	PRON
ajst-27525	169	16	derivatives	derivative	NOUN
ajst-27525	169	17	using	use	VERB
ajst-27525	169	18	multilayer	multilayer	ADJ
ajst-27525	169	19	feedforward	feedforward	NOUN
ajst-27525	169	20	networks	network	NOUN
ajst-27525	169	21	.	.	PUNCT
ajst-27525	170	1	neural	neural	ADJ
ajst-27525	170	2	networks	network	NOUN
ajst-27525	170	3	,	,	PUNCT
ajst-27525	170	4	1990	1990	NUM
ajst-27525	170	5	,	,	PUNCT
ajst-27525	170	6	3(5	3(5	NUM
ajst-27525	170	7	):	):	PUNCT
ajst-27525	170	8	551	551	NUM
ajst-27525	170	9	-	-	SYM
ajst-27525	170	10	560	560	NUM
ajst-27525	171	1	[	[	NOUN
ajst-27525	171	2	8	8	NUM
ajst-27525	171	3	]	]	X
ajst-27525	171	4	li	li	PROPN
ajst-27525	171	5	x.	x.	PROPN
ajst-27525	171	6	simultaneous	simultaneous	ADJ
ajst-27525	171	7	approximations	approximation	NOUN
ajst-27525	171	8	of	of	ADP
ajst-27525	171	9	multivariate	multivariate	NOUN
ajst-27525	171	10	functions	function	NOUN
ajst-27525	171	11	and	and	CCONJ
ajst-27525	171	12	their	their	PRON
ajst-27525	171	13	derivatives	derivative	NOUN
ajst-27525	171	14	by	by	ADP
ajst-27525	171	15	neural	neural	ADJ
ajst-27525	171	16	networks	network	NOUN
ajst-27525	171	17	with	with	ADP
ajst-27525	171	18	one	one	NUM
ajst-27525	171	19	hidden	hide	VERB
ajst-27525	171	20	layer	layer	NOUN
ajst-27525	171	21	.	.	PUNCT
ajst-27525	172	1	neurocomputing	neurocomputing	NOUN
ajst-27525	172	2	,	,	PUNCT
ajst-27525	172	3	1996	1996	NUM
ajst-27525	172	4	,	,	PUNCT
ajst-27525	172	5	12(4	12(4	NUM
ajst-27525	172	6	):	):	PUNCT
ajst-27525	172	7	327	327	NUM
ajst-27525	172	8	-	-	SYM
ajst-27525	172	9	343	343	NUM
ajst-27525	172	10	[	[	X
ajst-27525	172	11	9	9	NUM
ajst-27525	172	12	]	]	X
ajst-27525	172	13	lagaris	lagaris	NOUN
ajst-27525	172	14	i	i	PROPN
ajst-27525	172	15	e	e	PROPN
ajst-27525	172	16	,	,	PUNCT
ajst-27525	172	17	likas	likas	X
ajst-27525	172	18	a	a	PRON
ajst-27525	172	19	,	,	PUNCT
ajst-27525	172	20	fotiadis	fotiadis	INTJ
ajst-27525	172	21	d	d	X
ajst-27525	172	22	i.	i.	PROPN
ajst-27525	172	23	artificial	artificial	ADJ
ajst-27525	172	24	neural	neural	ADJ
ajst-27525	172	25	networks	network	NOUN
ajst-27525	172	26	for	for	ADP
ajst-27525	172	27	solving	solve	VERB
ajst-27525	172	28	ordinary	ordinary	ADJ
ajst-27525	172	29	and	and	CCONJ
ajst-27525	172	30	partial	partial	ADJ
ajst-27525	172	31	differential	differential	NOUN
ajst-27525	172	32	equations[j	equations[j	PROPN
ajst-27525	172	33	]	]	PUNCT
ajst-27525	172	34	.	.	PUNCT
ajst-27525	173	1	ieee	ieee	NOUN
ajst-27525	173	2	transactions	transaction	NOUN
ajst-27525	173	3	on	on	ADP
ajst-27525	173	4	neural	neural	ADJ
ajst-27525	173	5	networks	network	NOUN
ajst-27525	173	6	,	,	PUNCT
ajst-27525	173	7	1998	1998	NUM
ajst-27525	173	8	,	,	PUNCT
ajst-27525	173	9	9(5	9(5	NUM
ajst-27525	173	10	):	):	PUNCT
ajst-27525	173	11	987	987	NUM
ajst-27525	173	12	-	-	SYM
ajst-27525	173	13	1000	1000	NUM
ajst-27525	173	14	.	.	PUNCT
ajst-27525	174	1	[	[	X
ajst-27525	174	2	10	10	NUM
ajst-27525	174	3	]	]	PUNCT
ajst-27525	174	4	aarts	aart	NOUN
ajst-27525	174	5	l	l	NOUN
ajst-27525	174	6	p	p	X
ajst-27525	174	7	,	,	PUNCT
ajst-27525	174	8	van	van	PROPN
ajst-27525	174	9	der	der	NOUN
ajst-27525	174	10	veer	veer	NOUN
ajst-27525	174	11	p.	p.	NOUN
ajst-27525	174	12	neural	neural	ADJ
ajst-27525	174	13	network	network	NOUN
ajst-27525	174	14	method	method	NOUN
ajst-27525	174	15	for	for	ADP
ajst-27525	174	16	solving	solve	VERB
ajst-27525	174	17	partial	partial	ADJ
ajst-27525	174	18	differential	differential	NOUN
ajst-27525	174	19	equations[j	equations[j	PROPN
ajst-27525	174	20	]	]	PUNCT
ajst-27525	174	21	.	.	PUNCT
ajst-27525	175	1	neural	neural	ADJ
ajst-27525	175	2	processing	processing	NOUN
ajst-27525	175	3	letters	letter	NOUN
ajst-27525	175	4	,	,	PUNCT
ajst-27525	175	5	2001	2001	NUM
ajst-27525	175	6	,	,	PUNCT
ajst-27525	175	7	14	14	NUM
ajst-27525	175	8	:	:	SYM
ajst-27525	175	9	261	261	NUM
ajst-27525	175	10	-	-	SYM
ajst-27525	175	11	271	271	NUM
ajst-27525	175	12	.	.	PUNCT
ajst-27525	176	1	[	[	X
ajst-27525	176	2	11	11	NUM
ajst-27525	176	3	]	]	PUNCT
ajst-27525	176	4	ramuhalli	ramuhalli	NOUN
ajst-27525	176	5	p	p	NOUN
ajst-27525	176	6	,	,	PUNCT
ajst-27525	176	7	udpa	udpa	ADJ
ajst-27525	176	8	l	l	NOUN
ajst-27525	176	9	,	,	PUNCT
ajst-27525	176	10	udpa	udpa	PROPN
ajst-27525	176	11	s	s	PART
ajst-27525	176	12	s.	s.	PROPN
ajst-27525	176	13	finite	finite	PROPN
ajst-27525	176	14	-	-	ADJ
ajst-27525	176	15	element	element	ADJ
ajst-27525	176	16	neural	neural	ADJ
ajst-27525	176	17	networks	network	NOUN
ajst-27525	176	18	for	for	ADP
ajst-27525	176	19	solving	solve	VERB
ajst-27525	176	20	differential	differential	NOUN
ajst-27525	176	21	equations[j	equations[j	PROPN
ajst-27525	176	22	]	]	PUNCT
ajst-27525	176	23	.	.	PUNCT
ajst-27525	177	1	ieee	ieee	NOUN
ajst-27525	177	2	transactions	transaction	NOUN
ajst-27525	177	3	on	on	ADP
ajst-27525	177	4	neural	neural	ADJ
ajst-27525	177	5	networks	network	NOUN
ajst-27525	177	6	,	,	PUNCT
ajst-27525	177	7	2005	2005	NUM
ajst-27525	177	8	,	,	PUNCT
ajst-27525	177	9	16(6	16(6	NUM
ajst-27525	177	10	):	):	PUNCT
ajst-27525	177	11	1381	1381	NUM
ajst-27525	177	12	-	-	SYM
ajst-27525	177	13	1392	1392	NUM
ajst-27525	177	14	.	.	PUNCT
ajst-27525	178	1	[	[	X
ajst-27525	178	2	12	12	NUM
ajst-27525	178	3	]	]	X
ajst-27525	178	4	zha	zha	PROPN
ajst-27525	178	5	w	w	PROPN
ajst-27525	178	6	,	,	PUNCT
ajst-27525	178	7	zhang	zhang	PROPN
ajst-27525	178	8	w	w	PROPN
ajst-27525	178	9	,	,	PUNCT
ajst-27525	178	10	li	li	PROPN
ajst-27525	178	11	d	d	PROPN
ajst-27525	178	12	,	,	PUNCT
ajst-27525	178	13	et	et	PROPN
ajst-27525	178	14	al	al	PROPN
ajst-27525	178	15	.	.	PUNCT
ajst-27525	178	16	convolution	convolution	NOUN
ajst-27525	178	17	-	-	PUNCT
ajst-27525	178	18	based	base	VERB
ajst-27525	178	19	modelsolving	modelsolving	NOUN
ajst-27525	178	20	method	method	NOUN
ajst-27525	178	21	for	for	ADP
ajst-27525	178	22	three	three	NUM
ajst-27525	178	23	-	-	PUNCT
ajst-27525	178	24	dimensional	dimensional	ADJ
ajst-27525	178	25	,	,	PUNCT
ajst-27525	178	26	unsteady	unsteady	ADJ
ajst-27525	178	27	,	,	PUNCT
ajst-27525	178	28	partial	partial	ADJ
ajst-27525	178	29	differential	differential	NOUN
ajst-27525	178	30	equations[j	equations[j	PROPN
ajst-27525	178	31	]	]	PUNCT
ajst-27525	178	32	.	.	PUNCT
ajst-27525	179	1	neural	neural	ADJ
ajst-27525	179	2	computation	computation	NOUN
ajst-27525	179	3	,	,	PUNCT
ajst-27525	179	4	2022	2022	NUM
ajst-27525	179	5	,	,	PUNCT
ajst-27525	179	6	34(2	34(2	NUM
ajst-27525	179	7	):	):	PUNCT
ajst-27525	179	8	518	518	NUM
ajst-27525	179	9	-	-	SYM
ajst-27525	179	10	540	540	NUM
ajst-27525	179	11	.	.	PUNCT
ajst-27525	180	1	[	[	X
ajst-27525	180	2	13	13	NUM
ajst-27525	180	3	]	]	X
ajst-27525	180	4	liu	liu	PROPN
ajst-27525	180	5	z	z	PROPN
ajst-27525	180	6	,	,	PUNCT
ajst-27525	180	7	yang	yang	PROPN
ajst-27525	180	8	y	y	PROPN
ajst-27525	180	9	,	,	PUNCT
ajst-27525	180	10	cai	cai	PROPN
ajst-27525	180	11	q.	q.	PROPN
ajst-27525	180	12	neural	neural	PROPN
ajst-27525	180	13	network	network	NOUN
ajst-27525	180	14	as	as	ADP
ajst-27525	180	15	a	a	DET
ajst-27525	180	16	function	function	NOUN
ajst-27525	180	17	approximator	approximator	NOUN
ajst-27525	180	18	and	and	CCONJ
ajst-27525	180	19	its	its	PRON
ajst-27525	180	20	application	application	NOUN
ajst-27525	180	21	in	in	ADP
ajst-27525	180	22	solving	solve	VERB
ajst-27525	180	23	differential	differential	NOUN
ajst-27525	180	24	equations[j	equations[j	PROPN
ajst-27525	180	25	]	]	PUNCT
ajst-27525	180	26	.	.	PUNCT
ajst-27525	181	1	applied	apply	VERB
ajst-27525	181	2	mathematics	mathematic	NOUN
ajst-27525	181	3	and	and	CCONJ
ajst-27525	181	4	mechanics	mechanic	NOUN
ajst-27525	181	5	,	,	PUNCT
ajst-27525	181	6	2019	2019	NUM
ajst-27525	181	7	,	,	PUNCT
ajst-27525	181	8	40(2	40(2	NUM
ajst-27525	181	9	):	):	PUNCT
ajst-27525	181	10	237	237	NUM
ajst-27525	181	11	-	-	SYM
ajst-27525	181	12	248	248	NUM
ajst-27525	181	13	.	.	PUNCT
ajst-27525	182	1	[	[	X
ajst-27525	182	2	14	14	NUM
ajst-27525	182	3	]	]	X
ajst-27525	182	4	han	han	PROPN
ajst-27525	182	5	j	j	PROPN
ajst-27525	182	6	,	,	PUNCT
ajst-27525	182	7	jentzen	jentzen	PROPN
ajst-27525	182	8	a.	a.	NOUN
ajst-27525	182	9	deep	deep	PROPN
ajst-27525	182	10	learning	learning	NOUN
ajst-27525	182	11	-	-	PUNCT
ajst-27525	182	12	based	base	VERB
ajst-27525	182	13	numerical	numerical	ADJ
ajst-27525	182	14	methods	method	NOUN
ajst-27525	182	15	for	for	ADP
ajst-27525	182	16	high	high	ADJ
ajst-27525	182	17	-	-	PUNCT
ajst-27525	182	18	dimensional	dimensional	ADJ
ajst-27525	182	19	parabolic	parabolic	ADJ
ajst-27525	182	20	partial	partial	ADJ
ajst-27525	182	21	differential	differential	NOUN
ajst-27525	182	22	equations	equation	NOUN
ajst-27525	182	23	and	and	CCONJ
ajst-27525	182	24	backward	backward	ADJ
ajst-27525	182	25	stochastic	stochastic	ADJ
ajst-27525	182	26	differential	differential	NOUN
ajst-27525	182	27	equations[j	equations[j	PROPN
ajst-27525	182	28	]	]	PUNCT
ajst-27525	182	29	.	.	PUNCT
ajst-27525	183	1	communications	communication	NOUN
ajst-27525	183	2	in	in	ADP
ajst-27525	183	3	mathematics	mathematic	NOUN
ajst-27525	183	4	and	and	CCONJ
ajst-27525	183	5	statistics	statistic	NOUN
ajst-27525	183	6	,	,	PUNCT
ajst-27525	183	7	2017	2017	NUM
ajst-27525	183	8	,	,	PUNCT
ajst-27525	183	9	5(4	5(4	NUM
ajst-27525	183	10	):	):	PUNCT
ajst-27525	183	11	349	349	NUM
ajst-27525	183	12	-	-	SYM
ajst-27525	183	13	380	380	NUM
ajst-27525	183	14	.	.	PUNCT
ajst-27525	184	1	[	[	X
ajst-27525	184	2	15	15	NUM
ajst-27525	184	3	]	]	X
ajst-27525	184	4	han	han	PROPN
ajst-27525	184	5	j	j	PROPN
ajst-27525	184	6	,	,	PUNCT
ajst-27525	184	7	jentzen	jentzen	NOUN
ajst-27525	184	8	a	a	PRON
ajst-27525	184	9	,	,	PUNCT
ajst-27525	184	10	e	e	AUX
ajst-27525	184	11	w.	w.	NOUN
ajst-27525	184	12	solving	solve	VERB
ajst-27525	184	13	high	high	ADJ
ajst-27525	184	14	-	-	PUNCT
ajst-27525	184	15	dimensional	dimensional	ADJ
ajst-27525	184	16	partial	partial	ADJ
ajst-27525	184	17	differential	differential	NOUN
ajst-27525	184	18	equations	equation	NOUN
ajst-27525	184	19	using	use	VERB
ajst-27525	184	20	deep	deep	ADJ
ajst-27525	184	21	learning[j	learning[j	NOUN
ajst-27525	184	22	]	]	PUNCT
ajst-27525	184	23	.	.	PUNCT
ajst-27525	185	1	proceedings	proceeding	NOUN
ajst-27525	185	2	of	of	ADP
ajst-27525	185	3	the	the	DET
ajst-27525	185	4	national	national	PROPN
ajst-27525	185	5	academy	academy	PROPN
ajst-27525	185	6	of	of	ADP
ajst-27525	185	7	sciences	sciences	PROPN
ajst-27525	185	8	,	,	PUNCT
ajst-27525	185	9	2018	2018	NUM
ajst-27525	185	10	,	,	PUNCT
ajst-27525	185	11	115(34	115(34	NUM
ajst-27525	185	12	):	):	PUNCT
ajst-27525	185	13	8505	8505	NUM
ajst-27525	185	14	-	-	SYM
ajst-27525	185	15	8510	8510	NUM
ajst-27525	185	16	.	.	PUNCT
ajst-27525	186	1	[	[	X
ajst-27525	186	2	16	16	NUM
ajst-27525	186	3	]	]	PUNCT
ajst-27525	186	4	sirignano	sirignano	PROPN
ajst-27525	186	5	j	j	PROPN
ajst-27525	186	6	,	,	PUNCT
ajst-27525	186	7	spiliopoulos	spiliopoulos	PROPN
ajst-27525	186	8	k.	k.	PROPN
ajst-27525	186	9	dgm	dgm	PROPN
ajst-27525	186	10	:	:	PUNCT
ajst-27525	186	11	a	a	DET
ajst-27525	186	12	deep	deep	ADJ
ajst-27525	186	13	learning	learning	NOUN
ajst-27525	186	14	algorithm	algorithm	NOUN
ajst-27525	186	15	for	for	ADP
ajst-27525	186	16	solving	solve	VERB
ajst-27525	186	17	partial	partial	ADJ
ajst-27525	186	18	differential	differential	NOUN
ajst-27525	186	19	equations[j	equations[j	PROPN
ajst-27525	186	20	]	]	PUNCT
ajst-27525	186	21	.	.	PUNCT
ajst-27525	187	1	journal	journal	PROPN
ajst-27525	187	2	of	of	ADP
ajst-27525	187	3	computational	computational	ADJ
ajst-27525	187	4	physics	physics	NOUN
ajst-27525	187	5	,	,	PUNCT
ajst-27525	187	6	2018	2018	NUM
ajst-27525	187	7	,	,	PUNCT
ajst-27525	187	8	375	375	NUM
ajst-27525	187	9	:	:	SYM
ajst-27525	187	10	1339	1339	NUM
ajst-27525	187	11	-	-	SYM
ajst-27525	187	12	1364	1364	NUM
ajst-27525	187	13	.	.	PUNCT
ajst-27525	188	1	[	[	X
ajst-27525	188	2	17	17	NUM
ajst-27525	188	3	]	]	X
ajst-27525	188	4	kani	kani	X
ajst-27525	188	5	j	j	PROPN
ajst-27525	188	6	n	n	CCONJ
ajst-27525	188	7	,	,	PUNCT
ajst-27525	188	8	elsheikh	elsheikh	VERB
ajst-27525	188	9	a	a	DET
ajst-27525	188	10	h.	h.	NOUN
ajst-27525	188	11	reduced	reduce	VERB
ajst-27525	188	12	-	-	PUNCT
ajst-27525	188	13	order	order	NOUN
ajst-27525	188	14	modeling	modeling	NOUN
ajst-27525	188	15	of	of	ADP
ajst-27525	188	16	subsurface	subsurface	NOUN
ajst-27525	188	17	multi	multi	ADJ
ajst-27525	188	18	-	-	ADJ
ajst-27525	188	19	phase	phase	ADJ
ajst-27525	188	20	flow	flow	NOUN
ajst-27525	188	21	models	model	NOUN
ajst-27525	188	22	using	use	VERB
ajst-27525	188	23	deep	deep	ADJ
ajst-27525	188	24	residual	residual	ADJ
ajst-27525	188	25	recurrent	recurrent	ADJ
ajst-27525	188	26	neural	neural	ADJ
ajst-27525	188	27	networks[j	networks[j	PROPN
ajst-27525	188	28	]	]	PUNCT
ajst-27525	188	29	.	.	PUNCT
ajst-27525	189	1	transport	transport	NOUN
ajst-27525	189	2	in	in	ADP
ajst-27525	189	3	porous	porous	ADJ
ajst-27525	189	4	media	medium	NOUN
ajst-27525	189	5	,	,	PUNCT
ajst-27525	189	6	2019	2019	NUM
ajst-27525	189	7	,	,	PUNCT
ajst-27525	189	8	126	126	NUM
ajst-27525	189	9	:	:	PUNCT
ajst-27525	189	10	713	713	NUM
ajst-27525	189	11	-	-	SYM
ajst-27525	189	12	741	741	NUM
ajst-27525	189	13	.	.	PUNCT
ajst-27525	190	1	[	[	X
ajst-27525	190	2	18	18	NUM
ajst-27525	190	3	]	]	X
ajst-27525	190	4	raissi	raissi	PROPN
ajst-27525	190	5	m	m	NOUN
ajst-27525	190	6	,	,	PUNCT
ajst-27525	190	7	perdikaris	perdikaris	NOUN
ajst-27525	190	8	p	p	NOUN
ajst-27525	190	9	,	,	PUNCT
ajst-27525	190	10	karniadakis	karniadakis	PROPN
ajst-27525	190	11	g	g	PROPN
ajst-27525	190	12	e.	e.	PROPN
ajst-27525	190	13	physics	physics	PROPN
ajst-27525	190	14	-	-	PUNCT
ajst-27525	190	15	informed	inform	VERB
ajst-27525	190	16	neural	neural	ADJ
ajst-27525	190	17	networks	network	NOUN
ajst-27525	190	18	:	:	PUNCT
ajst-27525	190	19	a	a	DET
ajst-27525	190	20	deep	deep	ADJ
ajst-27525	190	21	learning	learning	NOUN
ajst-27525	190	22	framework	framework	NOUN
ajst-27525	190	23	for	for	ADP
ajst-27525	190	24	solving	solve	VERB
ajst-27525	190	25	forward	forward	ADV
ajst-27525	190	26	and	and	CCONJ
ajst-27525	190	27	inverse	inverse	NOUN
ajst-27525	190	28	problems	problem	NOUN
ajst-27525	190	29	involving	involve	VERB
ajst-27525	190	30	nonlinear	nonlinear	ADJ
ajst-27525	190	31	partial	partial	ADJ
ajst-27525	190	32	differential	differential	NOUN
ajst-27525	190	33	equations[j	equations[j	PROPN
ajst-27525	190	34	]	]	PUNCT
ajst-27525	190	35	.	.	PUNCT
ajst-27525	191	1	journal	journal	PROPN
ajst-27525	191	2	of	of	ADP
ajst-27525	191	3	computational	computational	ADJ
ajst-27525	191	4	physics	physics	NOUN
ajst-27525	191	5	,	,	PUNCT
ajst-27525	191	6	2019	2019	NUM
ajst-27525	191	7	,	,	PUNCT
ajst-27525	191	8	378	378	NUM
ajst-27525	191	9	:	:	PUNCT
ajst-27525	191	10	686	686	NUM
ajst-27525	191	11	-	-	SYM
ajst-27525	191	12	707	707	NUM
ajst-27525	191	13	.	.	PUNCT
ajst-27525	192	1	[	[	X
ajst-27525	192	2	19	19	NUM
ajst-27525	192	3	]	]	X
ajst-27525	192	4	meng	meng	PROPN
ajst-27525	192	5	x	x	PROPN
ajst-27525	192	6	,	,	PUNCT
ajst-27525	192	7	li	li	PROPN
ajst-27525	192	8	z	z	PROPN
ajst-27525	192	9	,	,	PUNCT
ajst-27525	192	10	zhang	zhang	PROPN
ajst-27525	192	11	d	d	PROPN
ajst-27525	192	12	,	,	PUNCT
ajst-27525	192	13	et	et	PROPN
ajst-27525	192	14	al	al	PROPN
ajst-27525	192	15	.	.	PROPN
ajst-27525	192	16	ppinn	ppinn	PROPN
ajst-27525	192	17	:	:	PUNCT
ajst-27525	192	18	parareal	parareal	NOUN
ajst-27525	192	19	physicsinformed	physicsinforme	VERB
ajst-27525	192	20	neural	neural	ADJ
ajst-27525	192	21	network	network	NOUN
ajst-27525	192	22	for	for	ADP
ajst-27525	192	23	time	time	NOUN
ajst-27525	192	24	-	-	PUNCT
ajst-27525	192	25	dependent	dependent	ADJ
ajst-27525	192	26	pdes[j	pdes[j	PROPN
ajst-27525	192	27	]	]	PUNCT
ajst-27525	192	28	.	.	PUNCT
ajst-27525	193	1	computer	computer	NOUN
ajst-27525	193	2	methods	method	NOUN
ajst-27525	193	3	in	in	ADP
ajst-27525	193	4	applied	applied	ADJ
ajst-27525	193	5	mechanics	mechanic	NOUN
ajst-27525	193	6	and	and	CCONJ
ajst-27525	193	7	engineering	engineering	NOUN
ajst-27525	193	8	,	,	PUNCT
ajst-27525	193	9	2020	2020	NUM
ajst-27525	193	10	,	,	PUNCT
ajst-27525	193	11	370	370	NUM
ajst-27525	193	12	:	:	SYM
ajst-27525	193	13	113250	113250	NUM
ajst-27525	193	14	.	.	PUNCT
ajst-27525	194	1	[	[	X
ajst-27525	194	2	20	20	NUM
ajst-27525	194	3	]	]	X
ajst-27525	194	4	jagtap	jagtap	NOUN
ajst-27525	194	5	a	a	DET
ajst-27525	194	6	d	d	PROPN
ajst-27525	194	7	,	,	PUNCT
ajst-27525	194	8	kawaguchi	kawaguchi	PROPN
ajst-27525	194	9	k	k	PROPN
ajst-27525	194	10	,	,	PUNCT
ajst-27525	194	11	karniadakis	karniadakis	PROPN
ajst-27525	194	12	g	g	PROPN
ajst-27525	194	13	e.	e.	PROPN
ajst-27525	194	14	adaptive	adaptive	PROPN
ajst-27525	194	15	activation	activation	NOUN
ajst-27525	194	16	functions	function	NOUN
ajst-27525	194	17	accelerate	accelerate	VERB
ajst-27525	194	18	convergence	convergence	NOUN
ajst-27525	194	19	in	in	ADP
ajst-27525	194	20	deep	deep	ADJ
ajst-27525	194	21	and	and	CCONJ
ajst-27525	194	22	physics	physics	NOUN
ajst-27525	194	23	-	-	PUNCT
ajst-27525	194	24	informed	inform	VERB
ajst-27525	194	25	neural	neural	ADJ
ajst-27525	194	26	networks[j	networks[j	PROPN
ajst-27525	194	27	]	]	X
ajst-27525	194	28	.	.	PUNCT
ajst-27525	195	1	journal	journal	PROPN
ajst-27525	195	2	of	of	ADP
ajst-27525	195	3	computational	computational	ADJ
ajst-27525	195	4	physics	physic	NOUN
ajst-27525	195	5	,	,	PUNCT
ajst-27525	195	6	2020	2020	NUM
ajst-27525	195	7	,	,	PUNCT
ajst-27525	195	8	404	404	NUM
ajst-27525	195	9	:	:	PUNCT
ajst-27525	195	10	109136	109136	NUM
ajst-27525	195	11	.	.	PUNCT
ajst-27525	196	1	[	[	X
ajst-27525	196	2	21	21	NUM
ajst-27525	196	3	]	]	X
ajst-27525	196	4	fraces	frace	NOUN
ajst-27525	196	5	c	c	PROPN
ajst-27525	196	6	g	g	NOUN
ajst-27525	196	7	,	,	PUNCT
ajst-27525	196	8	tchelepi	tchelepi	PROPN
ajst-27525	196	9	h.	h.	PROPN
ajst-27525	196	10	uncertainty	uncertainty	PROPN
ajst-27525	196	11	quantification	quantification	NOUN
ajst-27525	196	12	for	for	ADP
ajst-27525	196	13	transport	transport	NOUN
ajst-27525	196	14	in	in	ADP
ajst-27525	196	15	porous	porous	ADJ
ajst-27525	196	16	media	medium	NOUN
ajst-27525	196	17	using	use	VERB
ajst-27525	196	18	parameterized	parameterized	ADJ
ajst-27525	196	19	physics	physics	NOUN
ajst-27525	196	20	informed	inform	VERB
ajst-27525	196	21	neural	neural	ADJ
ajst-27525	196	22	networks[c]//spe	networks[c]//spe	PROPN
ajst-27525	196	23	reservoir	reservoir	PROPN
ajst-27525	196	24	simulation	simulation	NOUN
ajst-27525	196	25	conference	conference	PROPN
ajst-27525	196	26	?	?	PUNCT
ajst-27525	196	27	.	.	PUNCT
ajst-27525	197	1	spe	spe	PROPN
ajst-27525	197	2	,	,	PUNCT
ajst-27525	197	3	2023	2023	NUM
ajst-27525	197	4	:	:	PUNCT
ajst-27525	197	5	d011s004r003	d011s004r003	NOUN
ajst-27525	197	6	.	.	PUNCT
ajst-27525	198	1	[	[	X
ajst-27525	198	2	22	22	NUM
ajst-27525	198	3	]	]	X
ajst-27525	198	4	lu	lu	PROPN
ajst-27525	198	5	l	l	NOUN
ajst-27525	198	6	,	,	PUNCT
ajst-27525	198	7	jin	jin	NOUN
ajst-27525	198	8	p	p	X
ajst-27525	198	9	,	,	PUNCT
ajst-27525	198	10	karniadakis	karniadakis	PROPN
ajst-27525	198	11	g	g	PROPN
ajst-27525	198	12	e.	e.	PROPN
ajst-27525	198	13	deeponet	deeponet	PROPN
ajst-27525	198	14	:	:	PUNCT
ajst-27525	198	15	learning	learn	VERB
ajst-27525	198	16	nonlinear	nonlinear	ADJ
ajst-27525	198	17	operators	operator	NOUN
ajst-27525	198	18	for	for	ADP
ajst-27525	198	19	identifying	identify	VERB
ajst-27525	198	20	differential	differential	ADJ
ajst-27525	198	21	equations	equation	NOUN
ajst-27525	198	22	based	base	VERB
ajst-27525	198	23	on	on	ADP
ajst-27525	198	24	the	the	DET
ajst-27525	198	25	universal	universal	ADJ
ajst-27525	198	26	approximation	approximation	NOUN
ajst-27525	198	27	theorem	theorem	NOUN
ajst-27525	198	28	of	of	ADP
ajst-27525	198	29	operators[j	operators[j	PROPN
ajst-27525	198	30	]	]	PUNCT
ajst-27525	198	31	.	.	PUNCT
ajst-27525	199	1	arxiv	arxiv	PROPN
ajst-27525	199	2	preprint	preprint	PROPN
ajst-27525	199	3	arxiv:1910.03193	arxiv:1910.03193	NUM
ajst-27525	199	4	,	,	PUNCT
ajst-27525	199	5	2019	2019	NUM
ajst-27525	199	6	.	.	PUNCT
ajst-27525	200	1	[	[	X
ajst-27525	200	2	23	23	NUM
ajst-27525	200	3	]	]	X
ajst-27525	200	4	nelsen	nelsen	PROPN
ajst-27525	200	5	n	n	PROPN
ajst-27525	200	6	h	h	NOUN
ajst-27525	200	7	,	,	PUNCT
ajst-27525	200	8	stuart	stuart	PROPN
ajst-27525	200	9	a	a	DET
ajst-27525	200	10	m.	m.	NOUN
ajst-27525	200	11	the	the	DET
ajst-27525	200	12	random	random	ADJ
ajst-27525	200	13	feature	feature	NOUN
ajst-27525	200	14	model	model	NOUN
ajst-27525	200	15	for	for	ADP
ajst-27525	200	16	inputoutput	inputoutput	NOUN
ajst-27525	200	17	maps	map	NOUN
ajst-27525	200	18	between	between	ADP
ajst-27525	200	19	banach	banach	NOUN
ajst-27525	200	20	spaces[j	spaces[j	NOUN
ajst-27525	200	21	]	]	PUNCT
ajst-27525	200	22	.	.	PUNCT
ajst-27525	201	1	siam	siam	PROPN
ajst-27525	201	2	journal	journal	PROPN
ajst-27525	201	3	on	on	ADP
ajst-27525	201	4	scientific	scientific	ADJ
ajst-27525	201	5	computing	computing	NOUN
ajst-27525	201	6	,	,	PUNCT
ajst-27525	201	7	2021	2021	NUM
ajst-27525	201	8	,	,	PUNCT
ajst-27525	201	9	43(5	43(5	NUM
ajst-27525	201	10	):	):	PUNCT
ajst-27525	201	11	a3212	a3212	PROPN
ajst-27525	201	12	-	-	PUNCT
ajst-27525	201	13	a3243	a3243	PROPN
ajst-27525	201	14	.	.	PUNCT
ajst-27525	202	1	[	[	X
ajst-27525	202	2	24	24	NUM
ajst-27525	202	3	]	]	SYM
ajst-27525	202	4	patel	patel	PROPN
ajst-27525	202	5	r	r	PROPN
ajst-27525	202	6	g	g	PROPN
ajst-27525	202	7	,	,	PUNCT
ajst-27525	202	8	trask	trask	PROPN
ajst-27525	202	9	n	n	PROPN
ajst-27525	202	10	a	a	NOUN
ajst-27525	202	11	,	,	PUNCT
ajst-27525	202	12	wood	wood	NOUN
ajst-27525	202	13	m	m	NOUN
ajst-27525	202	14	a	a	NOUN
ajst-27525	202	15	,	,	PUNCT
ajst-27525	202	16	et	et	PROPN
ajst-27525	202	17	al	al	PROPN
ajst-27525	202	18	.	.	PUNCT
ajst-27525	203	1	a	a	DET
ajst-27525	203	2	physics	physics	NOUN
ajst-27525	203	3	-	-	PUNCT
ajst-27525	203	4	informed	inform	VERB
ajst-27525	203	5	operator	operator	NOUN
ajst-27525	203	6	regression	regression	NOUN
ajst-27525	203	7	framework	framework	NOUN
ajst-27525	203	8	for	for	ADP
ajst-27525	203	9	extracting	extract	VERB
ajst-27525	203	10	data	data	NOUN
ajst-27525	203	11	-	-	PUNCT
ajst-27525	203	12	driven	drive	VERB
ajst-27525	203	13	continuum	continuum	ADJ
ajst-27525	203	14	models[j	models[j	PROPN
ajst-27525	203	15	]	]	PUNCT
ajst-27525	203	16	.	.	PUNCT
ajst-27525	204	1	computer	computer	NOUN
ajst-27525	204	2	methods	method	NOUN
ajst-27525	204	3	in	in	ADP
ajst-27525	204	4	applied	applied	ADJ
ajst-27525	204	5	mechanics	mechanic	NOUN
ajst-27525	204	6	and	and	CCONJ
ajst-27525	204	7	engineering	engineering	NOUN
ajst-27525	204	8	,	,	PUNCT
ajst-27525	204	9	2021	2021	NUM
ajst-27525	204	10	,	,	PUNCT
ajst-27525	204	11	373	373	NUM
ajst-27525	204	12	:	:	SYM
ajst-27525	204	13	113500	113500	NUM
ajst-27525	204	14	.	.	PUNCT
ajst-27525	205	1	[	[	X
ajst-27525	205	2	25	25	NUM
ajst-27525	205	3	]	]	PUNCT
ajst-27525	205	4	hornik	hornik	X
ajst-27525	205	5	k	k	NOUN
ajst-27525	205	6	,	,	PUNCT
ajst-27525	205	7	stinchcombe	stinchcombe	PROPN
ajst-27525	205	8	m	m	PROPN
ajst-27525	205	9	,	,	PUNCT
ajst-27525	205	10	white	white	PROPN
ajst-27525	205	11	h.	h.	PROPN
ajst-27525	205	12	multilayer	multilayer	PROPN
ajst-27525	205	13	feedforward	feedforward	NOUN
ajst-27525	205	14	networks	network	NOUN
ajst-27525	205	15	are	be	AUX
ajst-27525	205	16	universal	universal	ADJ
ajst-27525	205	17	approximators[j	approximators[j	PROPN
ajst-27525	205	18	]	]	PUNCT
ajst-27525	205	19	.	.	PUNCT
ajst-27525	206	1	neural	neural	ADJ
ajst-27525	206	2	networks	network	NOUN
ajst-27525	206	3	,	,	PUNCT
ajst-27525	206	4	1989	1989	NUM
ajst-27525	206	5	,	,	PUNCT
ajst-27525	206	6	2(5	2(5	NUM
ajst-27525	206	7	):	):	PUNCT
ajst-27525	206	8	359	359	NUM
ajst-27525	206	9	-	-	SYM
ajst-27525	206	10	366	366	NUM
ajst-27525	206	11	.	.	PUNCT
ajst-27525	207	1	[	[	X
ajst-27525	207	2	26	26	NUM
ajst-27525	207	3	]	]	X
ajst-27525	207	4	lu	lu	PROPN
ajst-27525	207	5	l	l	NOUN
ajst-27525	207	6	,	,	PUNCT
ajst-27525	207	7	jin	jin	NOUN
ajst-27525	207	8	p	p	X
ajst-27525	207	9	,	,	PUNCT
ajst-27525	207	10	karniadakis	karniadakis	PROPN
ajst-27525	207	11	g	g	PROPN
ajst-27525	207	12	e.	e.	PROPN
ajst-27525	207	13	deeponet	deeponet	PROPN
ajst-27525	207	14	:	:	PUNCT
ajst-27525	207	15	learning	learn	VERB
ajst-27525	207	16	nonlinear	nonlinear	ADJ
ajst-27525	207	17	operators	operator	NOUN
ajst-27525	207	18	for	for	ADP
ajst-27525	207	19	identifying	identify	VERB
ajst-27525	207	20	differential	differential	ADJ
ajst-27525	207	21	equations	equation	NOUN
ajst-27525	207	22	based	base	VERB
ajst-27525	207	23	on	on	ADP
ajst-27525	207	24	the	the	DET
ajst-27525	207	25	universal	universal	ADJ
ajst-27525	207	26	approximation	approximation	NOUN
ajst-27525	207	27	theorem	theorem	NOUN
ajst-27525	207	28	of	of	ADP
ajst-27525	207	29	operators[j	operators[j	PROPN
ajst-27525	207	30	]	]	PUNCT
ajst-27525	207	31	.	.	PUNCT
ajst-27525	208	1	arxiv	arxiv	PROPN
ajst-27525	208	2	preprint	preprint	PROPN
ajst-27525	208	3	arxiv:1910.03193	arxiv:1910.03193	NUM
ajst-27525	208	4	,	,	PUNCT
ajst-27525	208	5	2019	2019	NUM
ajst-27525	208	6	.	.	PUNCT
ajst-27525	209	1	[	[	X
ajst-27525	209	2	27	27	NUM
ajst-27525	209	3	]	]	X
ajst-27525	209	4	li	li	PROPN
ajst-27525	209	5	z	z	PROPN
ajst-27525	209	6	,	,	PUNCT
ajst-27525	209	7	kovachki	kovachki	PROPN
ajst-27525	209	8	n	n	CCONJ
ajst-27525	209	9	,	,	PUNCT
ajst-27525	209	10	azizzadenesheli	azizzadenesheli	PROPN
ajst-27525	209	11	k	k	PROPN
ajst-27525	209	12	,	,	PUNCT
ajst-27525	209	13	et	et	PROPN
ajst-27525	210	1	al	al	PROPN
ajst-27525	210	2	.	.	PROPN
ajst-27525	211	1	fourier	fourier	PROPN
ajst-27525	211	2	neural	neural	ADJ
ajst-27525	211	3	operator	operator	NOUN
ajst-27525	211	4	for	for	ADP
ajst-27525	211	5	parametric	parametric	ADJ
ajst-27525	211	6	partial	partial	ADJ
ajst-27525	211	7	differential	differential	NOUN
ajst-27525	211	8	equations[j	equations[j	PROPN
ajst-27525	211	9	]	]	PUNCT
ajst-27525	211	10	.	.	PUNCT
ajst-27525	212	1	arxiv	arxiv	PROPN
ajst-27525	212	2	preprint	preprint	PROPN
ajst-27525	212	3	arxiv:2010.08895	arxiv:2010.08895	PROPN
ajst-27525	212	4	,	,	PUNCT
ajst-27525	212	5	2020	2020	NUM
ajst-27525	212	6	.	.	PUNCT
ajst-27525	213	1	187	187	NUM
ajst-27525	214	1	[	[	SYM
ajst-27525	214	2	28	28	NUM
ajst-27525	214	3	]	]	X
ajst-27525	214	4	zhang	zhang	PROPN
ajst-27525	214	5	k	k	PROPN
ajst-27525	214	6	,	,	PUNCT
ajst-27525	214	7	zuo	zuo	PROPN
ajst-27525	214	8	y	y	PROPN
ajst-27525	214	9	,	,	PUNCT
ajst-27525	214	10	zhao	zhao	PROPN
ajst-27525	214	11	h	h	PROPN
ajst-27525	214	12	,	,	PUNCT
ajst-27525	214	13	et	et	PROPN
ajst-27525	214	14	al	al	PROPN
ajst-27525	214	15	.	.	PROPN
ajst-27525	214	16	fourier	fourier	PROPN
ajst-27525	214	17	neural	neural	ADJ
ajst-27525	214	18	operator	operator	NOUN
ajst-27525	214	19	for	for	ADP
ajst-27525	214	20	solving	solve	VERB
ajst-27525	214	21	subsurface	subsurface	NOUN
ajst-27525	214	22	oil	oil	NOUN
ajst-27525	214	23	/	/	SYM
ajst-27525	214	24	water	water	NOUN
ajst-27525	214	25	two	two	NUM
ajst-27525	214	26	-	-	PUNCT
ajst-27525	214	27	phase	phase	NOUN
ajst-27525	214	28	flow	flow	NOUN
ajst-27525	214	29	partial	partial	ADJ
ajst-27525	214	30	differential	differential	NOUN
ajst-27525	214	31	equation[j	equation[j	NOUN
ajst-27525	214	32	]	]	PUNCT
ajst-27525	214	33	.	.	PUNCT
ajst-27525	215	1	spe	spe	PROPN
ajst-27525	215	2	journal	journal	PROPN
ajst-27525	215	3	,	,	PUNCT
ajst-27525	215	4	2022	2022	NUM
ajst-27525	215	5	,	,	PUNCT
ajst-27525	215	6	27(03	27(03	NUM
ajst-27525	215	7	):	):	PUNCT
ajst-27525	215	8	1815	1815	NUM
ajst-27525	215	9	-	-	SYM
ajst-27525	215	10	1830	1830	NUM
ajst-27525	215	11	.	.	PUNCT
ajst-27525	216	1	[	[	X
ajst-27525	216	2	29	29	NUM
ajst-27525	216	3	]	]	X
ajst-27525	216	4	du	du	PROPN
ajst-27525	216	5	y.	y.	PROPN
ajst-27525	216	6	neural	neural	ADJ
ajst-27525	216	7	operator	operator	NOUN
ajst-27525	216	8	for	for	ADP
ajst-27525	216	9	accelerating	accelerate	VERB
ajst-27525	216	10	coronal	coronal	ADJ
ajst-27525	216	11	magnetic	magnetic	ADJ
ajst-27525	216	12	field	field	NOUN
ajst-27525	216	13	computations	computation	NOUN
ajst-27525	216	14	in	in	ADP
ajst-27525	216	15	bifrost	bifrost	NOUN
ajst-27525	216	16	mhd	mhd	PROPN
ajst-27525	216	17	model[j	model[j	PROPN
ajst-27525	216	18	]	]	X
ajst-27525	216	19	.	.	PUNCT
ajst-27525	217	1	2024	2024	NUM
ajst-27525	217	2	.	.	PUNCT
ajst-27525	218	1	[	[	X
ajst-27525	218	2	30	30	NUM
ajst-27525	218	3	]	]	X
ajst-27525	218	4	wen	wen	PROPN
ajst-27525	218	5	g	g	PROPN
ajst-27525	218	6	,	,	PUNCT
ajst-27525	218	7	li	li	PROPN
ajst-27525	218	8	z	z	PROPN
ajst-27525	218	9	,	,	PUNCT
ajst-27525	218	10	azizzadenesheli	azizzadenesheli	PROPN
ajst-27525	218	11	k	k	PROPN
ajst-27525	218	12	,	,	PUNCT
ajst-27525	218	13	et	et	PROPN
ajst-27525	218	14	al	al	PROPN
ajst-27525	218	15	.	.	PUNCT
ajst-27525	219	1	u	u	PROPN
ajst-27525	219	2	-	-	PROPN
ajst-27525	219	3	fno	fno	PROPN
ajst-27525	219	4	—	—	PUNCT
ajst-27525	219	5	an	an	DET
ajst-27525	219	6	enhanced	enhanced	ADJ
ajst-27525	219	7	fourier	fourier	NOUN
ajst-27525	219	8	neural	neural	ADJ
ajst-27525	219	9	operator	operator	NOUN
ajst-27525	219	10	-	-	PUNCT
ajst-27525	219	11	based	base	VERB
ajst-27525	219	12	deep	deep	ADJ
ajst-27525	219	13	-	-	PUNCT
ajst-27525	219	14	learning	learn	VERB
ajst-27525	219	15	model	model	NOUN
ajst-27525	219	16	for	for	ADP
ajst-27525	219	17	multiphase	multiphase	PROPN
ajst-27525	219	18	flow[j	flow[j	PROPN
ajst-27525	219	19	]	]	PUNCT
ajst-27525	219	20	.	.	PUNCT
ajst-27525	220	1	advances	advance	NOUN
ajst-27525	220	2	in	in	ADP
ajst-27525	220	3	water	water	NOUN
ajst-27525	220	4	resources	resource	NOUN
ajst-27525	220	5	,	,	PUNCT
ajst-27525	220	6	2022	2022	NUM
ajst-27525	220	7	,	,	PUNCT
ajst-27525	220	8	163	163	NUM
ajst-27525	220	9	:	:	PUNCT
ajst-27525	220	10	104180	104180	NUM
ajst-27525	220	11	.	.	PUNCT
ajst-27525	221	1	[	[	X
ajst-27525	221	2	31	31	NUM
ajst-27525	221	3	]	]	X
ajst-27525	221	4	lehmann	lehmann	PROPN
ajst-27525	221	5	f	f	PROPN
ajst-27525	221	6	,	,	PUNCT
ajst-27525	221	7	gatti	gatti	PROPN
ajst-27525	221	8	f	f	PROPN
ajst-27525	221	9	,	,	PUNCT
ajst-27525	221	10	bertin	bertin	PROPN
ajst-27525	221	11	m	m	PROPN
ajst-27525	221	12	,	,	PUNCT
ajst-27525	221	13	et	et	PROPN
ajst-27525	221	14	al	al	PROPN
ajst-27525	221	15	.	.	PROPN
ajst-27525	222	1	3d	3d	NUM
ajst-27525	222	2	elastic	elastic	ADJ
ajst-27525	222	3	wave	wave	NOUN
ajst-27525	222	4	propagation	propagation	NOUN
ajst-27525	222	5	with	with	ADP
ajst-27525	222	6	a	a	DET
ajst-27525	222	7	factorized	factorize	VERB
ajst-27525	222	8	fourier	fourier	NOUN
ajst-27525	222	9	neural	neural	ADJ
ajst-27525	222	10	operator	operator	NOUN
ajst-27525	222	11	(	(	PUNCT
ajst-27525	222	12	ffno)[j	ffno)[j	PROPN
ajst-27525	222	13	]	]	PUNCT
ajst-27525	222	14	.	.	PUNCT
ajst-27525	223	1	computer	computer	NOUN
ajst-27525	223	2	methods	method	NOUN
ajst-27525	223	3	in	in	ADP
ajst-27525	223	4	applied	applied	ADJ
ajst-27525	223	5	mechanics	mechanic	NOUN
ajst-27525	223	6	and	and	CCONJ
ajst-27525	223	7	engineering	engineering	NOUN
ajst-27525	223	8	,	,	PUNCT
ajst-27525	223	9	2024	2024	NUM
ajst-27525	223	10	,	,	PUNCT
ajst-27525	223	11	420	420	NUM
ajst-27525	223	12	:	:	SYM
ajst-27525	223	13	116718	116718	NUM
ajst-27525	223	14	.	.	PUNCT
ajst-27525	224	1	[	[	X
ajst-27525	224	2	32	32	NUM
ajst-27525	224	3	]	]	X
ajst-27525	224	4	zhao	zhao	PROPN
ajst-27525	224	5	x	x	PROPN
ajst-27525	224	6	,	,	PUNCT
ajst-27525	224	7	chen	chen	PROPN
ajst-27525	224	8	x	x	PROPN
ajst-27525	224	9	,	,	PUNCT
ajst-27525	224	10	gong	gong	PROPN
ajst-27525	224	11	z	z	PROPN
ajst-27525	224	12	,	,	PUNCT
ajst-27525	224	13	et	et	PROPN
ajst-27525	224	14	al	al	PROPN
ajst-27525	224	15	.	.	PROPN
ajst-27525	224	16	recfno	recfno	PROPN
ajst-27525	224	17	:	:	PUNCT
ajst-27525	224	18	a	a	DET
ajst-27525	224	19	resolutioninvariant	resolutioninvariant	NOUN
ajst-27525	224	20	flow	flow	NOUN
ajst-27525	224	21	and	and	CCONJ
ajst-27525	224	22	heat	heat	NOUN
ajst-27525	224	23	field	field	NOUN
ajst-27525	224	24	reconstruction	reconstruction	NOUN
ajst-27525	224	25	method	method	NOUN
ajst-27525	224	26	from	from	ADP
ajst-27525	224	27	sparse	sparse	ADJ
ajst-27525	224	28	observations	observation	NOUN
ajst-27525	224	29	via	via	ADP
ajst-27525	224	30	fourier	fouri	ADJ
ajst-27525	224	31	neural	neural	ADJ
ajst-27525	224	32	operator[j	operator[j	NOUN
ajst-27525	224	33	]	]	PUNCT
ajst-27525	224	34	.	.	PUNCT
ajst-27525	225	1	international	international	ADJ
ajst-27525	225	2	journal	journal	PROPN
ajst-27525	225	3	of	of	ADP
ajst-27525	225	4	thermal	thermal	ADJ
ajst-27525	225	5	sciences	science	NOUN
ajst-27525	225	6	,	,	PUNCT
ajst-27525	225	7	2024	2024	NUM
ajst-27525	225	8	,	,	PUNCT
ajst-27525	225	9	195	195	NUM
ajst-27525	225	10	:	:	SYM
ajst-27525	225	11	108619	108619	NUM
ajst-27525	225	12	.	.	PUNCT