id	sid	tid	token	lemma	pos
ejpam-6803	1	1	european	european	PROPN
ejpam-6803	1	2	journal	journal	PROPN
ejpam-6803	1	3	of	of	ADP
ejpam-6803	1	4	pure	pure	ADJ
ejpam-6803	1	5	and	and	CCONJ
ejpam-6803	1	6	applied	applied	ADJ
ejpam-6803	1	7	mathematics	mathematic	NOUN
ejpam-6803	1	8	2025	2025	NUM
ejpam-6803	1	9	,	,	PUNCT
ejpam-6803	1	10	vol	vol	NOUN
ejpam-6803	1	11	.	.	PROPN
ejpam-6803	1	12	18	18	NUM
ejpam-6803	1	13	,	,	PUNCT
ejpam-6803	1	14	issue	issue	NOUN
ejpam-6803	1	15	4	4	NUM
ejpam-6803	1	16	,	,	PUNCT
ejpam-6803	1	17	article	article	NOUN
ejpam-6803	1	18	number	number	NOUN
ejpam-6803	1	19	6803	6803	NUM
ejpam-6803	1	20	issn	issn	PROPN
ejpam-6803	1	21	1307	1307	NUM
ejpam-6803	1	22	-	-	SYM
ejpam-6803	1	23	5543	5543	NUM
ejpam-6803	1	24	–	–	PUNCT
ejpam-6803	1	25	ejpam.com	ejpam.com	X
ejpam-6803	1	26	published	publish	VERB
ejpam-6803	1	27	by	by	ADP
ejpam-6803	1	28	new	new	PROPN
ejpam-6803	1	29	york	york	PROPN
ejpam-6803	1	30	business	business	PROPN
ejpam-6803	1	31	global	global	PROPN
ejpam-6803	1	32	data	data	NOUN
ejpam-6803	1	33	-	-	PUNCT
ejpam-6803	1	34	driven	drive	VERB
ejpam-6803	1	35	modeling	modeling	NOUN
ejpam-6803	1	36	of	of	ADP
ejpam-6803	1	37	boussinesq	boussinesq	ADJ
ejpam-6803	1	38	-	-	PUNCT
ejpam-6803	1	39	burgers	burger	NOUN
ejpam-6803	1	40	equations	equation	NOUN
ejpam-6803	1	41	:	:	PUNCT
ejpam-6803	1	42	comparing	compare	VERB
ejpam-6803	1	43	physics	physics	NOUN
ejpam-6803	1	44	-	-	PUNCT
ejpam-6803	1	45	informed	inform	VERB
ejpam-6803	1	46	neural	neural	ADJ
ejpam-6803	1	47	networks	network	NOUN
ejpam-6803	1	48	(	(	PUNCT
ejpam-6803	1	49	pinns	pinn	NOUN
ejpam-6803	1	50	)	)	PUNCT
ejpam-6803	1	51	with	with	ADP
ejpam-6803	1	52	exact	exact	ADJ
ejpam-6803	1	53	solutions	solution	NOUN
ejpam-6803	1	54	ahmad	ahmad	PROPN
ejpam-6803	1	55	shafee1,∗	shafee1,∗	PROPN
ejpam-6803	1	56	,	,	PUNCT
ejpam-6803	1	57	yousuf	yousuf	PROPN
ejpam-6803	1	58	alkhezi2	alkhezi2	PROPN
ejpam-6803	1	59	,	,	PUNCT
ejpam-6803	1	60	kavikumar	kavikumar	PROPN
ejpam-6803	1	61	jacob3	jacob3	NOUN
ejpam-6803	1	62	1	1	NUM
ejpam-6803	1	63	paaet	paaet	NOUN
ejpam-6803	1	64	,	,	PUNCT
ejpam-6803	1	65	college	college	NOUN
ejpam-6803	1	66	of	of	ADP
ejpam-6803	1	67	technological	technological	ADJ
ejpam-6803	1	68	studies	study	NOUN
ejpam-6803	1	69	,	,	PUNCT
ejpam-6803	1	70	laboratory	laboratory	NOUN
ejpam-6803	1	71	technology	technology	PROPN
ejpam-6803	1	72	department	department	PROPN
ejpam-6803	1	73	,	,	PUNCT
ejpam-6803	1	74	shuwaikh	shuwaikh	NOUN
ejpam-6803	1	75	70654	70654	NUM
ejpam-6803	1	76	,	,	PUNCT
ejpam-6803	1	77	kuwait	kuwait	PROPN
ejpam-6803	1	78	2	2	NUM
ejpam-6803	1	79	mathematics	mathematics	PROPN
ejpam-6803	1	80	department	department	NOUN
ejpam-6803	1	81	,	,	PUNCT
ejpam-6803	1	82	college	college	NOUN
ejpam-6803	1	83	of	of	ADP
ejpam-6803	1	84	basic	basic	ADJ
ejpam-6803	1	85	education	education	NOUN
ejpam-6803	1	86	,	,	PUNCT
ejpam-6803	1	87	public	public	ADJ
ejpam-6803	1	88	authority	authority	NOUN
ejpam-6803	1	89	for	for	ADP
ejpam-6803	1	90	applied	apply	VERB
ejpam-6803	1	91	education	education	NOUN
ejpam-6803	1	92	and	and	CCONJ
ejpam-6803	1	93	training	training	NOUN
ejpam-6803	1	94	(	(	PUNCT
ejpam-6803	1	95	paaet	paaet	NOUN
ejpam-6803	1	96	)	)	PUNCT
ejpam-6803	1	97	,	,	PUNCT
ejpam-6803	1	98	ardiya	ardiya	PROPN
ejpam-6803	1	99	,	,	PUNCT
ejpam-6803	1	100	kuwait	kuwait	PROPN
ejpam-6803	1	101	3	3	NUM
ejpam-6803	1	102	department	department	NOUN
ejpam-6803	1	103	of	of	ADP
ejpam-6803	1	104	mathematics	mathematic	NOUN
ejpam-6803	1	105	and	and	CCONJ
ejpam-6803	1	106	statistics	statistic	NOUN
ejpam-6803	1	107	,	,	PUNCT
ejpam-6803	1	108	faculty	faculty	NOUN
ejpam-6803	1	109	of	of	ADP
ejpam-6803	1	110	applied	apply	VERB
ejpam-6803	1	111	sciences	science	NOUN
ejpam-6803	1	112	and	and	CCONJ
ejpam-6803	1	113	technology	technology	NOUN
ejpam-6803	1	114	,	,	PUNCT
ejpam-6803	1	115	universiti	universiti	PROPN
ejpam-6803	1	116	tun	tun	PROPN
ejpam-6803	1	117	hussein	hussein	PROPN
ejpam-6803	1	118	onn	onn	PROPN
ejpam-6803	1	119	malaysia	malaysia	PROPN
ejpam-6803	1	120	,	,	PUNCT
ejpam-6803	1	121	pagoh	pagoh	PROPN
ejpam-6803	1	122	campus	campus	PROPN
ejpam-6803	1	123	,	,	PUNCT
ejpam-6803	1	124	84600	84600	NUM
ejpam-6803	1	125	pagoh	pagoh	NOUN
ejpam-6803	1	126	,	,	PUNCT
ejpam-6803	1	127	malaysia	malaysia	PROPN
ejpam-6803	1	128	abstract	abstract	NOUN
ejpam-6803	1	129	.	.	PUNCT
ejpam-6803	2	1	this	this	DET
ejpam-6803	2	2	paper	paper	NOUN
ejpam-6803	2	3	presents	present	VERB
ejpam-6803	2	4	a	a	DET
ejpam-6803	2	5	novel	novel	ADJ
ejpam-6803	2	6	deep	deep	ADJ
ejpam-6803	2	7	neural	neural	ADJ
ejpam-6803	2	8	network	network	NOUN
ejpam-6803	2	9	-	-	PUNCT
ejpam-6803	2	10	based	base	VERB
ejpam-6803	2	11	scheme	scheme	NOUN
ejpam-6803	2	12	for	for	ADP
ejpam-6803	2	13	generating	generate	VERB
ejpam-6803	2	14	approximate	approximate	ADJ
ejpam-6803	2	15	solutions	solution	NOUN
ejpam-6803	2	16	of	of	ADP
ejpam-6803	2	17	the	the	DET
ejpam-6803	2	18	coupled	couple	VERB
ejpam-6803	2	19	boussinesq	boussinesq	ADJ
ejpam-6803	2	20	-	-	PUNCT
ejpam-6803	2	21	burgers	burger	NOUN
ejpam-6803	2	22	equations	equation	NOUN
ejpam-6803	2	23	of	of	ADP
ejpam-6803	2	24	integer	integer	NOUN
ejpam-6803	2	25	order	order	NOUN
ejpam-6803	2	26	.	.	PUNCT
ejpam-6803	3	1	standard	standard	ADJ
ejpam-6803	3	2	numerical	numerical	ADJ
ejpam-6803	3	3	techniques	technique	NOUN
ejpam-6803	3	4	can	can	AUX
ejpam-6803	3	5	face	face	VERB
ejpam-6803	3	6	challenges	challenge	NOUN
ejpam-6803	3	7	in	in	ADP
ejpam-6803	3	8	the	the	DET
ejpam-6803	3	9	case	case	NOUN
ejpam-6803	3	10	of	of	ADP
ejpam-6803	3	11	these	these	DET
ejpam-6803	3	12	nonlinearly	nonlinearly	ADV
ejpam-6803	3	13	coupled	couple	VERB
ejpam-6803	3	14	systems	system	NOUN
ejpam-6803	3	15	,	,	PUNCT
ejpam-6803	3	16	in	in	ADP
ejpam-6803	3	17	particular	particular	ADJ
ejpam-6803	3	18	when	when	SCONJ
ejpam-6803	3	19	dealing	deal	VERB
ejpam-6803	3	20	with	with	ADP
ejpam-6803	3	21	high	high	ADJ
ejpam-6803	3	22	dimensions	dimension	NOUN
ejpam-6803	3	23	.	.	PUNCT
ejpam-6803	4	1	this	this	PRON
ejpam-6803	4	2	presented	present	VERB
ejpam-6803	4	3	work	work	NOUN
ejpam-6803	4	4	uses	use	VERB
ejpam-6803	4	5	feedforward	feedforward	NOUN
ejpam-6803	4	6	neural	neural	ADJ
ejpam-6803	4	7	networks	network	NOUN
ejpam-6803	4	8	to	to	PART
ejpam-6803	4	9	learn	learn	VERB
ejpam-6803	4	10	the	the	DET
ejpam-6803	4	11	solution	solution	NOUN
ejpam-6803	4	12	functions	function	NOUN
ejpam-6803	4	13	embed	embed	VERB
ejpam-6803	4	14	the	the	DET
ejpam-6803	4	15	physics	physics	NOUN
ejpam-6803	4	16	of	of	ADP
ejpam-6803	4	17	the	the	DET
ejpam-6803	4	18	problem	problem	NOUN
ejpam-6803	4	19	in	in	ADP
ejpam-6803	4	20	the	the	DET
ejpam-6803	4	21	learning	learning	NOUN
ejpam-6803	4	22	.	.	PUNCT
ejpam-6803	5	1	the	the	DET
ejpam-6803	5	2	residuals	residual	NOUN
ejpam-6803	5	3	of	of	ADP
ejpam-6803	5	4	the	the	DET
ejpam-6803	5	5	governing	govern	VERB
ejpam-6803	5	6	pdes	pde	NOUN
ejpam-6803	5	7	and	and	CCONJ
ejpam-6803	5	8	initial	initial	ADJ
ejpam-6803	5	9	condition	condition	NOUN
ejpam-6803	5	10	are	be	AUX
ejpam-6803	5	11	set	set	VERB
ejpam-6803	5	12	up	up	ADP
ejpam-6803	5	13	and	and	CCONJ
ejpam-6803	5	14	minimized	minimize	VERB
ejpam-6803	5	15	in	in	ADP
ejpam-6803	5	16	the	the	DET
ejpam-6803	5	17	structure	structure	NOUN
ejpam-6803	5	18	of	of	ADP
ejpam-6803	5	19	a	a	DET
ejpam-6803	5	20	composite	composite	ADJ
ejpam-6803	5	21	loss	loss	NOUN
ejpam-6803	5	22	function	function	NOUN
ejpam-6803	5	23	by	by	ADP
ejpam-6803	5	24	automatic	automatic	ADJ
ejpam-6803	5	25	differentiation	differentiation	NOUN
ejpam-6803	5	26	.	.	PUNCT
ejpam-6803	6	1	the	the	DET
ejpam-6803	6	2	networks	network	NOUN
ejpam-6803	6	3	are	be	AUX
ejpam-6803	6	4	optimized	optimize	VERB
ejpam-6803	6	5	through	through	ADP
ejpam-6803	6	6	gradient	gradient	NOUN
ejpam-6803	6	7	based	base	VERB
ejpam-6803	6	8	techniques	technique	NOUN
ejpam-6803	6	9	to	to	PART
ejpam-6803	6	10	determine	determine	VERB
ejpam-6803	6	11	a	a	DET
ejpam-6803	6	12	high	high	ADJ
ejpam-6803	6	13	accurate	accurate	ADJ
ejpam-6803	6	14	and	and	CCONJ
ejpam-6803	6	15	generalizable	generalizable	ADJ
ejpam-6803	6	16	networks	network	NOUN
ejpam-6803	6	17	over	over	ADP
ejpam-6803	6	18	the	the	DET
ejpam-6803	6	19	solution	solution	NOUN
ejpam-6803	6	20	domain	domain	NOUN
ejpam-6803	6	21	.	.	PUNCT
ejpam-6803	7	1	results	result	NOUN
ejpam-6803	7	2	show	show	VERB
ejpam-6803	7	3	that	that	SCONJ
ejpam-6803	7	4	the	the	DET
ejpam-6803	7	5	proposed	propose	VERB
ejpam-6803	7	6	neural	neural	ADJ
ejpam-6803	7	7	network	network	NOUN
ejpam-6803	7	8	model	model	NOUN
ejpam-6803	7	9	is	be	AUX
ejpam-6803	7	10	able	able	ADJ
ejpam-6803	7	11	to	to	PART
ejpam-6803	7	12	approximate	approximate	VERB
ejpam-6803	7	13	the	the	DET
ejpam-6803	7	14	complex	complex	ADJ
ejpam-6803	7	15	dynamics	dynamic	NOUN
ejpam-6803	7	16	and	and	CCONJ
ejpam-6803	7	17	is	be	AUX
ejpam-6803	7	18	in	in	ADP
ejpam-6803	7	19	very	very	ADV
ejpam-6803	7	20	good	good	ADJ
ejpam-6803	7	21	match	match	NOUN
ejpam-6803	7	22	with	with	ADP
ejpam-6803	7	23	the	the	DET
ejpam-6803	7	24	exact	exact	ADJ
ejpam-6803	7	25	solutions	solution	NOUN
ejpam-6803	7	26	where	where	SCONJ
ejpam-6803	7	27	they	they	PRON
ejpam-6803	7	28	exist	exist	VERB
ejpam-6803	7	29	.	.	PUNCT
ejpam-6803	8	1	the	the	DET
ejpam-6803	8	2	absolute	absolute	ADJ
ejpam-6803	8	3	error	error	NOUN
ejpam-6803	8	4	between	between	ADP
ejpam-6803	8	5	pinn	pinn	NOUN
ejpam-6803	8	6	and	and	CCONJ
ejpam-6803	8	7	exact	exact	ADJ
ejpam-6803	8	8	solution	solution	NOUN
ejpam-6803	8	9	is	be	AUX
ejpam-6803	8	10	in	in	ADP
ejpam-6803	8	11	the	the	DET
ejpam-6803	8	12	range	range	NOUN
ejpam-6803	8	13	of	of	ADP
ejpam-6803	8	14	10−4	10−4	NUM
ejpam-6803	8	15	to	to	ADP
ejpam-6803	8	16	10−3	10−3	NUM
ejpam-6803	8	17	,	,	PUNCT
ejpam-6803	8	18	indicating	indicate	VERB
ejpam-6803	8	19	the	the	DET
ejpam-6803	8	20	efficiency	efficiency	NOUN
ejpam-6803	8	21	of	of	ADP
ejpam-6803	8	22	the	the	DET
ejpam-6803	8	23	model	model	NOUN
ejpam-6803	8	24	.	.	PUNCT
ejpam-6803	9	1	2020	2020	NUM
ejpam-6803	9	2	mathematics	mathematics	PROPN
ejpam-6803	9	3	subject	subject	NOUN
ejpam-6803	9	4	classifications	classification	NOUN
ejpam-6803	9	5	:	:	PUNCT
ejpam-6803	9	6	35q35	35q35	NUM
ejpam-6803	9	7	,	,	PUNCT
ejpam-6803	9	8	65m75	65m75	NUM
ejpam-6803	9	9	,	,	PUNCT
ejpam-6803	9	10	68t07	68t07	NUM
ejpam-6803	9	11	key	key	ADJ
ejpam-6803	9	12	words	word	NOUN
ejpam-6803	9	13	and	and	CCONJ
ejpam-6803	9	14	phrases	phrase	NOUN
ejpam-6803	9	15	:	:	PUNCT
ejpam-6803	9	16	boussinesq	boussinesq	ADJ
ejpam-6803	9	17	-	-	PUNCT
ejpam-6803	9	18	burgers	burger	NOUN
ejpam-6803	9	19	equations	equation	NOUN
ejpam-6803	9	20	of	of	ADP
ejpam-6803	9	21	integer	integer	NOUN
ejpam-6803	9	22	order	order	NOUN
ejpam-6803	9	23	,	,	PUNCT
ejpam-6803	9	24	physics	physics	NOUN
ejpam-6803	9	25	-	-	PUNCT
ejpam-6803	9	26	informed	inform	VERB
ejpam-6803	9	27	neural	neural	ADJ
ejpam-6803	9	28	networks	network	NOUN
ejpam-6803	9	29	,	,	PUNCT
ejpam-6803	9	30	pinns	pinn	NOUN
ejpam-6803	9	31	,	,	PUNCT
ejpam-6803	9	32	nonlinear	nonlinear	ADJ
ejpam-6803	9	33	pdes	pde	NOUN
ejpam-6803	9	34	,	,	PUNCT
ejpam-6803	9	35	deep	deep	ADJ
ejpam-6803	9	36	learning	learning	NOUN
ejpam-6803	9	37	,	,	PUNCT
ejpam-6803	9	38	exact	exact	ADJ
ejpam-6803	9	39	solution	solution	NOUN
ejpam-6803	9	40	comparison	comparison	NOUN
ejpam-6803	9	41	,	,	PUNCT
ejpam-6803	9	42	data	data	NOUN
ejpam-6803	9	43	-	-	PUNCT
ejpam-6803	9	44	driven	drive	VERB
ejpam-6803	9	45	modeling	modeling	NOUN
ejpam-6803	9	46	,	,	PUNCT
ejpam-6803	9	47	pde	pde	NOUN
ejpam-6803	9	48	approximation	approximation	NOUN
ejpam-6803	9	49	1	1	NUM
ejpam-6803	9	50	.	.	PUNCT
ejpam-6803	10	1	introduction	introduction	NOUN
ejpam-6803	10	2	nonlinear	nonlinear	ADJ
ejpam-6803	10	3	dispersive	dispersive	ADJ
ejpam-6803	10	4	wave	wave	NOUN
ejpam-6803	10	5	effects	effect	NOUN
ejpam-6803	10	6	are	be	AUX
ejpam-6803	10	7	fundamental	fundamental	ADJ
ejpam-6803	10	8	in	in	ADP
ejpam-6803	10	9	fluid	fluid	ADJ
ejpam-6803	10	10	dynamic	dynamic	ADJ
ejpam-6803	10	11	systems	system	NOUN
ejpam-6803	10	12	.	.	PUNCT
ejpam-6803	11	1	one	one	NUM
ejpam-6803	11	2	such	such	ADJ
ejpam-6803	11	3	prototype	prototype	NOUN
ejpam-6803	11	4	is	be	AUX
ejpam-6803	11	5	the	the	DET
ejpam-6803	11	6	coupled	couple	VERB
ejpam-6803	11	7	integer	integer	NOUN
ejpam-6803	11	8	-	-	PUNCT
ejpam-6803	11	9	order	order	NOUN
ejpam-6803	11	10	boussinesq	boussinesq	ADJ
ejpam-6803	11	11	-	-	PUNCT
ejpam-6803	11	12	burgers	burger	NOUN
ejpam-6803	11	13	equation	equation	NOUN
ejpam-6803	11	14	(	(	PUNCT
ejpam-6803	11	15	bbe	bbe	NOUN
ejpam-6803	11	16	)	)	PUNCT
ejpam-6803	11	17	system	system	NOUN
ejpam-6803	11	18	that	that	PRON
ejpam-6803	11	19	describes	describe	VERB
ejpam-6803	11	20	the	the	DET
ejpam-6803	11	21	interplay	interplay	NOUN
ejpam-6803	11	22	between	between	ADP
ejpam-6803	11	23	horizontal	horizontal	ADJ
ejpam-6803	11	24	velocity	velocity	NOUN
ejpam-6803	11	25	and	and	CCONJ
ejpam-6803	11	26	wave	wave	NOUN
ejpam-6803	11	27	amplitude	amplitude	NOUN
ejpam-6803	11	28	in	in	ADP
ejpam-6803	11	29	shallow	shallow	ADJ
ejpam-6803	11	30	-	-	PUNCT
ejpam-6803	11	31	water	water	NOUN
ejpam-6803	11	32	∗corresponding	∗corresponde	VERB
ejpam-6803	11	33	author	author	NOUN
ejpam-6803	11	34	.	.	PUNCT
ejpam-6803	12	1	doi	doi	NOUN
ejpam-6803	12	2	:	:	PUNCT
ejpam-6803	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6803	https://doi.org/10.29020/nybg.ejpam.v18i4.6803	NOUN
ejpam-6803	12	4	email	email	NOUN
ejpam-6803	12	5	addresses	address	NOUN
ejpam-6803	12	6	:	:	PUNCT
ejpam-6803	12	7	ya.alkhezi@paaet.edu.kw	ya.alkhezi@paaet.edu.kw	ADV
ejpam-6803	12	8	(	(	PUNCT
ejpam-6803	12	9	y.	y.	PROPN
ejpam-6803	12	10	alkhezi	alkhezi	PROPN
ejpam-6803	12	11	)	)	PUNCT
ejpam-6803	12	12	,	,	PUNCT
ejpam-6803	12	13	kavi@uthm.edu.my	kavi@uthm.edu.my	X
ejpam-6803	12	14	(	(	PUNCT
ejpam-6803	12	15	k.	k.	PROPN
ejpam-6803	12	16	jacob	jacob	PROPN
ejpam-6803	12	17	)	)	PUNCT
ejpam-6803	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6803	13	1	1	1	NUM
ejpam-6803	13	2	copyright	copyright	NOUN
ejpam-6803	13	3	:	:	PUNCT
ejpam-6803	13	4	©	©	PROPN
ejpam-6803	13	5	2025	2025	NUM
ejpam-6803	13	6	the	the	DET
ejpam-6803	13	7	author(s	author(s	NOUN
ejpam-6803	13	8	)	)	PUNCT
ejpam-6803	13	9	.	.	PUNCT
ejpam-6803	14	1	(	(	PUNCT
ejpam-6803	14	2	cc	cc	NOUN
ejpam-6803	14	3	by	by	ADP
ejpam-6803	14	4	-	-	PUNCT
ejpam-6803	14	5	nc	nc	PROPN
ejpam-6803	14	6	4.0	4.0	NUM
ejpam-6803	14	7	)	)	PUNCT
ejpam-6803	14	8	a.	a.	NOUN
ejpam-6803	14	9	shafee	shafee	PROPN
ejpam-6803	14	10	et	et	PROPN
ejpam-6803	14	11	al	al	PROPN
ejpam-6803	14	12	.	.	PUNCT
ejpam-6803	14	13	/	/	SYM
ejpam-6803	14	14	eur	eur	PROPN
ejpam-6803	14	15	.	.	PUNCT
ejpam-6803	15	1	j.	j.	PROPN
ejpam-6803	15	2	pure	pure	PROPN
ejpam-6803	15	3	appl	appl	PROPN
ejpam-6803	15	4	.	.	PROPN
ejpam-6803	15	5	math	math	PROPN
ejpam-6803	15	6	,	,	PUNCT
ejpam-6803	15	7	18	18	NUM
ejpam-6803	15	8	(	(	PUNCT
ejpam-6803	15	9	4	4	NUM
ejpam-6803	15	10	)	)	PUNCT
ejpam-6803	15	11	(	(	PUNCT
ejpam-6803	15	12	2025	2025	NUM
ejpam-6803	15	13	)	)	PUNCT
ejpam-6803	15	14	,	,	PUNCT
ejpam-6803	15	15	6803	6803	NUM
ejpam-6803	15	16	2	2	NUM
ejpam-6803	15	17	of	of	ADP
ejpam-6803	15	18	18	18	NUM
ejpam-6803	15	19	or	or	CCONJ
ejpam-6803	15	20	porous	porous	ADJ
ejpam-6803	15	21	-	-	PUNCT
ejpam-6803	15	22	media	medium	NOUN
ejpam-6803	15	23	settings	setting	NOUN
ejpam-6803	15	24	[	[	X
ejpam-6803	15	25	1–3	1–3	NOUN
ejpam-6803	15	26	]	]	X
ejpam-6803	15	27	.	.	PUNCT
ejpam-6803	16	1	conventional	conventional	ADJ
ejpam-6803	16	2	numerical	numerical	ADJ
ejpam-6803	16	3	approaches	approach	NOUN
ejpam-6803	16	4	such	such	ADJ
ejpam-6803	16	5	as	as	ADP
ejpam-6803	16	6	the	the	DET
ejpam-6803	16	7	finite	finite	PROPN
ejpam-6803	16	8	differences	difference	NOUN
ejpam-6803	16	9	,	,	PUNCT
ejpam-6803	16	10	finite	finite	ADJ
ejpam-6803	16	11	elements	element	NOUN
ejpam-6803	16	12	,	,	PUNCT
ejpam-6803	16	13	spectral	spectral	ADJ
ejpam-6803	16	14	,	,	PUNCT
ejpam-6803	16	15	and	and	CCONJ
ejpam-6803	16	16	mesh	mesh	NOUN
ejpam-6803	16	17	-	-	PUNCT
ejpam-6803	16	18	free	free	ADJ
ejpam-6803	16	19	methods	method	NOUN
ejpam-6803	16	20	frequently	frequently	ADV
ejpam-6803	16	21	face	face	VERB
ejpam-6803	16	22	difficulty	difficulty	NOUN
ejpam-6803	16	23	in	in	ADP
ejpam-6803	16	24	resolving	resolve	VERB
ejpam-6803	16	25	with	with	ADP
ejpam-6803	16	26	accuracy	accuracy	NOUN
ejpam-6803	16	27	and	and	CCONJ
ejpam-6803	16	28	efficiency	efficiency	NOUN
ejpam-6803	16	29	these	these	DET
ejpam-6803	16	30	novel	novel	NOUN
ejpam-6803	16	31	,	,	PUNCT
ejpam-6803	16	32	complex	complex	ADJ
ejpam-6803	16	33	nonlinearness	nonlinearness	NOUN
ejpam-6803	16	34	,	,	PUNCT
ejpam-6803	16	35	in	in	ADP
ejpam-6803	16	36	particular	particular	ADJ
ejpam-6803	16	37	in	in	ADP
ejpam-6803	16	38	multi	multi	ADJ
ejpam-6803	16	39	-	-	ADJ
ejpam-6803	16	40	dimensional	dimensional	ADJ
ejpam-6803	16	41	or	or	CCONJ
ejpam-6803	16	42	highly	highly	ADV
ejpam-6803	16	43	coupled	couple	VERB
ejpam-6803	16	44	scenarios	scenario	NOUN
ejpam-6803	16	45	[	[	X
ejpam-6803	16	46	4–6	4–6	X
ejpam-6803	16	47	]	]	X
ejpam-6803	16	48	.	.	PUNCT
ejpam-6803	17	1	and	and	CCONJ
ejpam-6803	17	2	also	also	ADV
ejpam-6803	17	3	,	,	PUNCT
ejpam-6803	17	4	they	they	PRON
ejpam-6803	17	5	suffer	suffer	VERB
ejpam-6803	17	6	from	from	ADP
ejpam-6803	17	7	issues	issue	NOUN
ejpam-6803	17	8	such	such	ADJ
ejpam-6803	17	9	as	as	ADP
ejpam-6803	17	10	meshing	meshing	NOUN
ejpam-6803	17	11	,	,	PUNCT
ejpam-6803	17	12	numerical	numerical	ADJ
ejpam-6803	17	13	dispersion	dispersion	NOUN
ejpam-6803	17	14	,	,	PUNCT
ejpam-6803	17	15	stability	stability	NOUN
ejpam-6803	17	16	limitation	limitation	NOUN
ejpam-6803	17	17	and	and	CCONJ
ejpam-6803	17	18	computational	computational	ADJ
ejpam-6803	17	19	complexity	complexity	NOUN
ejpam-6803	18	1	[	[	X
ejpam-6803	18	2	7–9	7–9	X
ejpam-6803	18	3	]	]	X
ejpam-6803	18	4	.	.	PUNCT
ejpam-6803	19	1	moreover	moreover	ADV
ejpam-6803	19	2	,	,	PUNCT
ejpam-6803	19	3	the	the	DET
ejpam-6803	19	4	current	current	ADJ
ejpam-6803	19	5	research	research	NOUN
ejpam-6803	19	6	is	be	AUX
ejpam-6803	19	7	on	on	ADP
ejpam-6803	19	8	integer	integer	NOUN
ejpam-6803	19	9	-	-	PUNCT
ejpam-6803	19	10	order	order	NOUN
ejpam-6803	19	11	pdes	pde	NOUN
ejpam-6803	19	12	,	,	PUNCT
ejpam-6803	19	13	but	but	CCONJ
ejpam-6803	19	14	a	a	DET
ejpam-6803	19	15	prospective	prospective	ADJ
ejpam-6803	19	16	future	future	ADJ
ejpam-6803	19	17	extension	extension	NOUN
ejpam-6803	19	18	to	to	ADP
ejpam-6803	19	19	a	a	DET
ejpam-6803	19	20	fractional	fractional	ADJ
ejpam-6803	19	21	-	-	PUNCT
ejpam-6803	19	22	order	order	NOUN
ejpam-6803	19	23	bbe	bbe	NOUN
ejpam-6803	19	24	system	system	NOUN
ejpam-6803	19	25	would	would	AUX
ejpam-6803	19	26	be	be	AUX
ejpam-6803	19	27	an	an	DET
ejpam-6803	19	28	interesting	interesting	ADJ
ejpam-6803	19	29	route	route	NOUN
ejpam-6803	19	30	.	.	PUNCT
ejpam-6803	20	1	it	it	PRON
ejpam-6803	20	2	has	have	AUX
ejpam-6803	20	3	been	be	AUX
ejpam-6803	20	4	understood	understand	VERB
ejpam-6803	20	5	that	that	SCONJ
ejpam-6803	20	6	fractional	fractional	ADJ
ejpam-6803	20	7	representation	representation	NOUN
ejpam-6803	20	8	models	model	NOUN
ejpam-6803	20	9	are	be	AUX
ejpam-6803	20	10	more	more	ADV
ejpam-6803	20	11	realistic	realistic	ADJ
ejpam-6803	20	12	at	at	ADP
ejpam-6803	20	13	describing	describe	VERB
ejpam-6803	20	14	memory	memory	NOUN
ejpam-6803	20	15	and	and	CCONJ
ejpam-6803	20	16	hereditary	hereditary	ADJ
ejpam-6803	20	17	effects	effect	NOUN
ejpam-6803	20	18	in	in	ADP
ejpam-6803	20	19	real	real	ADJ
ejpam-6803	20	20	systems	system	NOUN
ejpam-6803	20	21	[	[	X
ejpam-6803	20	22	10–15	10–15	NUM
ejpam-6803	20	23	]	]	PUNCT
ejpam-6803	20	24	and	and	CCONJ
ejpam-6803	20	25	that	that	SCONJ
ejpam-6803	20	26	they	they	PRON
ejpam-6803	20	27	can	can	AUX
ejpam-6803	20	28	be	be	AUX
ejpam-6803	20	29	combined	combine	VERB
ejpam-6803	20	30	with	with	ADP
ejpam-6803	20	31	pinns	pinn	NOUN
ejpam-6803	20	32	to	to	PART
ejpam-6803	20	33	achieve	achieve	VERB
ejpam-6803	20	34	more	more	ADV
ejpam-6803	20	35	accurate	accurate	ADJ
ejpam-6803	20	36	and	and	CCONJ
ejpam-6803	20	37	realistic	realistic	ADJ
ejpam-6803	20	38	results	result	NOUN
ejpam-6803	20	39	.	.	PUNCT
ejpam-6803	21	1	in	in	ADP
ejpam-6803	21	2	previous	previous	ADJ
ejpam-6803	21	3	years	year	NOUN
ejpam-6803	21	4	,	,	PUNCT
ejpam-6803	21	5	deep	deep	ADJ
ejpam-6803	21	6	learning	learning	NOUN
ejpam-6803	21	7	(	(	PUNCT
ejpam-6803	21	8	dl	dl	INTJ
ejpam-6803	21	9	)	)	PUNCT
ejpam-6803	21	10	has	have	AUX
ejpam-6803	21	11	been	be	AUX
ejpam-6803	21	12	proposed	propose	VERB
ejpam-6803	21	13	as	as	ADP
ejpam-6803	21	14	a	a	DET
ejpam-6803	21	15	disruptive	disruptive	ADJ
ejpam-6803	21	16	alternative	alternative	NOUN
ejpam-6803	21	17	for	for	ADP
ejpam-6803	21	18	conventional	conventional	ADJ
ejpam-6803	21	19	pde	pde	NOUN
ejpam-6803	21	20	solvers	solver	NOUN
ejpam-6803	21	21	[	[	X
ejpam-6803	21	22	16–18	16–18	NUM
ejpam-6803	21	23	]	]	PUNCT
ejpam-6803	21	24	.	.	PUNCT
ejpam-6803	22	1	the	the	DET
ejpam-6803	22	2	universal	universal	ADJ
ejpam-6803	22	3	approximation	approximation	NOUN
ejpam-6803	22	4	theorem	theorem	NOUN
ejpam-6803	22	5	(	(	PUNCT
ejpam-6803	22	6	uat	uat	PROPN
ejpam-6803	22	7	)	)	PUNCT
ejpam-6803	22	8	indicates	indicate	VERB
ejpam-6803	22	9	fnns	fnn	NOUN
ejpam-6803	22	10	can	can	AUX
ejpam-6803	22	11	approximate	approximate	VERB
ejpam-6803	22	12	arbitrary	arbitrary	ADJ
ejpam-6803	22	13	continuous	continuous	ADJ
ejpam-6803	22	14	function	function	NOUN
ejpam-6803	22	15	under	under	ADP
ejpam-6803	22	16	certain	certain	ADJ
ejpam-6803	22	17	conditions	condition	NOUN
ejpam-6803	22	18	of	of	ADP
ejpam-6803	22	19	width	width	NOUN
ejpam-6803	22	20	or	or	CCONJ
ejpam-6803	22	21	depth	depth	NOUN
ejpam-6803	22	22	[	[	X
ejpam-6803	22	23	19	19	NUM
ejpam-6803	22	24	,	,	PUNCT
ejpam-6803	22	25	20	20	NUM
ejpam-6803	22	26	]	]	PUNCT
ejpam-6803	22	27	.	.	PUNCT
ejpam-6803	23	1	this	this	DET
ejpam-6803	23	2	theoretical	theoretical	ADJ
ejpam-6803	23	3	groundwork	groundwork	NOUN
ejpam-6803	23	4	facilitated	facilitate	VERB
ejpam-6803	23	5	the	the	DET
ejpam-6803	23	6	invention	invention	NOUN
ejpam-6803	23	7	of	of	ADP
ejpam-6803	23	8	method	method	NOUN
ejpam-6803	23	9	such	such	ADJ
ejpam-6803	23	10	as	as	ADP
ejpam-6803	23	11	neural	neural	ADJ
ejpam-6803	23	12	ordinary	ordinary	ADJ
ejpam-6803	23	13	differential	differential	ADJ
ejpam-6803	23	14	equations	equation	NOUN
ejpam-6803	23	15	(	(	PUNCT
ejpam-6803	23	16	neural	neural	ADJ
ejpam-6803	23	17	odes	ode	NOUN
ejpam-6803	23	18	)	)	PUNCT
ejpam-6803	24	1	[	[	X
ejpam-6803	24	2	21	21	NUM
ejpam-6803	24	3	]	]	X
ejpam-6803	24	4	,	,	PUNCT
ejpam-6803	24	5	deep	deep	ADJ
ejpam-6803	24	6	galerkin	galerkin	ADJ
ejpam-6803	24	7	method	method	NOUN
ejpam-6803	24	8	(	(	PUNCT
ejpam-6803	24	9	dgm	dgm	PROPN
ejpam-6803	24	10	)	)	PUNCT
ejpam-6803	25	1	[	[	X
ejpam-6803	25	2	22	22	NUM
ejpam-6803	25	3	]	]	PUNCT
ejpam-6803	25	4	,	,	PUNCT
ejpam-6803	25	5	and	and	CCONJ
ejpam-6803	25	6	deepbsde	deepbsde	PRON
ejpam-6803	26	1	[	[	X
ejpam-6803	26	2	23	23	NUM
ejpam-6803	26	3	]	]	PUNCT
ejpam-6803	26	4	,	,	PUNCT
ejpam-6803	26	5	which	which	PRON
ejpam-6803	26	6	all	all	PRON
ejpam-6803	26	7	exhibit	exhibit	VERB
ejpam-6803	26	8	the	the	DET
ejpam-6803	26	9	capability	capability	NOUN
ejpam-6803	26	10	of	of	ADP
ejpam-6803	26	11	neural	neural	ADJ
ejpam-6803	26	12	networks	network	NOUN
ejpam-6803	26	13	to	to	PART
ejpam-6803	26	14	extract	extract	VERB
ejpam-6803	26	15	solution	solution	NOUN
ejpam-6803	26	16	maps	map	NOUN
ejpam-6803	26	17	for	for	ADP
ejpam-6803	26	18	differential	differential	ADJ
ejpam-6803	26	19	equations	equation	NOUN
ejpam-6803	26	20	.	.	PUNCT
ejpam-6803	27	1	one	one	NUM
ejpam-6803	27	2	such	such	ADJ
ejpam-6803	27	3	paradigm	paradigm	NOUN
ejpam-6803	27	4	is	be	AUX
ejpam-6803	27	5	the	the	DET
ejpam-6803	27	6	physics	physics	NOUN
ejpam-6803	27	7	-	-	PUNCT
ejpam-6803	27	8	informed	inform	VERB
ejpam-6803	27	9	neural	neural	ADJ
ejpam-6803	27	10	networks	network	NOUN
ejpam-6803	27	11	(	(	PUNCT
ejpam-6803	27	12	pinns	pinn	NOUN
ejpam-6803	27	13	)	)	PUNCT
ejpam-6803	27	14	which	which	PRON
ejpam-6803	27	15	augments	augment	VERB
ejpam-6803	27	16	the	the	DET
ejpam-6803	27	17	training	training	NOUN
ejpam-6803	27	18	of	of	ADP
ejpam-6803	27	19	neural	neural	ADJ
ejpam-6803	27	20	networks	network	NOUN
ejpam-6803	27	21	with	with	ADP
ejpam-6803	27	22	the	the	DET
ejpam-6803	27	23	governing	govern	VERB
ejpam-6803	27	24	pdes	pde	NOUN
ejpam-6803	27	25	,	,	PUNCT
ejpam-6803	27	26	initial	initial	ADJ
ejpam-6803	27	27	and	and	CCONJ
ejpam-6803	27	28	boundary	boundary	ADJ
ejpam-6803	27	29	conditions	condition	NOUN
ejpam-6803	27	30	using	use	VERB
ejpam-6803	27	31	loss	loss	NOUN
ejpam-6803	27	32	functions	function	NOUN
ejpam-6803	27	33	to	to	PART
ejpam-6803	27	34	penalize	penalize	VERB
ejpam-6803	27	35	the	the	DET
ejpam-6803	27	36	residuals	residual	NOUN
ejpam-6803	27	37	[	[	X
ejpam-6803	27	38	24	24	NUM
ejpam-6803	27	39	]	]	PUNCT
ejpam-6803	27	40	.	.	PUNCT
ejpam-6803	28	1	the	the	DET
ejpam-6803	28	2	emerging	emerge	VERB
ejpam-6803	28	3	applications	application	NOUN
ejpam-6803	28	4	of	of	ADP
ejpam-6803	28	5	pinns	pinn	NOUN
ejpam-6803	28	6	have	have	AUX
ejpam-6803	28	7	demonstrated	demonstrate	VERB
ejpam-6803	28	8	their	their	PRON
ejpam-6803	28	9	efficiency	efficiency	NOUN
ejpam-6803	28	10	in	in	ADP
ejpam-6803	28	11	solving	solve	VERB
ejpam-6803	28	12	burgers	burger	NOUN
ejpam-6803	28	13	’	'	PUNCT
ejpam-6803	28	14	,	,	PUNCT
ejpam-6803	28	15	navier	navier	NOUN
ejpam-6803	28	16	-	-	PUNCT
ejpam-6803	28	17	stokes	stokes	PROPN
ejpam-6803	28	18	,	,	PUNCT
ejpam-6803	28	19	allen	allen	PROPN
ejpam-6803	28	20	-	-	PUNCT
ejpam-6803	28	21	cahn	cahn	PROPN
ejpam-6803	28	22	,	,	PUNCT
ejpam-6803	28	23	schrodinger	schrodinger	NOUN
ejpam-6803	28	24	,	,	PUNCT
ejpam-6803	28	25	boussinesq	boussinesq	ADJ
ejpam-6803	28	26	-	-	PUNCT
ejpam-6803	28	27	type	type	NOUN
ejpam-6803	28	28	models	model	NOUN
ejpam-6803	28	29	[	[	X
ejpam-6803	28	30	25–29	25–29	NOUN
ejpam-6803	28	31	]	]	PUNCT
ejpam-6803	28	32	.	.	PUNCT
ejpam-6803	29	1	extensions	extension	NOUN
ejpam-6803	29	2	of	of	ADP
ejpam-6803	29	3	the	the	DET
ejpam-6803	29	4	framework	framework	NOUN
ejpam-6803	29	5	such	such	ADJ
ejpam-6803	29	6	as	as	ADP
ejpam-6803	29	7	fpinns	fpinn	NOUN
ejpam-6803	29	8	for	for	ADP
ejpam-6803	29	9	fractional	fractional	ADJ
ejpam-6803	29	10	pdes	pde	NOUN
ejpam-6803	29	11	[	[	X
ejpam-6803	29	12	30	30	NUM
ejpam-6803	29	13	]	]	PUNCT
ejpam-6803	29	14	and	and	CCONJ
ejpam-6803	29	15	wavelet	wavelet	NOUN
ejpam-6803	29	16	-	-	PUNCT
ejpam-6803	29	17	pinns	pinns	NOUN
ejpam-6803	29	18	[	[	X
ejpam-6803	29	19	31	31	NUM
ejpam-6803	29	20	]	]	PUNCT
ejpam-6803	29	21	have	have	AUX
ejpam-6803	29	22	broadened	broaden	VERB
ejpam-6803	29	23	the	the	DET
ejpam-6803	29	24	versatility	versatility	NOUN
ejpam-6803	29	25	of	of	ADP
ejpam-6803	29	26	the	the	DET
ejpam-6803	29	27	framework	framework	NOUN
ejpam-6803	29	28	to	to	ADP
ejpam-6803	29	29	nonlocal	nonlocal	ADJ
ejpam-6803	29	30	operators	operator	NOUN
ejpam-6803	29	31	and	and	CCONJ
ejpam-6803	29	32	multi	multi	ADJ
ejpam-6803	29	33	-	-	ADJ
ejpam-6803	29	34	scale	scale	ADJ
ejpam-6803	29	35	applications	application	NOUN
ejpam-6803	29	36	.	.	PUNCT
ejpam-6803	30	1	the	the	DET
ejpam-6803	30	2	research	research	NOUN
ejpam-6803	30	3	has	have	AUX
ejpam-6803	30	4	been	be	AUX
ejpam-6803	30	5	concentrated	concentrate	VERB
ejpam-6803	30	6	on	on	ADP
ejpam-6803	30	7	improving	improve	VERB
ejpam-6803	30	8	the	the	DET
ejpam-6803	30	9	performance	performance	NOUN
ejpam-6803	30	10	of	of	ADP
ejpam-6803	30	11	pinn	pinn	NOUN
ejpam-6803	30	12	through	through	ADP
ejpam-6803	30	13	architectural	architectural	ADJ
ejpam-6803	30	14	modification	modification	NOUN
ejpam-6803	30	15	,	,	PUNCT
ejpam-6803	30	16	optimization	optimization	NOUN
ejpam-6803	30	17	methods	method	NOUN
ejpam-6803	30	18	,	,	PUNCT
ejpam-6803	30	19	and	and	CCONJ
ejpam-6803	30	20	the	the	DET
ejpam-6803	30	21	design	design	NOUN
ejpam-6803	30	22	for	for	ADP
ejpam-6803	30	23	activation	activation	NOUN
ejpam-6803	30	24	functions	function	NOUN
ejpam-6803	30	25	.	.	PUNCT
ejpam-6803	31	1	the	the	DET
ejpam-6803	31	2	resnets	resnet	NOUN
ejpam-6803	31	3	have	have	AUX
ejpam-6803	31	4	improved	improve	VERB
ejpam-6803	31	5	convergence	convergence	NOUN
ejpam-6803	31	6	[	[	X
ejpam-6803	31	7	32	32	NUM
ejpam-6803	31	8	]	]	PUNCT
ejpam-6803	31	9	.	.	PUNCT
ejpam-6803	32	1	nas	nas	PROPN
ejpam-6803	32	2	-	-	PUNCT
ejpam-6803	32	3	pinn	pinn	PROPN
ejpam-6803	32	4	applies	apply	VERB
ejpam-6803	32	5	neural	neural	ADJ
ejpam-6803	32	6	architecture	architecture	NOUN
ejpam-6803	32	7	search	search	NOUN
ejpam-6803	32	8	to	to	ADP
ejpam-6803	32	9	the	the	DET
ejpam-6803	32	10	optimization	optimization	NOUN
ejpam-6803	32	11	of	of	ADP
ejpam-6803	32	12	network	network	NOUN
ejpam-6803	32	13	depth	depth	NOUN
ejpam-6803	32	14	and	and	CCONJ
ejpam-6803	32	15	width	width	VERB
ejpam-6803	32	16	for	for	ADP
ejpam-6803	32	17	various	various	ADJ
ejpam-6803	32	18	pdes	pde	NOUN
ejpam-6803	32	19	types	type	NOUN
ejpam-6803	32	20	[	[	X
ejpam-6803	32	21	33	33	NUM
ejpam-6803	32	22	]	]	PUNCT
ejpam-6803	32	23	.	.	PUNCT
ejpam-6803	33	1	hybrid	hybrid	ADJ
ejpam-6803	33	2	activation	activation	NOUN
ejpam-6803	33	3	functions	function	NOUN
ejpam-6803	33	4	based	base	VERB
ejpam-6803	33	5	on	on	ADP
ejpam-6803	33	6	tanh	tanh	NOUN
ejpam-6803	33	7	,	,	PUNCT
ejpam-6803	33	8	swish	swish	ADJ
ejpam-6803	33	9	and	and	CCONJ
ejpam-6803	33	10	wavelets	wavelet	NOUN
ejpam-6803	33	11	have	have	AUX
ejpam-6803	33	12	improved	improve	VERB
ejpam-6803	33	13	stability	stability	NOUN
ejpam-6803	33	14	and	and	CCONJ
ejpam-6803	33	15	residual	residual	ADJ
ejpam-6803	33	16	reduction	reduction	NOUN
ejpam-6803	33	17	in	in	ADP
ejpam-6803	33	18	training	training	NOUN
ejpam-6803	33	19	[	[	X
ejpam-6803	33	20	34	34	NUM
ejpam-6803	33	21	]	]	PUNCT
ejpam-6803	33	22	.	.	PUNCT
ejpam-6803	34	1	outside	outside	ADP
ejpam-6803	34	2	of	of	ADP
ejpam-6803	34	3	the	the	DET
ejpam-6803	34	4	pinn	pinn	NOUN
ejpam-6803	34	5	framework	framework	NOUN
ejpam-6803	34	6	,	,	PUNCT
ejpam-6803	34	7	’	'	PUNCT
ejpam-6803	34	8	neural	neural	ADJ
ejpam-6803	34	9	operators	operator	NOUN
ejpam-6803	34	10	’	'	PUNCT
ejpam-6803	34	11	,	,	PUNCT
ejpam-6803	34	12	in	in	ADP
ejpam-6803	34	13	particular	particular	ADJ
ejpam-6803	34	14	the	the	DET
ejpam-6803	34	15	fourier	fourier	NOUN
ejpam-6803	34	16	neural	neural	ADJ
ejpam-6803	34	17	operator	operator	NOUN
ejpam-6803	34	18	(	(	PUNCT
ejpam-6803	34	19	fno	fno	PROPN
ejpam-6803	34	20	)	)	PUNCT
ejpam-6803	34	21	,	,	PUNCT
ejpam-6803	34	22	have	have	AUX
ejpam-6803	34	23	been	be	AUX
ejpam-6803	34	24	able	able	ADJ
ejpam-6803	34	25	learn	learn	VERB
ejpam-6803	34	26	operators	operator	NOUN
ejpam-6803	34	27	of	of	ADP
ejpam-6803	34	28	solutions	solution	NOUN
ejpam-6803	34	29	to	to	PART
ejpam-6803	34	30	entire	entire	VERB
ejpam-6803	34	31	families	family	NOUN
ejpam-6803	34	32	of	of	ADP
ejpam-6803	34	33	pdes	pde	NOUN
ejpam-6803	34	34	at	at	ADP
ejpam-6803	34	35	a	a	DET
ejpam-6803	34	36	remarkable	remarkable	ADJ
ejpam-6803	34	37	level	level	NOUN
ejpam-6803	34	38	of	of	ADP
ejpam-6803	34	39	generality	generality	NOUN
ejpam-6803	34	40	[	[	X
ejpam-6803	34	41	35	35	NUM
ejpam-6803	34	42	]	]	PUNCT
ejpam-6803	34	43	.	.	PUNCT
ejpam-6803	35	1	fno	fno	PROPN
ejpam-6803	35	2	works	work	VERB
ejpam-6803	35	3	particularly	particularly	ADV
ejpam-6803	35	4	well	well	ADV
ejpam-6803	35	5	for	for	ADP
ejpam-6803	35	6	parametric	parametric	ADJ
ejpam-6803	35	7	problems	problem	NOUN
ejpam-6803	35	8	such	such	ADJ
ejpam-6803	35	9	as	as	ADP
ejpam-6803	35	10	with	with	ADP
ejpam-6803	35	11	varying	vary	VERB
ejpam-6803	35	12	reynolds	reynold	NOUN
ejpam-6803	35	13	number	number	NOUN
ejpam-6803	35	14	or	or	CCONJ
ejpam-6803	35	15	forcing	force	VERB
ejpam-6803	35	16	functions	function	NOUN
ejpam-6803	35	17	,	,	PUNCT
ejpam-6803	35	18	and	and	CCONJ
ejpam-6803	35	19	supports	support	VERB
ejpam-6803	35	20	zero	zero	NUM
ejpam-6803	35	21	-	-	PUNCT
ejpam-6803	35	22	shot	shot	NOUN
ejpam-6803	35	23	inference	inference	NOUN
ejpam-6803	35	24	at	at	ADP
ejpam-6803	35	25	new	new	ADJ
ejpam-6803	35	26	resolutions	resolution	NOUN
ejpam-6803	35	27	[	[	X
ejpam-6803	35	28	36–38	36–38	NUM
ejpam-6803	35	29	]	]	PUNCT
ejpam-6803	35	30	.	.	PUNCT
ejpam-6803	36	1	cuda	cuda	PROPN
ejpam-6803	36	2	-	-	PUNCT
ejpam-6803	36	3	gpu	gpu	PROPN
ejpam-6803	36	4	implementations	implementation	NOUN
ejpam-6803	36	5	are	be	AUX
ejpam-6803	36	6	three	three	NUM
ejpam-6803	36	7	orders	order	NOUN
ejpam-6803	36	8	of	of	ADP
ejpam-6803	36	9	magnitude	magnitude	NOUN
ejpam-6803	36	10	faster	fast	ADV
ejpam-6803	36	11	than	than	ADP
ejpam-6803	36	12	classical	classical	ADJ
ejpam-6803	36	13	solvers	solver	NOUN
ejpam-6803	36	14	in	in	ADP
ejpam-6803	36	15	evaluating	evaluate	VERB
ejpam-6803	36	16	at	at	ADP
ejpam-6803	36	17	positions	position	NOUN
ejpam-6803	36	18	[	[	X
ejpam-6803	36	19	39	39	NUM
ejpam-6803	36	20	]	]	PUNCT
ejpam-6803	36	21	.	.	PUNCT
ejpam-6803	37	1	this	this	DET
ejpam-6803	37	2	paper	paper	NOUN
ejpam-6803	37	3	generalizes	generalize	VERB
ejpam-6803	37	4	these	these	DET
ejpam-6803	37	5	developments	development	NOUN
ejpam-6803	37	6	to	to	ADP
ejpam-6803	37	7	the	the	DET
ejpam-6803	37	8	integer	integer	NOUN
ejpam-6803	37	9	-	-	PUNCT
ejpam-6803	37	10	order	order	NOUN
ejpam-6803	37	11	coupled	couple	VERB
ejpam-6803	37	12	bbe	bbe	NOUN
ejpam-6803	37	13	system	system	NOUN
ejpam-6803	37	14	.	.	PUNCT
ejpam-6803	38	1	we	we	PRON
ejpam-6803	38	2	introduce	introduce	VERB
ejpam-6803	38	3	here	here	ADV
ejpam-6803	38	4	a	a	DET
ejpam-6803	38	5	dual	dual	ADJ
ejpam-6803	38	6	-	-	PUNCT
ejpam-6803	38	7	network	network	NOUN
ejpam-6803	38	8	pinn	pinn	NOUN
ejpam-6803	38	9	architecture	architecture	NOUN
ejpam-6803	38	10	that	that	PRON
ejpam-6803	38	11	learns	learn	VERB
ejpam-6803	38	12	the	the	DET
ejpam-6803	38	13	fields	field	NOUN
ejpam-6803	38	14	ϕ(α	ϕ(α	PROPN
ejpam-6803	38	15	,	,	PUNCT
ejpam-6803	38	16	β	β	NOUN
ejpam-6803	38	17	)	)	PUNCT
ejpam-6803	38	18	and	and	CCONJ
ejpam-6803	38	19	ρ(α	ρ(α	NOUN
ejpam-6803	38	20	,	,	PUNCT
ejpam-6803	38	21	β	β	NOUN
ejpam-6803	38	22	)	)	PUNCT
ejpam-6803	38	23	jointly	jointly	ADV
ejpam-6803	38	24	,	,	PUNCT
ejpam-6803	38	25	incorporating	incorporate	VERB
ejpam-6803	38	26	the	the	DET
ejpam-6803	38	27	differential	differential	ADJ
ejpam-6803	38	28	constraints	constraint	NOUN
ejpam-6803	38	29	of	of	ADP
ejpam-6803	38	30	the	the	DET
ejpam-6803	38	31	system	system	NOUN
ejpam-6803	38	32	into	into	ADP
ejpam-6803	38	33	a	a	DET
ejpam-6803	38	34	composite	composite	ADJ
ejpam-6803	38	35	loss	loss	NOUN
ejpam-6803	38	36	.	.	PUNCT
ejpam-6803	39	1	we	we	PRON
ejpam-6803	39	2	adopt	adopt	VERB
ejpam-6803	39	3	some	some	PRON
ejpam-6803	39	4	of	of	ADP
ejpam-6803	39	5	the	the	DET
ejpam-6803	39	6	standard	standard	ADJ
ejpam-6803	39	7	practices	practice	NOUN
ejpam-6803	39	8	:	:	PUNCT
ejpam-6803	39	9	residual	residual	ADJ
ejpam-6803	39	10	minimization	minimization	NOUN
ejpam-6803	39	11	,	,	PUNCT
ejpam-6803	39	12	auto	auto	NOUN
ejpam-6803	39	13	-	-	PUNCT
ejpam-6803	39	14	differentiation	differentiation	NOUN
ejpam-6803	39	15	,	,	PUNCT
ejpam-6803	39	16	architecture	architecture	NOUN
ejpam-6803	39	17	optimization	optimization	NOUN
ejpam-6803	39	18	,	,	PUNCT
ejpam-6803	39	19	and	and	CCONJ
ejpam-6803	39	20	adaptive	adaptive	ADJ
ejpam-6803	39	21	training	training	NOUN
ejpam-6803	39	22	by	by	ADP
ejpam-6803	39	23	adam	adam	PROPN
ejpam-6803	39	24	with	with	ADP
ejpam-6803	39	25	quasi	quasi	PROPN
ejpam-6803	39	26	-	-	PROPN
ejpam-6803	39	27	newton	newton	PROPN
ejpam-6803	39	28	refinement	refinement	NOUN
ejpam-6803	40	1	[	[	X
ejpam-6803	40	2	40	40	NUM
ejpam-6803	40	3	]	]	PUNCT
ejpam-6803	40	4	.	.	PUNCT
ejpam-6803	41	1	we	we	PRON
ejpam-6803	41	2	benchmark	benchmark	VERB
ejpam-6803	41	3	the	the	DET
ejpam-6803	41	4	proposed	propose	VERB
ejpam-6803	41	5	approach	approach	NOUN
ejpam-6803	41	6	to	to	ADP
ejpam-6803	41	7	classical	classical	ADJ
ejpam-6803	41	8	solvers	solver	NOUN
ejpam-6803	41	9	using	use	VERB
ejpam-6803	41	10	the	the	DET
ejpam-6803	41	11	type	type	NOUN
ejpam-6803	41	12	of	of	ADP
ejpam-6803	41	13	initial	initial	ADJ
ejpam-6803	41	14	conditions	condition	NOUN
ejpam-6803	41	15	and	and	CCONJ
ejpam-6803	41	16	discuss	discuss	VERB
ejpam-6803	41	17	the	the	DET
ejpam-6803	41	18	potential	potential	ADJ
ejpam-6803	41	19	generality	generality	NOUN
ejpam-6803	41	20	.	.	PUNCT
ejpam-6803	42	1	in	in	ADP
ejpam-6803	42	2	contrast	contrast	NOUN
ejpam-6803	42	3	to	to	ADP
ejpam-6803	42	4	other	other	ADJ
ejpam-6803	42	5	numerical	numerical	ADJ
ejpam-6803	42	6	or	or	CCONJ
ejpam-6803	42	7	analytical	analytical	ADJ
ejpam-6803	42	8	a.	a.	NOUN
ejpam-6803	42	9	shafee	shafee	PROPN
ejpam-6803	42	10	et	et	PROPN
ejpam-6803	42	11	al	al	PROPN
ejpam-6803	42	12	.	.	PUNCT
ejpam-6803	42	13	/	/	SYM
ejpam-6803	42	14	eur	eur	PROPN
ejpam-6803	42	15	.	.	PUNCT
ejpam-6803	43	1	j.	j.	PROPN
ejpam-6803	43	2	pure	pure	PROPN
ejpam-6803	43	3	appl	appl	PROPN
ejpam-6803	43	4	.	.	PROPN
ejpam-6803	43	5	math	math	PROPN
ejpam-6803	43	6	,	,	PUNCT
ejpam-6803	43	7	18	18	NUM
ejpam-6803	43	8	(	(	PUNCT
ejpam-6803	43	9	4	4	NUM
ejpam-6803	43	10	)	)	PUNCT
ejpam-6803	43	11	(	(	PUNCT
ejpam-6803	43	12	2025	2025	NUM
ejpam-6803	43	13	)	)	PUNCT
ejpam-6803	43	14	,	,	PUNCT
ejpam-6803	43	15	6803	6803	NUM
ejpam-6803	43	16	3	3	NUM
ejpam-6803	43	17	of	of	ADP
ejpam-6803	43	18	18	18	NUM
ejpam-6803	43	19	discretization	discretization	NOUN
ejpam-6803	43	20	or	or	CCONJ
ejpam-6803	43	21	perturbation	perturbation	NOUN
ejpam-6803	43	22	-	-	PUNCT
ejpam-6803	43	23	based	base	VERB
ejpam-6803	43	24	methods	method	NOUN
ejpam-6803	43	25	that	that	PRON
ejpam-6803	43	26	explicitly	explicitly	ADV
ejpam-6803	43	27	depend	depend	VERB
ejpam-6803	43	28	on	on	ADP
ejpam-6803	43	29	a	a	DET
ejpam-6803	43	30	discrete	discrete	ADJ
ejpam-6803	43	31	form	form	NOUN
ejpam-6803	43	32	of	of	ADP
ejpam-6803	43	33	a	a	DET
ejpam-6803	43	34	governing	govern	VERB
ejpam-6803	43	35	equation	equation	NOUN
ejpam-6803	43	36	of	of	ADP
ejpam-6803	43	37	interest	interest	NOUN
ejpam-6803	44	1	,	,	PUNCT
ejpam-6803	44	2	the	the	DET
ejpam-6803	44	3	pinn	pinn	NOUN
ejpam-6803	44	4	framework	framework	NOUN
ejpam-6803	44	5	directly	directly	ADV
ejpam-6803	44	6	incorporates	incorporate	VERB
ejpam-6803	44	7	the	the	DET
ejpam-6803	44	8	underlying	underlie	VERB
ejpam-6803	44	9	physics	physics	NOUN
ejpam-6803	44	10	into	into	ADP
ejpam-6803	44	11	the	the	DET
ejpam-6803	44	12	loss	loss	NOUN
ejpam-6803	44	13	of	of	ADP
ejpam-6803	44	14	a	a	DET
ejpam-6803	44	15	neural	neural	ADJ
ejpam-6803	44	16	network	network	NOUN
ejpam-6803	44	17	,	,	PUNCT
ejpam-6803	44	18	making	make	VERB
ejpam-6803	44	19	the	the	DET
ejpam-6803	44	20	neural	neural	ADJ
ejpam-6803	44	21	network	network	NOUN
ejpam-6803	44	22	able	able	ADJ
ejpam-6803	44	23	to	to	PART
ejpam-6803	44	24	obtain	obtain	VERB
ejpam-6803	44	25	accurate	accurate	ADJ
ejpam-6803	44	26	approximations	approximation	NOUN
ejpam-6803	44	27	without	without	ADP
ejpam-6803	44	28	the	the	DET
ejpam-6803	44	29	need	need	NOUN
ejpam-6803	44	30	to	to	PART
ejpam-6803	44	31	generate	generate	VERB
ejpam-6803	44	32	a	a	DET
ejpam-6803	44	33	mesh	mesh	NOUN
ejpam-6803	44	34	.	.	PUNCT
ejpam-6803	45	1	the	the	DET
ejpam-6803	45	2	findings	finding	NOUN
ejpam-6803	45	3	indicate	indicate	VERB
ejpam-6803	45	4	that	that	SCONJ
ejpam-6803	45	5	pinns	pinn	NOUN
ejpam-6803	45	6	are	be	AUX
ejpam-6803	45	7	capable	capable	ADJ
ejpam-6803	45	8	of	of	ADP
ejpam-6803	45	9	reliably	reliably	ADV
ejpam-6803	45	10	modeling	model	VERB
ejpam-6803	45	11	the	the	DET
ejpam-6803	45	12	nonlinear	nonlinear	ADJ
ejpam-6803	45	13	dynamics	dynamic	NOUN
ejpam-6803	45	14	of	of	ADP
ejpam-6803	45	15	velocity	velocity	NOUN
ejpam-6803	45	16	and	and	CCONJ
ejpam-6803	45	17	surface	surface	NOUN
ejpam-6803	45	18	height	height	NOUN
ejpam-6803	45	19	fields	field	NOUN
ejpam-6803	45	20	with	with	ADP
ejpam-6803	45	21	low	low	ADJ
ejpam-6803	45	22	errors	error	NOUN
ejpam-6803	45	23	throughout	throughout	ADP
ejpam-6803	45	24	the	the	DET
ejpam-6803	45	25	spatio	spatio	PROPN
ejpam-6803	45	26	-	-	PUNCT
ejpam-6803	45	27	temporal	temporal	ADJ
ejpam-6803	45	28	domain	domain	NOUN
ejpam-6803	45	29	[	[	X
ejpam-6803	45	30	41–45	41–45	NUM
ejpam-6803	45	31	]	]	PUNCT
ejpam-6803	45	32	.	.	PUNCT
ejpam-6803	46	1	the	the	DET
ejpam-6803	46	2	rest	rest	NOUN
ejpam-6803	46	3	of	of	ADP
ejpam-6803	46	4	this	this	DET
ejpam-6803	46	5	paper	paper	NOUN
ejpam-6803	46	6	is	be	AUX
ejpam-6803	46	7	organized	organize	VERB
ejpam-6803	46	8	as	as	SCONJ
ejpam-6803	46	9	follows	follow	VERB
ejpam-6803	46	10	.	.	PUNCT
ejpam-6803	47	1	section	section	NOUN
ejpam-6803	47	2	2	2	NUM
ejpam-6803	47	3	describes	describe	VERB
ejpam-6803	47	4	the	the	DET
ejpam-6803	47	5	pde	pde	NOUN
ejpam-6803	47	6	system	system	NOUN
ejpam-6803	47	7	and	and	CCONJ
ejpam-6803	47	8	the	the	DET
ejpam-6803	47	9	pinn	pinn	NOUN
ejpam-6803	47	10	model	model	NOUN
ejpam-6803	47	11	.	.	PUNCT
ejpam-6803	48	1	in	in	ADP
ejpam-6803	48	2	section	section	NOUN
ejpam-6803	48	3	3	3	NUM
ejpam-6803	48	4	,	,	PUNCT
ejpam-6803	48	5	we	we	PRON
ejpam-6803	48	6	present	present	VERB
ejpam-6803	48	7	extensive	extensive	ADJ
ejpam-6803	48	8	numerical	numerical	ADJ
ejpam-6803	48	9	results	result	NOUN
ejpam-6803	48	10	and	and	CCONJ
ejpam-6803	48	11	comparisons	comparison	NOUN
ejpam-6803	48	12	.	.	PUNCT
ejpam-6803	49	1	in	in	ADP
ejpam-6803	49	2	section	section	NOUN
ejpam-6803	49	3	4	4	NUM
ejpam-6803	49	4	,	,	PUNCT
ejpam-6803	49	5	we	we	PRON
ejpam-6803	49	6	summarize	summarize	VERB
ejpam-6803	49	7	the	the	DET
ejpam-6803	49	8	main	main	ADJ
ejpam-6803	49	9	results	result	NOUN
ejpam-6803	49	10	.	.	PUNCT
ejpam-6803	50	1	2	2	X
ejpam-6803	50	2	.	.	X
ejpam-6803	50	3	methodology	methodology	NOUN
ejpam-6803	50	4	this	this	DET
ejpam-6803	50	5	paper	paper	NOUN
ejpam-6803	50	6	presents	present	VERB
ejpam-6803	50	7	a	a	DET
ejpam-6803	50	8	methodological	methodological	ADJ
ejpam-6803	50	9	framework	framework	NOUN
ejpam-6803	50	10	for	for	ADP
ejpam-6803	50	11	solving	solve	VERB
ejpam-6803	50	12	the	the	DET
ejpam-6803	50	13	system	system	NOUN
ejpam-6803	50	14	of	of	ADP
ejpam-6803	50	15	boussinesqburgers	boussinesqburger	NOUN
ejpam-6803	50	16	equations	equation	NOUN
ejpam-6803	50	17	(	(	PUNCT
ejpam-6803	50	18	bbe	bbe	NOUN
ejpam-6803	50	19	)	)	PUNCT
ejpam-6803	50	20	by	by	ADP
ejpam-6803	50	21	pinns	pinn	NOUN
ejpam-6803	50	22	.	.	PUNCT
ejpam-6803	51	1	first	first	ADV
ejpam-6803	51	2	we	we	PRON
ejpam-6803	51	3	introduce	introduce	VERB
ejpam-6803	51	4	the	the	DET
ejpam-6803	51	5	general	general	ADJ
ejpam-6803	51	6	structure	structure	NOUN
ejpam-6803	51	7	of	of	ADP
ejpam-6803	51	8	multilayer	multilayer	ADJ
ejpam-6803	51	9	perceptrons	perceptron	NOUN
ejpam-6803	51	10	(	(	PUNCT
ejpam-6803	51	11	mlps	mlp	NOUN
ejpam-6803	51	12	)	)	PUNCT
ejpam-6803	51	13	,	,	PUNCT
ejpam-6803	51	14	which	which	PRON
ejpam-6803	51	15	is	be	AUX
ejpam-6803	51	16	the	the	DET
ejpam-6803	51	17	root	root	NOUN
ejpam-6803	51	18	topology	topology	NOUN
ejpam-6803	51	19	that	that	PRON
ejpam-6803	51	20	underlies	underlie	VERB
ejpam-6803	51	21	a	a	DET
ejpam-6803	51	22	neural	neural	ADJ
ejpam-6803	51	23	network	network	NOUN
ejpam-6803	51	24	.	.	PUNCT
ejpam-6803	52	1	subsequently	subsequently	ADV
ejpam-6803	52	2	,	,	PUNCT
ejpam-6803	52	3	we	we	PRON
ejpam-6803	52	4	examine	examine	VERB
ejpam-6803	52	5	the	the	DET
ejpam-6803	52	6	process	process	NOUN
ejpam-6803	52	7	of	of	ADP
ejpam-6803	52	8	working	work	VERB
ejpam-6803	52	9	out	out	ADP
ejpam-6803	52	10	pinns	pinn	NOUN
ejpam-6803	52	11	.	.	PUNCT
ejpam-6803	53	1	the	the	DET
ejpam-6803	53	2	governing	govern	VERB
ejpam-6803	53	3	equations	equation	NOUN
ejpam-6803	53	4	are	be	AUX
ejpam-6803	53	5	automatically	automatically	ADV
ejpam-6803	53	6	incorporated	incorporate	VERB
ejpam-6803	53	7	into	into	ADP
ejpam-6803	53	8	the	the	DET
ejpam-6803	53	9	training	training	NOUN
ejpam-6803	53	10	process	process	NOUN
ejpam-6803	53	11	through	through	ADP
ejpam-6803	53	12	the	the	DET
ejpam-6803	53	13	use	use	NOUN
ejpam-6803	53	14	of	of	ADP
ejpam-6803	53	15	automatic	automatic	ADJ
ejpam-6803	53	16	differentiation	differentiation	NOUN
ejpam-6803	53	17	.	.	PUNCT
ejpam-6803	54	1	the	the	DET
ejpam-6803	54	2	flow	flow	NOUN
ejpam-6803	54	3	chart	chart	NOUN
ejpam-6803	54	4	of	of	ADP
ejpam-6803	54	5	the	the	DET
ejpam-6803	54	6	model	model	NOUN
ejpam-6803	54	7	is	be	AUX
ejpam-6803	54	8	given	give	VERB
ejpam-6803	54	9	in	in	ADP
ejpam-6803	54	10	1	1	NUM
ejpam-6803	54	11	.	.	PUNCT
ejpam-6803	54	12	figure	figure	NOUN
ejpam-6803	54	13	1	1	NUM
ejpam-6803	54	14	:	:	PUNCT
ejpam-6803	54	15	flow	flow	VERB
ejpam-6803	54	16	chart	chart	NOUN
ejpam-6803	54	17	of	of	ADP
ejpam-6803	54	18	the	the	DET
ejpam-6803	54	19	proposed	propose	VERB
ejpam-6803	54	20	problem	problem	NOUN
ejpam-6803	54	21	.	.	PUNCT
ejpam-6803	55	1	2.1	2.1	NUM
ejpam-6803	55	2	.	.	PUNCT
ejpam-6803	56	1	multilayer	multilayer	ADJ
ejpam-6803	56	2	perceptrons	perceptron	NOUN
ejpam-6803	56	3	(	(	PUNCT
ejpam-6803	56	4	mlps	mlp	NOUN
ejpam-6803	56	5	)	)	PUNCT
ejpam-6803	56	6	deep	deep	ADJ
ejpam-6803	56	7	neural	neural	ADJ
ejpam-6803	56	8	networks	network	NOUN
ejpam-6803	56	9	are	be	AUX
ejpam-6803	56	10	universal	universal	ADJ
ejpam-6803	56	11	approximators	approximator	NOUN
ejpam-6803	56	12	for	for	ADP
ejpam-6803	56	13	continuous	continuous	ADJ
ejpam-6803	56	14	functions	function	NOUN
ejpam-6803	56	15	that	that	PRON
ejpam-6803	56	16	are	be	AUX
ejpam-6803	56	17	made	make	VERB
ejpam-6803	56	18	up	up	ADP
ejpam-6803	56	19	of	of	ADP
ejpam-6803	56	20	multi	multi	ADJ
ejpam-6803	56	21	-	-	ADJ
ejpam-6803	56	22	layer	layer	ADJ
ejpam-6803	56	23	functions	function	NOUN
ejpam-6803	56	24	made	make	VERB
ejpam-6803	56	25	up	up	ADP
ejpam-6803	56	26	of	of	ADP
ejpam-6803	56	27	nonlinear	nonlinear	ADJ
ejpam-6803	56	28	operations	operation	NOUN
ejpam-6803	56	29	.	.	PUNCT
ejpam-6803	57	1	namely	namely	ADV
ejpam-6803	57	2	,	,	PUNCT
ejpam-6803	57	3	deep	deep	ADJ
ejpam-6803	57	4	neural	neural	ADJ
ejpam-6803	57	5	a.	a.	NOUN
ejpam-6803	57	6	shafee	shafee	PROPN
ejpam-6803	57	7	et	et	PROPN
ejpam-6803	57	8	al	al	PROPN
ejpam-6803	57	9	.	.	PUNCT
ejpam-6803	57	10	/	/	SYM
ejpam-6803	57	11	eur	eur	PROPN
ejpam-6803	57	12	.	.	PUNCT
ejpam-6803	58	1	j.	j.	PROPN
ejpam-6803	58	2	pure	pure	PROPN
ejpam-6803	58	3	appl	appl	PROPN
ejpam-6803	58	4	.	.	PROPN
ejpam-6803	58	5	math	math	PROPN
ejpam-6803	58	6	,	,	PUNCT
ejpam-6803	58	7	18	18	NUM
ejpam-6803	58	8	(	(	PUNCT
ejpam-6803	58	9	4	4	NUM
ejpam-6803	58	10	)	)	PUNCT
ejpam-6803	58	11	(	(	PUNCT
ejpam-6803	58	12	2025	2025	NUM
ejpam-6803	58	13	)	)	PUNCT
ejpam-6803	58	14	,	,	PUNCT
ejpam-6803	58	15	6803	6803	NUM
ejpam-6803	58	16	4	4	NUM
ejpam-6803	58	17	of	of	ADP
ejpam-6803	58	18	18	18	NUM
ejpam-6803	58	19	networks	network	NOUN
ejpam-6803	58	20	(	(	PUNCT
ejpam-6803	58	21	dnns	dnns	ADJ
ejpam-6803	58	22	)	)	PUNCT
ejpam-6803	58	23	consist	consist	NOUN
ejpam-6803	58	24	of	of	ADP
ejpam-6803	58	25	multiple	multiple	ADJ
ejpam-6803	58	26	layers	layer	NOUN
ejpam-6803	58	27	of	of	ADP
ejpam-6803	58	28	nonlinear	nonlinear	ADJ
ejpam-6803	58	29	operations	operation	NOUN
ejpam-6803	58	30	.	.	PUNCT
ejpam-6803	59	1	every	every	DET
ejpam-6803	59	2	layer	layer	NOUN
ejpam-6803	59	3	consists	consist	VERB
ejpam-6803	59	4	from	from	ADP
ejpam-6803	59	5	various	various	ADJ
ejpam-6803	59	6	neurons	neuron	NOUN
ejpam-6803	59	7	,	,	PUNCT
ejpam-6803	59	8	and	and	CCONJ
ejpam-6803	59	9	each	each	DET
ejpam-6803	59	10	neuron	neuron	NOUN
ejpam-6803	59	11	performs	perform	VERB
ejpam-6803	59	12	a	a	DET
ejpam-6803	59	13	linear	linear	ADJ
ejpam-6803	59	14	modification	modification	NOUN
ejpam-6803	59	15	followed	follow	VERB
ejpam-6803	59	16	by	by	ADP
ejpam-6803	59	17	rectification	rectification	NOUN
ejpam-6803	59	18	;	;	PUNCT
ejpam-6803	59	19	from	from	ADP
ejpam-6803	59	20	there	there	PRON
ejpam-6803	59	21	the	the	DET
ejpam-6803	59	22	modified	modify	VERB
ejpam-6803	59	23	outputs	output	NOUN
ejpam-6803	59	24	are	be	AUX
ejpam-6803	59	25	sent	send	VERB
ejpam-6803	59	26	through	through	ADP
ejpam-6803	59	27	another	another	DET
ejpam-6803	59	28	string	string	NOUN
ejpam-6803	59	29	of	of	ADP
ejpam-6803	59	30	smaller	small	ADJ
ejpam-6803	59	31	neural	neural	ADJ
ejpam-6803	59	32	layers	layer	NOUN
ejpam-6803	59	33	.	.	PUNCT
ejpam-6803	60	1	multilayer	multilayer	ADJ
ejpam-6803	60	2	perceptrons	perceptron	NOUN
ejpam-6803	60	3	(	(	PUNCT
ejpam-6803	60	4	mlps	mlp	NOUN
ejpam-6803	60	5	)	)	PUNCT
ejpam-6803	61	1	[	[	X
ejpam-6803	61	2	46	46	NUM
ejpam-6803	61	3	]	]	PUNCT
ejpam-6803	61	4	,	,	PUNCT
ejpam-6803	61	5	also	also	ADV
ejpam-6803	61	6	know	know	VERB
ejpam-6803	61	7	as	as	ADP
ejpam-6803	61	8	fully	fully	ADV
ejpam-6803	61	9	connected	connected	ADJ
ejpam-6803	61	10	networks	network	NOUN
ejpam-6803	61	11	,	,	PUNCT
ejpam-6803	61	12	are	be	AUX
ejpam-6803	61	13	one	one	NUM
ejpam-6803	61	14	of	of	ADP
ejpam-6803	61	15	the	the	DET
ejpam-6803	61	16	simplest	simple	ADJ
ejpam-6803	61	17	and	and	CCONJ
ejpam-6803	61	18	most	most	ADV
ejpam-6803	61	19	commonly	commonly	ADV
ejpam-6803	61	20	used	use	VERB
ejpam-6803	61	21	architectures	architecture	NOUN
ejpam-6803	61	22	.	.	PUNCT
ejpam-6803	62	1	the	the	DET
ejpam-6803	62	2	input	input	NOUN
ejpam-6803	62	3	coordinates	coordinate	NOUN
ejpam-6803	62	4	denote	denote	VERB
ejpam-6803	62	5	the	the	DET
ejpam-6803	62	6	points	point	NOUN
ejpam-6803	62	7	about	about	ADP
ejpam-6803	62	8	which	which	PRON
ejpam-6803	62	9	we	we	PRON
ejpam-6803	62	10	want	want	VERB
ejpam-6803	62	11	to	to	PART
ejpam-6803	62	12	predict	predict	VERB
ejpam-6803	62	13	output	output	NOUN
ejpam-6803	62	14	.	.	PUNCT
ejpam-6803	63	1	the	the	DET
ejpam-6803	63	2	output	output	NOUN
ejpam-6803	63	3	from	from	ADP
ejpam-6803	63	4	our	our	PRON
ejpam-6803	63	5	network	network	NOUN
ejpam-6803	63	6	denoted	denote	VERB
ejpam-6803	63	7	as	as	ADP
ejpam-6803	63	8	fθ(α	fθ(α	NOUN
ejpam-6803	63	9	)	)	PUNCT
ejpam-6803	63	10	=	=	PUNCT
ejpam-6803	64	1	[	[	X
ejpam-6803	64	2	ϕ̂(α	ϕ̂(α	PRON
ejpam-6803	64	3	)	)	PUNCT
ejpam-6803	64	4	,	,	PUNCT
ejpam-6803	64	5	ρ̂(α	ρ̂(α	PROPN
ejpam-6803	64	6	)	)	PUNCT
ejpam-6803	64	7	]	]	PUNCT
ejpam-6803	64	8	in	in	ADP
ejpam-6803	64	9	terms	term	NOUN
ejpam-6803	64	10	of	of	ADP
ejpam-6803	64	11	its	its	PRON
ejpam-6803	64	12	weights	weight	NOUN
ejpam-6803	64	13	and	and	CCONJ
ejpam-6803	64	14	biases	bias	NOUN
ejpam-6803	64	15	is	be	AUX
ejpam-6803	64	16	given	give	VERB
ejpam-6803	64	17	by	by	ADP
ejpam-6803	64	18	θ	θ	PROPN
ejpam-6803	64	19	.	.	PUNCT
ejpam-6803	64	20	an	an	DET
ejpam-6803	64	21	mlp	mlp	NOUN
ejpam-6803	64	22	with	with	ADP
ejpam-6803	64	23	l	l	NOUN
ejpam-6803	64	24	layers	layer	NOUN
ejpam-6803	64	25	can	can	AUX
ejpam-6803	64	26	be	be	AUX
ejpam-6803	64	27	thought	think	VERB
ejpam-6803	64	28	of	of	ADP
ejpam-6803	64	29	as	as	ADP
ejpam-6803	64	30	an	an	DET
ejpam-6803	64	31	iterative	iterative	NOUN
ejpam-6803	64	32	function	function	NOUN
ejpam-6803	64	33	:	:	PUNCT
ejpam-6803	64	34	z(i	z(i	NUM
ejpam-6803	64	35	)	)	PUNCT
ejpam-6803	64	36	=	=	SYM
ejpam-6803	64	37	σ(i	σ(i	PROPN
ejpam-6803	64	38	)	)	PUNCT
ejpam-6803	64	39	(	(	PUNCT
ejpam-6803	64	40	w(i)z(i−1	w(i)z(i−1	PROPN
ejpam-6803	64	41	)	)	PUNCT
ejpam-6803	64	42	+	+	CCONJ
ejpam-6803	64	43	b(i	b(i	NOUN
ejpam-6803	64	44	)	)	PUNCT
ejpam-6803	64	45	)	)	PUNCT
ejpam-6803	64	46	,	,	PUNCT
ejpam-6803	64	47	i	i	PRON
ejpam-6803	64	48	=	=	NOUN
ejpam-6803	64	49	1	1	NUM
ejpam-6803	64	50	,	,	PUNCT
ejpam-6803	64	51	.	.	PUNCT
ejpam-6803	64	52	.	.	PUNCT
ejpam-6803	65	1	.	.	PUNCT
ejpam-6803	66	1	,	,	PUNCT
ejpam-6803	66	2	l	l	NOUN
ejpam-6803	66	3	,	,	PUNCT
ejpam-6803	66	4	(	(	PUNCT
ejpam-6803	66	5	1	1	X
ejpam-6803	66	6	)	)	PUNCT
ejpam-6803	66	7	where	where	SCONJ
ejpam-6803	66	8	z(0	z(0	AUX
ejpam-6803	66	9	)	)	PUNCT
ejpam-6803	66	10	=	=	SYM
ejpam-6803	66	11	α	α	NOUN
ejpam-6803	66	12	,	,	PUNCT
ejpam-6803	66	13	and	and	CCONJ
ejpam-6803	66	14	σ(i	σ(i	NOUN
ejpam-6803	66	15	)	)	PUNCT
ejpam-6803	66	16	(	(	PUNCT
ejpam-6803	66	17	·	·	PUNCT
ejpam-6803	66	18	)	)	PUNCT
ejpam-6803	66	19	is	be	AUX
ejpam-6803	66	20	the	the	DET
ejpam-6803	66	21	activation	activation	NOUN
ejpam-6803	66	22	function	function	NOUN
ejpam-6803	66	23	for	for	ADP
ejpam-6803	66	24	layer	layer	NOUN
ejpam-6803	66	25	i	i	PRON
ejpam-6803	66	26	(	(	PUNCT
ejpam-6803	66	27	for	for	ADP
ejpam-6803	66	28	example	example	NOUN
ejpam-6803	66	29	,	,	PUNCT
ejpam-6803	66	30	tanh	tanh	PROPN
ejpam-6803	66	31	)	)	PUNCT
ejpam-6803	66	32	.	.	PUNCT
ejpam-6803	67	1	the	the	DET
ejpam-6803	67	2	intermediate	intermediate	ADJ
ejpam-6803	67	3	output	output	NOUN
ejpam-6803	67	4	z(l	z(l	NOUN
ejpam-6803	67	5	)	)	PUNCT
ejpam-6803	67	6	provides	provide	VERB
ejpam-6803	67	7	the	the	DET
ejpam-6803	67	8	network	network	NOUN
ejpam-6803	67	9	prediction	prediction	NOUN
ejpam-6803	67	10	for	for	ADP
ejpam-6803	67	11	[	[	X
ejpam-6803	67	12	ϕ(α	ϕ(α	PROPN
ejpam-6803	67	13	,	,	PUNCT
ejpam-6803	67	14	β	β	NOUN
ejpam-6803	67	15	)	)	PUNCT
ejpam-6803	67	16	,	,	PUNCT
ejpam-6803	67	17	ρ(α	ρ(α	NOUN
ejpam-6803	67	18	,	,	PUNCT
ejpam-6803	67	19	β	β	NOUN
ejpam-6803	67	20	)	)	PUNCT
ejpam-6803	67	21	]	]	PUNCT
ejpam-6803	67	22	.	.	PUNCT
ejpam-6803	68	1	2.2	2.2	NUM
ejpam-6803	68	2	.	.	PUNCT
ejpam-6803	69	1	physics	physics	NOUN
ejpam-6803	69	2	-	-	PUNCT
ejpam-6803	69	3	informed	inform	VERB
ejpam-6803	69	4	neural	neural	ADJ
ejpam-6803	69	5	networks	network	NOUN
ejpam-6803	69	6	(	(	PUNCT
ejpam-6803	69	7	pinns	pinns	ADJ
ejpam-6803	69	8	)	)	PUNCT
ejpam-6803	69	9	physics	physics	NOUN
ejpam-6803	69	10	-	-	PUNCT
ejpam-6803	69	11	informed	inform	VERB
ejpam-6803	69	12	neural	neural	ADJ
ejpam-6803	69	13	networks	network	NOUN
ejpam-6803	69	14	(	(	PUNCT
ejpam-6803	69	15	pinns	pinn	NOUN
ejpam-6803	69	16	)	)	PUNCT
ejpam-6803	69	17	are	be	AUX
ejpam-6803	69	18	a	a	DET
ejpam-6803	69	19	typical	typical	ADJ
ejpam-6803	69	20	deep	deep	ADJ
ejpam-6803	69	21	learning	learning	NOUN
ejpam-6803	69	22	approach	approach	NOUN
ejpam-6803	69	23	to	to	ADP
ejpam-6803	69	24	solving	solve	VERB
ejpam-6803	69	25	complex	complex	ADJ
ejpam-6803	69	26	forward	forward	ADV
ejpam-6803	69	27	and	and	CCONJ
ejpam-6803	69	28	inverse	inverse	NOUN
ejpam-6803	69	29	problems	problem	NOUN
ejpam-6803	69	30	governed	govern	VERB
ejpam-6803	69	31	by	by	ADP
ejpam-6803	69	32	partial	partial	ADJ
ejpam-6803	69	33	differential	differential	ADJ
ejpam-6803	69	34	equations	equation	NOUN
ejpam-6803	69	35	(	(	PUNCT
ejpam-6803	69	36	pdes	pde	NOUN
ejpam-6803	69	37	)	)	PUNCT
ejpam-6803	69	38	by	by	ADP
ejpam-6803	69	39	injecting	inject	VERB
ejpam-6803	69	40	physical	physical	ADJ
ejpam-6803	69	41	laws	law	NOUN
ejpam-6803	69	42	into	into	ADP
ejpam-6803	69	43	the	the	DET
ejpam-6803	69	44	neural	neural	ADJ
ejpam-6803	69	45	network	network	NOUN
ejpam-6803	69	46	architecture	architecture	NOUN
ejpam-6803	69	47	.	.	PUNCT
ejpam-6803	70	1	in	in	ADP
ejpam-6803	70	2	this	this	DET
ejpam-6803	70	3	method	method	NOUN
ejpam-6803	70	4	we	we	PRON
ejpam-6803	70	5	treat	treat	VERB
ejpam-6803	70	6	the	the	DET
ejpam-6803	70	7	equations	equation	NOUN
ejpam-6803	70	8	of	of	ADP
ejpam-6803	70	9	motion	motion	NOUN
ejpam-6803	70	10	of	of	ADP
ejpam-6803	70	11	the	the	DET
ejpam-6803	70	12	system	system	NOUN
ejpam-6803	70	13	as	as	ADP
ejpam-6803	70	14	soft	soft	ADJ
ejpam-6803	70	15	constraints	constraint	NOUN
ejpam-6803	70	16	during	during	ADP
ejpam-6803	70	17	training	training	NOUN
ejpam-6803	70	18	.	.	PUNCT
ejpam-6803	71	1	the	the	DET
ejpam-6803	71	2	key	key	ADJ
ejpam-6803	71	3	idea	idea	NOUN
ejpam-6803	71	4	is	be	AUX
ejpam-6803	71	5	to	to	PART
ejpam-6803	71	6	incorporate	incorporate	VERB
ejpam-6803	71	7	the	the	DET
ejpam-6803	71	8	differential	differential	ADJ
ejpam-6803	71	9	structure	structure	NOUN
ejpam-6803	71	10	of	of	ADP
ejpam-6803	71	11	the	the	DET
ejpam-6803	71	12	physics	physics	NOUN
ejpam-6803	71	13	-	-	PUNCT
ejpam-6803	71	14	based	base	VERB
ejpam-6803	71	15	model	model	NOUN
ejpam-6803	71	16	by	by	ADP
ejpam-6803	71	17	automatic	automatic	ADJ
ejpam-6803	71	18	differentiation	differentiation	NOUN
ejpam-6803	71	19	into	into	ADP
ejpam-6803	71	20	the	the	DET
ejpam-6803	71	21	training	training	NOUN
ejpam-6803	71	22	without	without	ADP
ejpam-6803	71	23	having	having	AUX
ejpam-6803	71	24	labeled	label	VERB
ejpam-6803	71	25	data	datum	NOUN
ejpam-6803	71	26	at	at	ADP
ejpam-6803	71	27	each	each	DET
ejpam-6803	71	28	spatiotemporal	spatiotemporal	ADJ
ejpam-6803	71	29	point	point	NOUN
ejpam-6803	71	30	.	.	PUNCT
ejpam-6803	72	1	in	in	ADP
ejpam-6803	72	2	this	this	DET
ejpam-6803	72	3	work	work	NOUN
ejpam-6803	72	4	,	,	PUNCT
ejpam-6803	72	5	we	we	PRON
ejpam-6803	72	6	use	use	VERB
ejpam-6803	72	7	pinns	pinn	NOUN
ejpam-6803	72	8	to	to	PART
ejpam-6803	72	9	solve	solve	VERB
ejpam-6803	72	10	the	the	DET
ejpam-6803	72	11	coupled	couple	VERB
ejpam-6803	72	12	bbe	bbe	NOUN
ejpam-6803	72	13	given	give	VERB
ejpam-6803	72	14	as	as	ADP
ejpam-6803	72	15	:	:	PUNCT
ejpam-6803	72	16	∂ϕ(α	∂ϕ(α	PROPN
ejpam-6803	72	17	,	,	PUNCT
ejpam-6803	72	18	β	β	X
ejpam-6803	72	19	)	)	PUNCT
ejpam-6803	72	20	∂β	∂β	PROPN
ejpam-6803	72	21	+	+	CCONJ
ejpam-6803	72	22	∂ρ(α	∂ρ(α	PROPN
ejpam-6803	72	23	,	,	PUNCT
ejpam-6803	72	24	β	β	NOUN
ejpam-6803	72	25	)	)	PUNCT
ejpam-6803	72	26	∂α	∂α	PROPN
ejpam-6803	72	27	+	+	CCONJ
ejpam-6803	72	28	ϕ(α	ϕ(α	PROPN
ejpam-6803	72	29	,	,	PUNCT
ejpam-6803	72	30	β	β	X
ejpam-6803	72	31	)	)	PUNCT
ejpam-6803	72	32	∂ϕ(α	∂ϕ(α	PROPN
ejpam-6803	72	33	,	,	PUNCT
ejpam-6803	72	34	β	β	X
ejpam-6803	72	35	)	)	PUNCT
ejpam-6803	73	1	∂α	∂α	PROPN
ejpam-6803	73	2	=	=	SYM
ejpam-6803	73	3	0	0	NUM
ejpam-6803	73	4	,	,	PUNCT
ejpam-6803	73	5	∂ρ(α	∂ρ(α	PROPN
ejpam-6803	73	6	,	,	PUNCT
ejpam-6803	73	7	β	β	NOUN
ejpam-6803	73	8	)	)	PUNCT
ejpam-6803	74	1	∂β	∂β	PROPN
ejpam-6803	74	2	+	+	CCONJ
ejpam-6803	74	3	∂	∂	NUM
ejpam-6803	74	4	∂α	∂α	PROPN
ejpam-6803	74	5	(	(	PUNCT
ejpam-6803	74	6	ϕ(α	ϕ(α	PROPN
ejpam-6803	74	7	,	,	PUNCT
ejpam-6803	74	8	β)ρ(α	β)ρ(α	X
ejpam-6803	74	9	,	,	PUNCT
ejpam-6803	74	10	β	β	NOUN
ejpam-6803	74	11	)	)	PUNCT
ejpam-6803	74	12	)	)	PUNCT
ejpam-6803	75	1	+	+	CCONJ
ejpam-6803	75	2	∂3ϕ(α	∂3ϕ(α	NOUN
ejpam-6803	75	3	,	,	PUNCT
ejpam-6803	75	4	β	β	X
ejpam-6803	75	5	)	)	PUNCT
ejpam-6803	75	6	∂α3	∂α3	PROPN
ejpam-6803	75	7	=	=	SYM
ejpam-6803	75	8	0	0	NUM
ejpam-6803	75	9	,	,	PUNCT
ejpam-6803	75	10	(	(	PUNCT
ejpam-6803	75	11	2	2	X
ejpam-6803	75	12	)	)	PUNCT
ejpam-6803	75	13	where	where	SCONJ
ejpam-6803	75	14	α	α	PROPN
ejpam-6803	75	15	∈	∈	PROPN
ejpam-6803	75	16	ω	ω	NOUN
ejpam-6803	75	17	⊂	⊂	PROPN
ejpam-6803	75	18	r	r	NOUN
ejpam-6803	75	19	is	be	AUX
ejpam-6803	75	20	a	a	DET
ejpam-6803	75	21	spatial	spatial	ADJ
ejpam-6803	75	22	variable	variable	NOUN
ejpam-6803	75	23	,	,	PUNCT
ejpam-6803	75	24	and	and	CCONJ
ejpam-6803	75	25	β	β	X
ejpam-6803	75	26	∈	∈	PROPN
ejpam-6803	76	1	[	[	X
ejpam-6803	76	2	0	0	NUM
ejpam-6803	76	3	,	,	PUNCT
ejpam-6803	76	4	t	t	PROPN
ejpam-6803	76	5	]	]	PUNCT
ejpam-6803	76	6	is	be	AUX
ejpam-6803	76	7	time	time	NOUN
ejpam-6803	76	8	.	.	PUNCT
ejpam-6803	77	1	here	here	ADV
ejpam-6803	77	2	,	,	PUNCT
ejpam-6803	77	3	respectively	respectively	ADV
ejpam-6803	77	4	,	,	PUNCT
ejpam-6803	77	5	ϕ(α	ϕ(α	PROPN
ejpam-6803	77	6	,	,	PUNCT
ejpam-6803	77	7	β	β	NOUN
ejpam-6803	77	8	)	)	PUNCT
ejpam-6803	77	9	represents	represent	VERB
ejpam-6803	77	10	the	the	DET
ejpam-6803	77	11	horizontal	horizontal	ADJ
ejpam-6803	77	12	velocity	velocity	NOUN
ejpam-6803	77	13	field	field	NOUN
ejpam-6803	77	14	and	and	CCONJ
ejpam-6803	77	15	ρ(α	ρ(α	NOUN
ejpam-6803	77	16	,	,	PUNCT
ejpam-6803	77	17	β	β	X
ejpam-6803	77	18	)	)	PUNCT
ejpam-6803	77	19	the	the	DET
ejpam-6803	77	20	water	water	NOUN
ejpam-6803	77	21	surface	surface	NOUN
ejpam-6803	77	22	height	height	NOUN
ejpam-6803	77	23	.	.	PUNCT
ejpam-6803	78	1	initial	initial	ADJ
ejpam-6803	78	2	conditions	condition	NOUN
ejpam-6803	78	3	for	for	ADP
ejpam-6803	78	4	the	the	DET
ejpam-6803	78	5	system	system	NOUN
ejpam-6803	78	6	:	:	PUNCT
ejpam-6803	78	7	ϕ(α	ϕ(α	NUM
ejpam-6803	78	8	,	,	PUNCT
ejpam-6803	78	9	0	0	NUM
ejpam-6803	78	10	)	)	PUNCT
ejpam-6803	78	11	=	=	SYM
ejpam-6803	78	12	1	1	NUM
ejpam-6803	78	13	+	+	NUM
ejpam-6803	78	14	tanh	tanh	PROPN
ejpam-6803	78	15	(	(	PUNCT
ejpam-6803	78	16	α	α	NOUN
ejpam-6803	78	17	2	2	NUM
ejpam-6803	78	18	)	)	PUNCT
ejpam-6803	78	19	,	,	PUNCT
ejpam-6803	78	20	ρ(α	ρ(α	NOUN
ejpam-6803	78	21	,	,	PUNCT
ejpam-6803	78	22	0	0	NUM
ejpam-6803	78	23	)	)	PUNCT
ejpam-6803	78	24	=	=	SYM
ejpam-6803	78	25	1	1	NUM
ejpam-6803	78	26	2	2	NUM
ejpam-6803	78	27	−	−	NUM
ejpam-6803	78	28	1	1	NUM
ejpam-6803	78	29	2	2	NUM
ejpam-6803	78	30	tanh2	tanh2	NOUN
ejpam-6803	78	31	(	(	PUNCT
ejpam-6803	78	32	α	α	NOUN
ejpam-6803	78	33	2	2	NUM
ejpam-6803	78	34	)	)	PUNCT
ejpam-6803	78	35	.	.	PUNCT
ejpam-6803	79	1	(	(	PUNCT
ejpam-6803	79	2	3	3	X
ejpam-6803	79	3	)	)	PUNCT
ejpam-6803	79	4	a.	a.	NOUN
ejpam-6803	79	5	shafee	shafee	PROPN
ejpam-6803	79	6	et	et	PROPN
ejpam-6803	79	7	al	al	PROPN
ejpam-6803	79	8	.	.	PUNCT
ejpam-6803	79	9	/	/	SYM
ejpam-6803	79	10	eur	eur	PROPN
ejpam-6803	79	11	.	.	PUNCT
ejpam-6803	80	1	j.	j.	PROPN
ejpam-6803	80	2	pure	pure	PROPN
ejpam-6803	80	3	appl	appl	PROPN
ejpam-6803	80	4	.	.	PROPN
ejpam-6803	80	5	math	math	PROPN
ejpam-6803	80	6	,	,	PUNCT
ejpam-6803	80	7	18	18	NUM
ejpam-6803	80	8	(	(	PUNCT
ejpam-6803	80	9	4	4	NUM
ejpam-6803	80	10	)	)	PUNCT
ejpam-6803	80	11	(	(	PUNCT
ejpam-6803	80	12	2025	2025	NUM
ejpam-6803	80	13	)	)	PUNCT
ejpam-6803	80	14	,	,	PUNCT
ejpam-6803	80	15	6803	6803	NUM
ejpam-6803	80	16	5	5	NUM
ejpam-6803	80	17	of	of	ADP
ejpam-6803	80	18	18	18	NUM
ejpam-6803	80	19	the	the	DET
ejpam-6803	80	20	exact	exact	ADJ
ejpam-6803	80	21	solution	solution	NOUN
ejpam-6803	80	22	of	of	ADP
ejpam-6803	80	23	the	the	DET
ejpam-6803	80	24	model	model	NOUN
ejpam-6803	80	25	is	be	AUX
ejpam-6803	80	26	given	give	VERB
ejpam-6803	80	27	as	as	ADP
ejpam-6803	80	28	:	:	PUNCT
ejpam-6803	80	29	ϕ(α	ϕ(α	PROPN
ejpam-6803	80	30	,	,	PUNCT
ejpam-6803	80	31	β	β	X
ejpam-6803	80	32	)	)	PUNCT
ejpam-6803	80	33	=	=	SYM
ejpam-6803	81	1	1	1	NUM
ejpam-6803	81	2	+	+	NUM
ejpam-6803	81	3	tanh	tanh	PROPN
ejpam-6803	81	4	(	(	PUNCT
ejpam-6803	81	5	α−	α−	ADP
ejpam-6803	81	6	β	β	X
ejpam-6803	81	7	2	2	NUM
ejpam-6803	81	8	)	)	PUNCT
ejpam-6803	81	9	,	,	PUNCT
ejpam-6803	81	10	ρ(α	ρ(α	NOUN
ejpam-6803	81	11	,	,	PUNCT
ejpam-6803	81	12	β	β	X
ejpam-6803	81	13	)	)	PUNCT
ejpam-6803	81	14	=	=	SYM
ejpam-6803	81	15	1	1	NUM
ejpam-6803	81	16	2	2	NUM
ejpam-6803	81	17	−	−	NUM
ejpam-6803	81	18	1	1	NUM
ejpam-6803	81	19	2	2	NUM
ejpam-6803	81	20	tanh2	tanh2	NOUN
ejpam-6803	81	21	(	(	PUNCT
ejpam-6803	81	22	α−	α−	ADP
ejpam-6803	81	23	β	β	X
ejpam-6803	81	24	2	2	NUM
ejpam-6803	81	25	)	)	PUNCT
ejpam-6803	81	26	.	.	PUNCT
ejpam-6803	82	1	(	(	PUNCT
ejpam-6803	82	2	4	4	X
ejpam-6803	82	3	)	)	PUNCT
ejpam-6803	82	4	as	as	ADP
ejpam-6803	82	5	an	an	DET
ejpam-6803	82	6	input	input	NOUN
ejpam-6803	82	7	we	we	PRON
ejpam-6803	82	8	apply	apply	VERB
ejpam-6803	82	9	the	the	DET
ejpam-6803	82	10	spatio	spatio	PROPN
ejpam-6803	82	11	-	-	PUNCT
ejpam-6803	82	12	temporal	temporal	ADJ
ejpam-6803	82	13	coordinates	coordinate	NOUN
ejpam-6803	82	14	(	(	PUNCT
ejpam-6803	82	15	α	α	X
ejpam-6803	82	16	,	,	PUNCT
ejpam-6803	82	17	β	β	NOUN
ejpam-6803	82	18	)	)	PUNCT
ejpam-6803	82	19	,	,	PUNCT
ejpam-6803	82	20	and	and	CCONJ
ejpam-6803	82	21	as	as	ADP
ejpam-6803	82	22	an	an	DET
ejpam-6803	82	23	output	output	NOUN
ejpam-6803	82	24	there	there	PRON
ejpam-6803	82	25	are	be	AUX
ejpam-6803	82	26	predicted	predict	VERB
ejpam-6803	82	27	solutions	solution	NOUN
ejpam-6803	82	28	ϕ̂(α	ϕ̂(α	ADP
ejpam-6803	82	29	,	,	PUNCT
ejpam-6803	82	30	β	β	NOUN
ejpam-6803	82	31	)	)	PUNCT
ejpam-6803	82	32	and	and	CCONJ
ejpam-6803	82	33	ρ̂(α	ρ̂(α	PROPN
ejpam-6803	82	34	,	,	PUNCT
ejpam-6803	82	35	β	β	NOUN
ejpam-6803	82	36	)	)	PUNCT
ejpam-6803	82	37	,	,	PUNCT
ejpam-6803	82	38	and	and	CCONJ
ejpam-6803	82	39	(	(	PUNCT
ejpam-6803	82	40	fθ(α	fθ(α	PROPN
ejpam-6803	82	41	,	,	PUNCT
ejpam-6803	82	42	β	β	NOUN
ejpam-6803	82	43	)	)	PUNCT
ejpam-6803	83	1	=	=	NOUN
ejpam-6803	84	1	[	[	X
ejpam-6803	84	2	ϕ̂(α	ϕ̂(α	ADP
ejpam-6803	84	3	,	,	PUNCT
ejpam-6803	84	4	β	β	NOUN
ejpam-6803	84	5	)	)	PUNCT
ejpam-6803	84	6	,	,	PUNCT
ejpam-6803	84	7	ρ̂(α	ρ̂(α	PROPN
ejpam-6803	84	8	,	,	PUNCT
ejpam-6803	84	9	β	β	NOUN
ejpam-6803	84	10	)	)	PUNCT
ejpam-6803	84	11	]	]	PUNCT
ejpam-6803	84	12	θ	θ	X
ejpam-6803	84	13	)	)	PUNCT
ejpam-6803	84	14	means	mean	VERB
ejpam-6803	84	15	network	network	NOUN
ejpam-6803	84	16	parameters	parameter	NOUN
ejpam-6803	84	17	(	(	PUNCT
ejpam-6803	84	18	weights	weight	NOUN
ejpam-6803	84	19	and	and	CCONJ
ejpam-6803	84	20	bias	bias	NOUN
ejpam-6803	84	21	)	)	PUNCT
ejpam-6803	84	22	.	.	PUNCT
ejpam-6803	85	1	to	to	PART
ejpam-6803	85	2	implement	implement	VERB
ejpam-6803	85	3	the	the	DET
ejpam-6803	85	4	dynamics	dynamic	NOUN
ejpam-6803	85	5	given	give	VERB
ejpam-6803	85	6	by	by	ADP
ejpam-6803	85	7	equations	equation	NOUN
ejpam-6803	85	8	2	2	NUM
ejpam-6803	85	9	,	,	PUNCT
ejpam-6803	85	10	we	we	PRON
ejpam-6803	85	11	construct	construct	VERB
ejpam-6803	85	12	residual	residual	ADJ
ejpam-6803	85	13	functions	function	NOUN
ejpam-6803	85	14	r1(α	r1(α	PROPN
ejpam-6803	85	15	,	,	PUNCT
ejpam-6803	85	16	β	β	NOUN
ejpam-6803	85	17	)	)	PUNCT
ejpam-6803	85	18	and	and	CCONJ
ejpam-6803	85	19	r2(α	r2(α	NOUN
ejpam-6803	85	20	,	,	PUNCT
ejpam-6803	85	21	β	β	NOUN
ejpam-6803	85	22	)	)	PUNCT
ejpam-6803	85	23	with	with	ADP
ejpam-6803	85	24	automatic	automatic	ADJ
ejpam-6803	85	25	differentiation	differentiation	NOUN
ejpam-6803	85	26	:	:	PUNCT
ejpam-6803	85	27	r1(α	r1(α	PROPN
ejpam-6803	85	28	,	,	PUNCT
ejpam-6803	85	29	β	β	X
ejpam-6803	85	30	;	;	PUNCT
ejpam-6803	85	31	θϕ	θϕ	NOUN
ejpam-6803	85	32	,	,	PUNCT
ejpam-6803	85	33	θρ	θρ	NOUN
ejpam-6803	85	34	)	)	PUNCT
ejpam-6803	85	35	=	=	NOUN
ejpam-6803	85	36	∂ϕ̂	∂ϕ̂	X
ejpam-6803	85	37	∂β	∂β	PROPN
ejpam-6803	86	1	+	+	CCONJ
ejpam-6803	86	2	∂ρ̂	∂ρ̂	NOUN
ejpam-6803	86	3	∂α	∂α	PROPN
ejpam-6803	86	4	+	+	CCONJ
ejpam-6803	86	5	ϕ̂	ϕ̂	X
ejpam-6803	86	6	∂ϕ̂	∂ϕ̂	ADJ
ejpam-6803	87	1	∂α	∂α	PROPN
ejpam-6803	87	2	,	,	PUNCT
ejpam-6803	87	3	r2(α	r2(α	PROPN
ejpam-6803	87	4	,	,	PUNCT
ejpam-6803	87	5	β	β	X
ejpam-6803	87	6	;	;	PUNCT
ejpam-6803	87	7	θϕ	θϕ	NOUN
ejpam-6803	87	8	,	,	PUNCT
ejpam-6803	87	9	θρ	θρ	NOUN
ejpam-6803	87	10	)	)	PUNCT
ejpam-6803	87	11	=	=	NOUN
ejpam-6803	87	12	∂ρ̂	∂ρ̂	VERB
ejpam-6803	88	1	∂β	∂β	PROPN
ejpam-6803	88	2	+	+	CCONJ
ejpam-6803	88	3	∂	∂	NUM
ejpam-6803	88	4	∂α	∂α	PROPN
ejpam-6803	88	5	(	(	PUNCT
ejpam-6803	88	6	ϕ̂ρ̂	ϕ̂ρ̂	NOUN
ejpam-6803	88	7	)	)	PUNCT
ejpam-6803	88	8	+	+	CCONJ
ejpam-6803	89	1	∂3ϕ̂	∂3ϕ̂	PROPN
ejpam-6803	89	2	∂α3	∂α3	PROPN
ejpam-6803	89	3	.	.	PUNCT
ejpam-6803	90	1	(	(	PUNCT
ejpam-6803	90	2	5	5	X
ejpam-6803	90	3	)	)	PUNCT
ejpam-6803	90	4	these	these	DET
ejpam-6803	90	5	residuals	residual	NOUN
ejpam-6803	90	6	are	be	AUX
ejpam-6803	90	7	minimized	minimize	VERB
ejpam-6803	90	8	across	across	ADP
ejpam-6803	90	9	the	the	DET
ejpam-6803	90	10	provided	provide	VERB
ejpam-6803	90	11	spatio	spatio	NOUN
ejpam-6803	90	12	-	-	PUNCT
ejpam-6803	90	13	temporal	temporal	ADJ
ejpam-6803	90	14	domain	domain	NOUN
ejpam-6803	90	15	so	so	SCONJ
ejpam-6803	90	16	that	that	SCONJ
ejpam-6803	90	17	the	the	DET
ejpam-6803	90	18	neural	neural	ADJ
ejpam-6803	90	19	network	network	NOUN
ejpam-6803	90	20	outputs	output	NOUN
ejpam-6803	90	21	satisfy	satisfy	VERB
ejpam-6803	90	22	the	the	DET
ejpam-6803	90	23	pde	pde	NOUN
ejpam-6803	90	24	system	system	NOUN
ejpam-6803	90	25	.	.	PUNCT
ejpam-6803	91	1	these	these	DET
ejpam-6803	91	2	residuals	residual	NOUN
ejpam-6803	91	3	include	include	VERB
ejpam-6803	91	4	both	both	DET
ejpam-6803	91	5	first	first	ADJ
ejpam-6803	91	6	and	and	CCONJ
ejpam-6803	91	7	higher	high	ADJ
ejpam-6803	91	8	order	order	NOUN
ejpam-6803	91	9	derivatives	derivative	NOUN
ejpam-6803	91	10	e.g.	e.g.	ADV
ejpam-6803	91	11	∂3ϕ̂/∂α3	∂3ϕ̂/∂α3	PROPN
ejpam-6803	91	12	,	,	PUNCT
ejpam-6803	91	13	which	which	PRON
ejpam-6803	91	14	are	be	AUX
ejpam-6803	91	15	effectively	effectively	ADV
ejpam-6803	91	16	computed	compute	VERB
ejpam-6803	91	17	via	via	ADP
ejpam-6803	91	18	reverse	reverse	NOUN
ejpam-6803	91	19	-	-	PUNCT
ejpam-6803	91	20	mode	mode	NOUN
ejpam-6803	91	21	automatic	automatic	ADJ
ejpam-6803	91	22	differentiation	differentiation	NOUN
ejpam-6803	91	23	libraries	library	NOUN
ejpam-6803	91	24	(	(	PUNCT
ejpam-6803	91	25	e.g.	e.g.	ADV
ejpam-6803	91	26	tensorflow	tensorflow	NOUN
ejpam-6803	91	27	,	,	PUNCT
ejpam-6803	91	28	or	or	CCONJ
ejpam-6803	91	29	pytorch	pytorch	NOUN
ejpam-6803	91	30	)	)	PUNCT
ejpam-6803	91	31	.	.	PUNCT
ejpam-6803	92	1	the	the	DET
ejpam-6803	92	2	neural	neural	ADJ
ejpam-6803	92	3	network	network	NOUN
ejpam-6803	92	4	is	be	AUX
ejpam-6803	92	5	a	a	DET
ejpam-6803	92	6	feed	feed	NOUN
ejpam-6803	92	7	-	-	PUNCT
ejpam-6803	92	8	forward	forward	NOUN
ejpam-6803	92	9	network	network	NOUN
ejpam-6803	92	10	with	with	ADP
ejpam-6803	92	11	several	several	ADJ
ejpam-6803	92	12	layered	layered	ADJ
ejpam-6803	92	13	fully	fully	ADV
ejpam-6803	92	14	connected	connected	ADJ
ejpam-6803	92	15	units	unit	NOUN
ejpam-6803	92	16	,	,	PUNCT
ejpam-6803	92	17	each	each	PRON
ejpam-6803	92	18	with	with	ADP
ejpam-6803	92	19	nonlinear	nonlinear	ADJ
ejpam-6803	92	20	activation	activation	NOUN
ejpam-6803	92	21	functions	function	NOUN
ejpam-6803	92	22	(	(	PUNCT
ejpam-6803	92	23	e.g.	e.g.	ADV
ejpam-6803	92	24	tanh	tanh	NOUN
ejpam-6803	92	25	)	)	PUNCT
ejpam-6803	92	26	as	as	ADV
ejpam-6803	92	27	well	well	ADV
ejpam-6803	92	28	as	as	ADP
ejpam-6803	92	29	a	a	DET
ejpam-6803	92	30	linearly	linearly	ADV
ejpam-6803	92	31	combined	combine	VERB
ejpam-6803	92	32	output	output	NOUN
ejpam-6803	92	33	layer	layer	NOUN
ejpam-6803	92	34	.	.	PUNCT
ejpam-6803	93	1	the	the	DET
ejpam-6803	93	2	value	value	NOUN
ejpam-6803	93	3	estimater	estimater	NOUN
ejpam-6803	93	4	fθ	fθ	ADJ
ejpam-6803	93	5	is	be	AUX
ejpam-6803	93	6	differentiable	differentiable	ADJ
ejpam-6803	93	7	and	and	CCONJ
ejpam-6803	93	8	the	the	DET
ejpam-6803	93	9	output	output	NOUN
ejpam-6803	93	10	can	can	AUX
ejpam-6803	93	11	approximate	approximate	VERB
ejpam-6803	93	12	strongly	strongly	ADV
ejpam-6803	93	13	non	non	ADJ
ejpam-6803	93	14	-	-	ADJ
ejpam-6803	93	15	convex	convex	ADJ
ejpam-6803	93	16	solution	solution	NOUN
ejpam-6803	93	17	manifolds	manifold	NOUN
ejpam-6803	93	18	because	because	SCONJ
ejpam-6803	93	19	of	of	ADP
ejpam-6803	93	20	the	the	DET
ejpam-6803	93	21	universal	universal	ADJ
ejpam-6803	93	22	approximation	approximation	NOUN
ejpam-6803	93	23	theorem	theorem	NOUN
ejpam-6803	93	24	of	of	ADP
ejpam-6803	93	25	neural	neural	ADJ
ejpam-6803	93	26	networks	network	NOUN
ejpam-6803	93	27	.	.	PUNCT
ejpam-6803	94	1	the	the	DET
ejpam-6803	94	2	spatial	spatial	ADJ
ejpam-6803	94	3	and	and	CCONJ
ejpam-6803	94	4	temporal	temporal	ADJ
ejpam-6803	94	5	derivatives	derivative	NOUN
ejpam-6803	94	6	are	be	AUX
ejpam-6803	94	7	computed	compute	VERB
ejpam-6803	94	8	through	through	ADP
ejpam-6803	94	9	the	the	DET
ejpam-6803	94	10	tensorflow	tensorflow	NOUN
ejpam-6803	94	11	and	and	CCONJ
ejpam-6803	94	12	gradienttape	gradienttape	NOUN
ejpam-6803	94	13	,	,	PUNCT
ejpam-6803	94	14	which	which	PRON
ejpam-6803	94	15	records	record	VERB
ejpam-6803	94	16	operations	operation	NOUN
ejpam-6803	94	17	for	for	ADP
ejpam-6803	94	18	automatic	automatic	ADJ
ejpam-6803	94	19	differentiation	differentiation	NOUN
ejpam-6803	94	20	.	.	PUNCT
ejpam-6803	95	1	thus	thus	ADV
ejpam-6803	95	2	,	,	PUNCT
ejpam-6803	95	3	it	it	PRON
ejpam-6803	95	4	provides	provide	VERB
ejpam-6803	95	5	a	a	DET
ejpam-6803	95	6	way	way	NOUN
ejpam-6803	95	7	to	to	PART
ejpam-6803	95	8	compute	compute	VERB
ejpam-6803	95	9	derivatives	derivative	NOUN
ejpam-6803	95	10	,	,	PUNCT
ejpam-6803	95	11	such	such	ADJ
ejpam-6803	95	12	as	as	ADP
ejpam-6803	95	13	:	:	PUNCT
ejpam-6803	95	14	∂ϕ̂	∂ϕ̂	ADP
ejpam-6803	95	15	∂α	∂α	PROPN
ejpam-6803	95	16	,	,	PUNCT
ejpam-6803	95	17	∂2ϕ̂	∂2ϕ̂	PROPN
ejpam-6803	95	18	∂α2	∂α2	NOUN
ejpam-6803	95	19	,	,	PUNCT
ejpam-6803	95	20	∂ϕ̂	∂ϕ̂	X
ejpam-6803	95	21	∂β	∂β	PROPN
ejpam-6803	95	22	,	,	PUNCT
ejpam-6803	95	23	∂3ϕ̂	∂3ϕ̂	PROPN
ejpam-6803	95	24	∂α3	∂α3	PROPN
ejpam-6803	95	25	,	,	PUNCT
ejpam-6803	95	26	and	and	CCONJ
ejpam-6803	95	27	corresponding	correspond	VERB
ejpam-6803	95	28	terms	term	NOUN
ejpam-6803	95	29	for	for	ADP
ejpam-6803	95	30	ρ̂.	ρ̂.	NOUN
ejpam-6803	95	31	the	the	DET
ejpam-6803	95	32	residuals	residual	NOUN
ejpam-6803	95	33	r1	r1	NOUN
ejpam-6803	95	34	and	and	CCONJ
ejpam-6803	95	35	r2	r2	PROPN
ejpam-6803	95	36	are	be	AUX
ejpam-6803	95	37	imposed	impose	VERB
ejpam-6803	95	38	at	at	ADP
ejpam-6803	95	39	a	a	DET
ejpam-6803	95	40	collection	collection	NOUN
ejpam-6803	95	41	of	of	ADP
ejpam-6803	95	42	collocation	collocation	NOUN
ejpam-6803	95	43	points	point	NOUN
ejpam-6803	95	44	(	(	PUNCT
ejpam-6803	95	45	αj	αj	NOUN
ejpam-6803	95	46	,	,	PUNCT
ejpam-6803	95	47	βj	βj	PRON
ejpam-6803	95	48	)	)	PUNCT
ejpam-6803	95	49	in	in	ADP
ejpam-6803	95	50	the	the	DET
ejpam-6803	95	51	interior	interior	NOUN
ejpam-6803	95	52	of	of	ADP
ejpam-6803	95	53	the	the	DET
ejpam-6803	95	54	domain	domain	NOUN
ejpam-6803	95	55	.	.	PUNCT
ejpam-6803	96	1	as	as	SCONJ
ejpam-6803	96	2	the	the	DET
ejpam-6803	96	3	network	network	NOUN
ejpam-6803	96	4	learns	learn	VERB
ejpam-6803	96	5	the	the	DET
ejpam-6803	96	6	solution	solution	NOUN
ejpam-6803	96	7	variables	variable	VERB
ejpam-6803	96	8	ϕ̂	ϕ̂	PUNCT
ejpam-6803	96	9	and	and	CCONJ
ejpam-6803	96	10	ρ̂	ρ̂	NUM
ejpam-6803	96	11	,	,	PUNCT
ejpam-6803	96	12	it	it	PRON
ejpam-6803	96	13	also	also	ADV
ejpam-6803	96	14	minimizes	minimize	VERB
ejpam-6803	96	15	the	the	DET
ejpam-6803	96	16	pde	pde	NOUN
ejpam-6803	96	17	residues	residue	NOUN
ejpam-6803	96	18	at	at	ADP
ejpam-6803	96	19	these	these	DET
ejpam-6803	96	20	collocation	collocation	NOUN
ejpam-6803	96	21	points	point	NOUN
ejpam-6803	96	22	,	,	PUNCT
ejpam-6803	96	23	such	such	ADJ
ejpam-6803	96	24	that	that	SCONJ
ejpam-6803	96	25	the	the	DET
ejpam-6803	96	26	network	network	NOUN
ejpam-6803	96	27	predictions	prediction	NOUN
ejpam-6803	96	28	adhere	adhere	VERB
ejpam-6803	96	29	to	to	ADP
ejpam-6803	96	30	the	the	DET
ejpam-6803	96	31	bbe	bbe	PROPN
ejpam-6803	96	32	dynamics	dynamic	NOUN
ejpam-6803	96	33	.	.	PUNCT
ejpam-6803	97	1	this	this	PRON
ejpam-6803	97	2	makes	make	VERB
ejpam-6803	97	3	it	it	PRON
ejpam-6803	97	4	so	so	SCONJ
ejpam-6803	97	5	that	that	SCONJ
ejpam-6803	97	6	pinns	pinn	NOUN
ejpam-6803	97	7	generalize	generalize	VERB
ejpam-6803	97	8	well	well	ADV
ejpam-6803	97	9	into	into	ADP
ejpam-6803	97	10	low	low	ADJ
ejpam-6803	97	11	-	-	PUNCT
ejpam-6803	97	12	data	data	NOUN
ejpam-6803	97	13	regimes	regime	NOUN
ejpam-6803	97	14	,	,	PUNCT
ejpam-6803	97	15	as	as	SCONJ
ejpam-6803	97	16	the	the	DET
ejpam-6803	97	17	governing	govern	VERB
ejpam-6803	97	18	physics	physics	NOUN
ejpam-6803	97	19	provide	provide	VERB
ejpam-6803	97	20	a	a	DET
ejpam-6803	97	21	strong	strong	ADJ
ejpam-6803	97	22	inductive	inductive	ADJ
ejpam-6803	97	23	bias	bias	NOUN
ejpam-6803	97	24	.	.	PUNCT
ejpam-6803	98	1	moreover	moreover	ADV
ejpam-6803	98	2	,	,	PUNCT
ejpam-6803	98	3	as	as	SCONJ
ejpam-6803	98	4	they	they	PRON
ejpam-6803	98	5	do	do	AUX
ejpam-6803	98	6	not	not	PART
ejpam-6803	98	7	require	require	VERB
ejpam-6803	98	8	any	any	DET
ejpam-6803	98	9	discretization	discretization	NOUN
ejpam-6803	98	10	,	,	PUNCT
ejpam-6803	98	11	they	they	PRON
ejpam-6803	98	12	are	be	AUX
ejpam-6803	98	13	very	very	ADV
ejpam-6803	98	14	appropriate	appropriate	ADJ
ejpam-6803	98	15	for	for	ADP
ejpam-6803	98	16	complex	complex	ADJ
ejpam-6803	98	17	systems	system	NOUN
ejpam-6803	98	18	such	such	ADJ
ejpam-6803	98	19	as	as	ADP
ejpam-6803	98	20	the	the	DET
ejpam-6803	98	21	bbe	bbe	PROPN
ejpam-6803	98	22	system	system	NOUN
ejpam-6803	98	23	.	.	PUNCT
ejpam-6803	99	1	a.	a.	NOUN
ejpam-6803	99	2	shafee	shafee	PROPN
ejpam-6803	99	3	et	et	PROPN
ejpam-6803	99	4	al	al	PROPN
ejpam-6803	99	5	.	.	PUNCT
ejpam-6803	99	6	/	/	SYM
ejpam-6803	99	7	eur	eur	PROPN
ejpam-6803	99	8	.	.	PUNCT
ejpam-6803	100	1	j.	j.	PROPN
ejpam-6803	100	2	pure	pure	PROPN
ejpam-6803	100	3	appl	appl	PROPN
ejpam-6803	100	4	.	.	PROPN
ejpam-6803	100	5	math	math	PROPN
ejpam-6803	100	6	,	,	PUNCT
ejpam-6803	100	7	18	18	NUM
ejpam-6803	100	8	(	(	PUNCT
ejpam-6803	100	9	4	4	NUM
ejpam-6803	100	10	)	)	PUNCT
ejpam-6803	100	11	(	(	PUNCT
ejpam-6803	100	12	2025	2025	NUM
ejpam-6803	100	13	)	)	PUNCT
ejpam-6803	100	14	,	,	PUNCT
ejpam-6803	100	15	6803	6803	NUM
ejpam-6803	100	16	6	6	NUM
ejpam-6803	100	17	of	of	ADP
ejpam-6803	100	18	18	18	NUM
ejpam-6803	100	19	2.3	2.3	NUM
ejpam-6803	100	20	.	.	PUNCT
ejpam-6803	101	1	neural	neural	ADJ
ejpam-6803	101	2	network	network	NOUN
ejpam-6803	101	3	approximation	approximation	NOUN
ejpam-6803	101	4	let	let	VERB
ejpam-6803	101	5	ϕ̂(α	ϕ̂(α	VERB
ejpam-6803	101	6	,	,	PUNCT
ejpam-6803	101	7	β	β	X
ejpam-6803	101	8	;	;	PUNCT
ejpam-6803	101	9	θϕ	θϕ	NOUN
ejpam-6803	101	10	)	)	PUNCT
ejpam-6803	101	11	and	and	CCONJ
ejpam-6803	101	12	ρ̂(α	ρ̂(α	PROPN
ejpam-6803	101	13	,	,	PUNCT
ejpam-6803	101	14	β	β	X
ejpam-6803	101	15	;	;	PUNCT
ejpam-6803	101	16	θρ	θρ	NOUN
ejpam-6803	101	17	)	)	PUNCT
ejpam-6803	101	18	be	be	VERB
ejpam-6803	101	19	the	the	DET
ejpam-6803	101	20	neural	neural	ADJ
ejpam-6803	101	21	network	network	NOUN
ejpam-6803	101	22	approximations	approximation	NOUN
ejpam-6803	101	23	to	to	ADP
ejpam-6803	101	24	the	the	DET
ejpam-6803	101	25	true	true	ADJ
ejpam-6803	101	26	solutions	solution	NOUN
ejpam-6803	101	27	ϕ(α	ϕ(α	PROPN
ejpam-6803	101	28	,	,	PUNCT
ejpam-6803	101	29	β	β	NOUN
ejpam-6803	101	30	)	)	PUNCT
ejpam-6803	101	31	and	and	CCONJ
ejpam-6803	101	32	ρ(α	ρ(α	NOUN
ejpam-6803	101	33	,	,	PUNCT
ejpam-6803	101	34	β	β	NOUN
ejpam-6803	101	35	)	)	PUNCT
ejpam-6803	101	36	,	,	PUNCT
ejpam-6803	101	37	respectively	respectively	ADV
ejpam-6803	101	38	.	.	PUNCT
ejpam-6803	102	1	the	the	DET
ejpam-6803	102	2	parameter	parameter	NOUN
ejpam-6803	102	3	sets	set	VERB
ejpam-6803	102	4	θϕ	θϕ	NOUN
ejpam-6803	102	5	,	,	PUNCT
ejpam-6803	102	6	θρ	θρ	PRON
ejpam-6803	102	7	are	be	AUX
ejpam-6803	102	8	the	the	DET
ejpam-6803	102	9	trainable	trainable	ADJ
ejpam-6803	102	10	weights	weight	NOUN
ejpam-6803	102	11	and	and	CCONJ
ejpam-6803	102	12	biases	bias	NOUN
ejpam-6803	102	13	of	of	ADP
ejpam-6803	102	14	the	the	DET
ejpam-6803	102	15	networks	network	NOUN
ejpam-6803	102	16	.	.	PUNCT
ejpam-6803	103	1	both	both	DET
ejpam-6803	103	2	networks	network	NOUN
ejpam-6803	103	3	take	take	VERB
ejpam-6803	103	4	the	the	DET
ejpam-6803	103	5	input	input	NOUN
ejpam-6803	103	6	pair	pair	NOUN
ejpam-6803	103	7	(	(	PUNCT
ejpam-6803	103	8	α	α	NOUN
ejpam-6803	103	9	,	,	PUNCT
ejpam-6803	103	10	β	β	NOUN
ejpam-6803	103	11	)	)	PUNCT
ejpam-6803	103	12	as	as	ADP
ejpam-6803	103	13	an	an	DET
ejpam-6803	103	14	input	input	NOUN
ejpam-6803	103	15	and	and	CCONJ
ejpam-6803	103	16	output	output	VERB
ejpam-6803	103	17	a	a	DET
ejpam-6803	103	18	scalar	scalar	ADJ
ejpam-6803	103	19	approximation	approximation	NOUN
ejpam-6803	103	20	of	of	ADP
ejpam-6803	103	21	the	the	DET
ejpam-6803	103	22	solution	solution	NOUN
ejpam-6803	103	23	component	component	NOUN
ejpam-6803	103	24	.	.	PUNCT
ejpam-6803	104	1	2.4	2.4	NUM
ejpam-6803	104	2	.	.	PUNCT
ejpam-6803	105	1	loss	loss	NOUN
ejpam-6803	105	2	function	function	NOUN
ejpam-6803	105	3	design	design	VERB
ejpam-6803	105	4	the	the	DET
ejpam-6803	105	5	total	total	ADJ
ejpam-6803	105	6	loss	loss	NOUN
ejpam-6803	105	7	function	function	PROPN
ejpam-6803	105	8	l(θϕ	l(θϕ	PROPN
ejpam-6803	105	9	,	,	PUNCT
ejpam-6803	105	10	θρ	θρ	NOUN
ejpam-6803	105	11	)	)	PUNCT
ejpam-6803	105	12	consists	consist	VERB
ejpam-6803	105	13	of	of	ADP
ejpam-6803	105	14	two	two	NUM
ejpam-6803	105	15	components	component	NOUN
ejpam-6803	105	16	:	:	PUNCT
ejpam-6803	105	17	l(θϕ	l(θϕ	NOUN
ejpam-6803	105	18	,	,	PUNCT
ejpam-6803	105	19	θρ	θρ	NOUN
ejpam-6803	105	20	)	)	PUNCT
ejpam-6803	105	21	=	=	SYM
ejpam-6803	105	22	lic	lic	PROPN
ejpam-6803	105	23	+	+	CCONJ
ejpam-6803	105	24	lpde	lpde	ADJ
ejpam-6803	105	25	.	.	PUNCT
ejpam-6803	106	1	(	(	PUNCT
ejpam-6803	106	2	6	6	X
ejpam-6803	106	3	)	)	PUNCT
ejpam-6803	106	4	initial	initial	ADJ
ejpam-6803	106	5	condition	condition	NOUN
ejpam-6803	106	6	loss	loss	NOUN
ejpam-6803	106	7	lic	lic	NOUN
ejpam-6803	106	8	=	=	SYM
ejpam-6803	106	9	1	1	NUM
ejpam-6803	106	10	ni	ni	PROPN
ejpam-6803	106	11	ni∑	ni∑	PROPN
ejpam-6803	106	12	i=1	i=1	PROPN
ejpam-6803	107	1	[	[	PUNCT
ejpam-6803	107	2	|ϕ̂(αi	|ϕ̂(αi	PROPN
ejpam-6803	107	3	,	,	PUNCT
ejpam-6803	107	4	0)−	0)−	PUNCT
ejpam-6803	107	5	f(αi)|2	f(αi)|2	PROPN
ejpam-6803	108	1	+	+	CCONJ
ejpam-6803	108	2	|ρ̂(αi	|ρ̂(αi	PROPN
ejpam-6803	108	3	,	,	PUNCT
ejpam-6803	108	4	0)−	0)−	PUNCT
ejpam-6803	109	1	g(αi)|2	g(αi)|2	VERB
ejpam-6803	109	2	]	]	PUNCT
ejpam-6803	109	3	,	,	PUNCT
ejpam-6803	109	4	(	(	PUNCT
ejpam-6803	109	5	7	7	X
ejpam-6803	109	6	)	)	PUNCT
ejpam-6803	109	7	where	where	SCONJ
ejpam-6803	109	8	{	{	PUNCT
ejpam-6803	109	9	αi}ni	αi}ni	PROPN
ejpam-6803	109	10	i=1	i=1	PROPN
ejpam-6803	109	11	are	be	AUX
ejpam-6803	109	12	collocation	collocation	NOUN
ejpam-6803	109	13	points	point	NOUN
ejpam-6803	109	14	in	in	ADP
ejpam-6803	109	15	the	the	DET
ejpam-6803	109	16	spatial	spatial	ADJ
ejpam-6803	109	17	domain	domain	NOUN
ejpam-6803	109	18	at	at	ADP
ejpam-6803	109	19	time	time	NOUN
ejpam-6803	109	20	β	β	X
ejpam-6803	109	21	=	=	SYM
ejpam-6803	109	22	0	0	X
ejpam-6803	109	23	.	.	PUNCT
ejpam-6803	109	24	pde	pde	PROPN
ejpam-6803	109	25	residual	residual	ADJ
ejpam-6803	109	26	loss	loss	NOUN
ejpam-6803	109	27	lpde	lpde	NOUN
ejpam-6803	109	28	=	=	SYM
ejpam-6803	110	1	1	1	NUM
ejpam-6803	110	2	nr	nr	PROPN
ejpam-6803	110	3	nr∑	nr∑	PROPN
ejpam-6803	110	4	r=1	r=1	NOUN
ejpam-6803	110	5	[	[	PUNCT
ejpam-6803	110	6	|r1(αr	|r1(αr	ADJ
ejpam-6803	110	7	,	,	PUNCT
ejpam-6803	110	8	βr)|2	βr)|2	PROPN
ejpam-6803	110	9	+	+	CCONJ
ejpam-6803	110	10	|r2(αr	|r2(αr	NOUN
ejpam-6803	110	11	,	,	PUNCT
ejpam-6803	110	12	βr)|2	βr)|2	PROPN
ejpam-6803	110	13	]	]	PUNCT
ejpam-6803	110	14	,	,	PUNCT
ejpam-6803	110	15	(	(	PUNCT
ejpam-6803	110	16	8)	8)	NUM
ejpam-6803	110	17	where	where	SCONJ
ejpam-6803	110	18	{	{	PUNCT
ejpam-6803	110	19	(	(	PUNCT
ejpam-6803	110	20	αr	αr	PROPN
ejpam-6803	110	21	,	,	PUNCT
ejpam-6803	110	22	βr)}nr	βr)}nr	NOUN
ejpam-6803	110	23	r=1	r=1	NOUN
ejpam-6803	110	24	are	be	AUX
ejpam-6803	110	25	the	the	DET
ejpam-6803	110	26	residual	residual	ADJ
ejpam-6803	110	27	points	point	NOUN
ejpam-6803	110	28	sampled	sample	VERB
ejpam-6803	110	29	from	from	ADP
ejpam-6803	110	30	the	the	DET
ejpam-6803	110	31	interior	interior	NOUN
ejpam-6803	110	32	of	of	ADP
ejpam-6803	110	33	the	the	DET
ejpam-6803	110	34	domain	domain	NOUN
ejpam-6803	110	35	.	.	PUNCT
ejpam-6803	111	1	2.5	2.5	NUM
ejpam-6803	111	2	.	.	PUNCT
ejpam-6803	111	3	optimization	optimization	NOUN
ejpam-6803	111	4	and	and	CCONJ
ejpam-6803	111	5	training	train	VERB
ejpam-6803	111	6	the	the	DET
ejpam-6803	111	7	only	only	ADJ
ejpam-6803	111	8	parameter	parameter	NOUN
ejpam-6803	111	9	is	be	AUX
ejpam-6803	111	10	minimized	minimize	VERB
ejpam-6803	111	11	with	with	ADP
ejpam-6803	111	12	respect	respect	NOUN
ejpam-6803	111	13	to	to	ADP
ejpam-6803	111	14	the	the	DET
ejpam-6803	111	15	total	total	ADJ
ejpam-6803	111	16	loss	loss	NOUN
ejpam-6803	111	17	l	l	NOUN
ejpam-6803	111	18	by	by	ADP
ejpam-6803	111	19	gradient	gradient	NOUN
ejpam-6803	111	20	based	base	VERB
ejpam-6803	111	21	optimization	optimization	NOUN
ejpam-6803	111	22	methods	method	NOUN
ejpam-6803	111	23	like	like	ADP
ejpam-6803	111	24	adam	adam	PROPN
ejpam-6803	111	25	.	.	PUNCT
ejpam-6803	112	1	the	the	DET
ejpam-6803	112	2	gradients	gradient	NOUN
ejpam-6803	112	3	θϕ	θϕ	NOUN
ejpam-6803	112	4	and	and	CCONJ
ejpam-6803	112	5	θρ	θρ	PROPN
ejpam-6803	112	6	w.r.t	w.r.t	VERB
ejpam-6803	112	7	the	the	DET
ejpam-6803	112	8	parameters	parameter	NOUN
ejpam-6803	112	9	are	be	AUX
ejpam-6803	112	10	calculated	calculate	VERB
ejpam-6803	112	11	via	via	ADP
ejpam-6803	112	12	automatic	automatic	ADJ
ejpam-6803	112	13	differentiation	differentiation	NOUN
ejpam-6803	112	14	.	.	PUNCT
ejpam-6803	113	1	the	the	DET
ejpam-6803	113	2	optimization	optimization	NOUN
ejpam-6803	113	3	problem	problem	NOUN
ejpam-6803	113	4	can	can	AUX
ejpam-6803	113	5	be	be	AUX
ejpam-6803	113	6	expressed	express	VERB
ejpam-6803	113	7	as	as	ADP
ejpam-6803	113	8	:	:	PUNCT
ejpam-6803	113	9	(	(	PUNCT
ejpam-6803	113	10	θ∗ϕ	θ∗ϕ	PROPN
ejpam-6803	113	11	,	,	PUNCT
ejpam-6803	113	12	θ	θ	PROPN
ejpam-6803	113	13	∗	∗	NOUN
ejpam-6803	113	14	ρ	ρ	NOUN
ejpam-6803	113	15	)	)	PUNCT
ejpam-6803	113	16	=	=	SYM
ejpam-6803	113	17	arg	arg	NOUN
ejpam-6803	113	18	min	min	PROPN
ejpam-6803	113	19	θϕ,θρ	θϕ,θρ	PROPN
ejpam-6803	113	20	l(θϕ	l(θϕ	PROPN
ejpam-6803	113	21	,	,	PUNCT
ejpam-6803	113	22	θρ	θρ	NOUN
ejpam-6803	113	23	)	)	PUNCT
ejpam-6803	113	24	,	,	PUNCT
ejpam-6803	113	25	(	(	PUNCT
ejpam-6803	113	26	9	9	X
ejpam-6803	113	27	)	)	PUNCT
ejpam-6803	113	28	where	where	SCONJ
ejpam-6803	113	29	θ∗ϕ	θ∗ϕ	NUM
ejpam-6803	113	30	and	and	CCONJ
ejpam-6803	113	31	θ∗ρ	θ∗ρ	NUM
ejpam-6803	113	32	are	be	AUX
ejpam-6803	113	33	optimal	optimal	ADJ
ejpam-6803	113	34	parameter	parameter	NOUN
ejpam-6803	113	35	sets	set	NOUN
ejpam-6803	113	36	.	.	PUNCT
ejpam-6803	114	1	the	the	DET
ejpam-6803	114	2	associated	associated	ADJ
ejpam-6803	114	3	neural	neural	ADJ
ejpam-6803	114	4	networks	network	NOUN
ejpam-6803	114	5	ϕ̂(α	ϕ̂(α	PART
ejpam-6803	114	6	,	,	PUNCT
ejpam-6803	114	7	β	β	X
ejpam-6803	114	8	;	;	PUNCT
ejpam-6803	114	9	θ∗ϕ	θ∗ϕ	NUM
ejpam-6803	114	10	)	)	PUNCT
ejpam-6803	114	11	and	and	CCONJ
ejpam-6803	114	12	ρ̂(α	ρ̂(α	PROPN
ejpam-6803	114	13	,	,	PUNCT
ejpam-6803	114	14	β	β	X
ejpam-6803	114	15	;	;	PUNCT
ejpam-6803	114	16	θ∗ρ	θ∗ρ	X
ejpam-6803	114	17	)	)	PUNCT
ejpam-6803	114	18	provide	provide	VERB
ejpam-6803	114	19	approximations	approximation	NOUN
ejpam-6803	114	20	of	of	ADP
ejpam-6803	114	21	the	the	DET
ejpam-6803	114	22	true	true	ADJ
ejpam-6803	114	23	solution	solution	NOUN
ejpam-6803	114	24	of	of	ADP
ejpam-6803	114	25	the	the	DET
ejpam-6803	114	26	pde	pde	NOUN
ejpam-6803	114	27	system	system	NOUN
ejpam-6803	114	28	.	.	PUNCT
ejpam-6803	115	1	3	3	X
ejpam-6803	115	2	.	.	NOUN
ejpam-6803	115	3	results	result	NOUN
ejpam-6803	115	4	and	and	CCONJ
ejpam-6803	115	5	discussion	discussion	NOUN
ejpam-6803	115	6	the	the	DET
ejpam-6803	115	7	section	section	NOUN
ejpam-6803	115	8	illustrates	illustrate	VERB
ejpam-6803	115	9	the	the	DET
ejpam-6803	115	10	simulation	simulation	NOUN
ejpam-6803	115	11	of	of	ADP
ejpam-6803	115	12	complex	complex	ADJ
ejpam-6803	115	13	systems	system	NOUN
ejpam-6803	115	14	of	of	ADP
ejpam-6803	115	15	coupled	couple	VERB
ejpam-6803	115	16	nonlinear	nonlinear	PROPN
ejpam-6803	115	17	integerorder	integerorder	PROPN
ejpam-6803	115	18	bbe	bbe	PROPN
ejpam-6803	115	19	equations	equation	NOUN
ejpam-6803	115	20	,	,	PUNCT
ejpam-6803	115	21	by	by	ADP
ejpam-6803	115	22	using	use	VERB
ejpam-6803	115	23	physics	physics	NOUN
ejpam-6803	115	24	-	-	PUNCT
ejpam-6803	115	25	informed	inform	VERB
ejpam-6803	115	26	neural	neural	ADJ
ejpam-6803	115	27	networks	network	NOUN
ejpam-6803	115	28	(	(	PUNCT
ejpam-6803	115	29	pinns	pinn	NOUN
ejpam-6803	115	30	)	)	PUNCT
ejpam-6803	115	31	.	.	PUNCT
ejpam-6803	116	1	these	these	DET
ejpam-6803	116	2	equations	equation	NOUN
ejpam-6803	116	3	describe	describe	VERB
ejpam-6803	116	4	the	the	DET
ejpam-6803	116	5	propagation	propagation	NOUN
ejpam-6803	116	6	of	of	ADP
ejpam-6803	116	7	shallow	shallow	ADJ
ejpam-6803	116	8	water	water	NOUN
ejpam-6803	116	9	waves	wave	NOUN
ejpam-6803	116	10	and	and	CCONJ
ejpam-6803	116	11	dispersive	dispersive	ADJ
ejpam-6803	116	12	effects	effect	NOUN
ejpam-6803	116	13	.	.	PUNCT
ejpam-6803	117	1	the	the	DET
ejpam-6803	117	2	pinn	pinn	PROPN
ejpam-6803	117	3	a.	a.	NOUN
ejpam-6803	117	4	shafee	shafee	PROPN
ejpam-6803	117	5	et	et	PROPN
ejpam-6803	117	6	al	al	PROPN
ejpam-6803	117	7	.	.	PUNCT
ejpam-6803	117	8	/	/	SYM
ejpam-6803	117	9	eur	eur	PROPN
ejpam-6803	117	10	.	.	PUNCT
ejpam-6803	118	1	j.	j.	PROPN
ejpam-6803	118	2	pure	pure	PROPN
ejpam-6803	118	3	appl	appl	PROPN
ejpam-6803	118	4	.	.	PROPN
ejpam-6803	118	5	math	math	PROPN
ejpam-6803	118	6	,	,	PUNCT
ejpam-6803	118	7	18	18	NUM
ejpam-6803	118	8	(	(	PUNCT
ejpam-6803	118	9	4	4	NUM
ejpam-6803	118	10	)	)	PUNCT
ejpam-6803	118	11	(	(	PUNCT
ejpam-6803	118	12	2025	2025	NUM
ejpam-6803	118	13	)	)	PUNCT
ejpam-6803	118	14	,	,	PUNCT
ejpam-6803	118	15	6803	6803	NUM
ejpam-6803	118	16	7	7	NUM
ejpam-6803	118	17	of	of	ADP
ejpam-6803	118	18	18	18	NUM
ejpam-6803	118	19	framework	framework	NOUN
ejpam-6803	118	20	is	be	AUX
ejpam-6803	118	21	implemented	implement	VERB
ejpam-6803	118	22	using	use	VERB
ejpam-6803	118	23	python	python	NOUN
ejpam-6803	118	24	with	with	ADP
ejpam-6803	118	25	tensorflow	tensorflow	NOUN
ejpam-6803	118	26	.	.	PUNCT
ejpam-6803	119	1	we	we	PRON
ejpam-6803	119	2	used	use	VERB
ejpam-6803	119	3	500	500	NUM
ejpam-6803	119	4	training	training	NOUN
ejpam-6803	119	5	epochs	epoch	NOUN
ejpam-6803	119	6	,	,	PUNCT
ejpam-6803	119	7	which	which	PRON
ejpam-6803	119	8	was	be	AUX
ejpam-6803	119	9	empirically	empirically	ADV
ejpam-6803	119	10	set	set	VERB
ejpam-6803	119	11	to	to	PART
ejpam-6803	119	12	give	give	VERB
ejpam-6803	119	13	a	a	DET
ejpam-6803	119	14	tradeoff	tradeoff	NOUN
ejpam-6803	119	15	between	between	ADP
ejpam-6803	119	16	accuracy	accuracy	NOUN
ejpam-6803	119	17	in	in	ADP
ejpam-6803	119	18	convergence	convergence	NOUN
ejpam-6803	119	19	and	and	CCONJ
ejpam-6803	119	20	computational	computational	ADJ
ejpam-6803	119	21	efficiency	efficiency	NOUN
ejpam-6803	119	22	,	,	PUNCT
ejpam-6803	119	23	as	as	ADP
ejpam-6803	119	24	longer	long	ADJ
ejpam-6803	119	25	training	training	NOUN
ejpam-6803	119	26	did	do	AUX
ejpam-6803	119	27	not	not	PART
ejpam-6803	119	28	significantly	significantly	ADV
ejpam-6803	119	29	benefit	benefit	VERB
ejpam-6803	119	30	the	the	DET
ejpam-6803	119	31	results	result	NOUN
ejpam-6803	119	32	.	.	PUNCT
ejpam-6803	120	1	a	a	DET
ejpam-6803	120	2	feed	feed	NOUN
ejpam-6803	120	3	-	-	PUNCT
ejpam-6803	120	4	forward	forward	ADV
ejpam-6803	120	5	neural	neural	ADJ
ejpam-6803	120	6	network	network	NOUN
ejpam-6803	120	7	,	,	PUNCT
ejpam-6803	120	8	with	with	ADP
ejpam-6803	120	9	multiple	multiple	ADJ
ejpam-6803	120	10	hidden	hide	VERB
ejpam-6803	120	11	layers	layer	NOUN
ejpam-6803	120	12	of	of	ADP
ejpam-6803	120	13	nodes	node	NOUN
ejpam-6803	120	14	with	with	ADP
ejpam-6803	120	15	nonlinear	nonlinear	ADJ
ejpam-6803	120	16	activation	activation	NOUN
ejpam-6803	120	17	functions	function	NOUN
ejpam-6803	120	18	,	,	PUNCT
ejpam-6803	120	19	was	be	AUX
ejpam-6803	120	20	developed	develop	VERB
ejpam-6803	120	21	to	to	PART
ejpam-6803	120	22	approximate	approximate	VERB
ejpam-6803	120	23	the	the	DET
ejpam-6803	120	24	solution	solution	NOUN
ejpam-6803	120	25	.	.	PUNCT
ejpam-6803	121	1	a	a	DET
ejpam-6803	121	2	combination	combination	NOUN
ejpam-6803	121	3	of	of	ADP
ejpam-6803	121	4	adam	adam	PROPN
ejpam-6803	121	5	optimizer	optimizer	NOUN
ejpam-6803	121	6	strategie	strategie	NOUN
ejpam-6803	121	7	were	be	AUX
ejpam-6803	121	8	performed	perform	VERB
ejpam-6803	121	9	in	in	ADP
ejpam-6803	121	10	training	training	NOUN
ejpam-6803	121	11	,	,	PUNCT
ejpam-6803	121	12	and	and	CCONJ
ejpam-6803	121	13	a	a	DET
ejpam-6803	121	14	physics	physics	NOUN
ejpam-6803	121	15	-	-	PUNCT
ejpam-6803	121	16	informed	inform	VERB
ejpam-6803	121	17	loss	loss	NOUN
ejpam-6803	121	18	was	be	AUX
ejpam-6803	121	19	constructed	construct	VERB
ejpam-6803	121	20	to	to	PART
ejpam-6803	121	21	simultaneously	simultaneously	ADV
ejpam-6803	121	22	enforce	enforce	VERB
ejpam-6803	121	23	the	the	DET
ejpam-6803	121	24	governing	govern	VERB
ejpam-6803	121	25	pdes	pde	NOUN
ejpam-6803	121	26	and	and	CCONJ
ejpam-6803	121	27	the	the	DET
ejpam-6803	121	28	initial	initial	ADJ
ejpam-6803	121	29	conditions	condition	NOUN
ejpam-6803	121	30	with	with	ADP
ejpam-6803	121	31	no	no	DET
ejpam-6803	121	32	labeled	label	VERB
ejpam-6803	121	33	solution	solution	NOUN
ejpam-6803	121	34	data	datum	NOUN
ejpam-6803	121	35	available	available	ADJ
ejpam-6803	121	36	.	.	PUNCT
ejpam-6803	122	1	to	to	PART
ejpam-6803	122	2	investigate	investigate	VERB
ejpam-6803	122	3	the	the	DET
ejpam-6803	122	4	training	training	NOUN
ejpam-6803	122	5	dynamics	dynamic	NOUN
ejpam-6803	122	6	and	and	CCONJ
ejpam-6803	122	7	internal	internal	ADJ
ejpam-6803	122	8	structure	structure	NOUN
ejpam-6803	122	9	of	of	ADP
ejpam-6803	122	10	the	the	DET
ejpam-6803	122	11	model	model	NOUN
ejpam-6803	122	12	,	,	PUNCT
ejpam-6803	122	13	histogram	histogram	NOUN
ejpam-6803	122	14	and	and	CCONJ
ejpam-6803	122	15	kernel	kernel	PROPN
ejpam-6803	122	16	density	density	PROPN
ejpam-6803	122	17	estimation	estimation	PROPN
ejpam-6803	122	18	(	(	PUNCT
ejpam-6803	122	19	kde	kde	NOUN
ejpam-6803	122	20	)	)	PUNCT
ejpam-6803	122	21	plots	plot	NOUN
ejpam-6803	122	22	of	of	ADP
ejpam-6803	122	23	the	the	DET
ejpam-6803	122	24	weight	weight	NOUN
ejpam-6803	122	25	distributions	distribution	NOUN
ejpam-6803	122	26	at	at	ADP
ejpam-6803	122	27	hidden	hidden	ADJ
ejpam-6803	122	28	layers	layer	NOUN
ejpam-6803	122	29	are	be	AUX
ejpam-6803	122	30	plotted	plot	VERB
ejpam-6803	122	31	shown	show	VERB
ejpam-6803	122	32	in	in	ADP
ejpam-6803	122	33	figure	figure	NOUN
ejpam-6803	122	34	2	2	NUM
ejpam-6803	122	35	.	.	PUNCT
ejpam-6803	123	1	the	the	DET
ejpam-6803	123	2	spread	spread	NOUN
ejpam-6803	123	3	,	,	PUNCT
ejpam-6803	123	4	mean	mean	VERB
ejpam-6803	123	5	,	,	PUNCT
ejpam-6803	123	6	and	and	CCONJ
ejpam-6803	123	7	variance	variance	NOUN
ejpam-6803	123	8	of	of	ADP
ejpam-6803	123	9	learned	learn	VERB
ejpam-6803	123	10	parameters	parameter	NOUN
ejpam-6803	123	11	are	be	AUX
ejpam-6803	123	12	visualized	visualize	VERB
ejpam-6803	123	13	to	to	PART
ejpam-6803	123	14	provide	provide	VERB
ejpam-6803	123	15	understanding	understanding	NOUN
ejpam-6803	123	16	on	on	ADP
ejpam-6803	123	17	the	the	DET
ejpam-6803	123	18	extent	extent	NOUN
ejpam-6803	123	19	the	the	DET
ejpam-6803	123	20	model	model	NOUN
ejpam-6803	123	21	can	can	AUX
ejpam-6803	123	22	represent	represent	VERB
ejpam-6803	123	23	complex	complex	ADJ
ejpam-6803	123	24	dynamics	dynamic	NOUN
ejpam-6803	123	25	.	.	PUNCT
ejpam-6803	124	1	the	the	DET
ejpam-6803	124	2	comparison	comparison	NOUN
ejpam-6803	124	3	of	of	ADP
ejpam-6803	124	4	the	the	DET
ejpam-6803	124	5	model	model	NOUN
ejpam-6803	124	6	behavior	behavior	NOUN
ejpam-6803	124	7	is	be	AUX
ejpam-6803	124	8	performed	perform	VERB
ejpam-6803	124	9	through	through	ADP
ejpam-6803	124	10	training	training	NOUN
ejpam-6803	124	11	loss	loss	NOUN
ejpam-6803	124	12	evolutions	evolution	NOUN
ejpam-6803	124	13	,	,	PUNCT
ejpam-6803	124	14	prediction	prediction	NOUN
ejpam-6803	124	15	versus	versus	ADP
ejpam-6803	124	16	exact	exact	ADJ
ejpam-6803	124	17	solutions	solution	NOUN
ejpam-6803	124	18	on	on	ADP
ejpam-6803	124	19	surface	surface	NOUN
ejpam-6803	124	20	and	and	CCONJ
ejpam-6803	124	21	in	in	ADP
ejpam-6803	124	22	distribution	distribution	NOUN
ejpam-6803	124	23	of	of	ADP
ejpam-6803	124	24	the	the	DET
ejpam-6803	124	25	absolute	absolute	ADJ
ejpam-6803	124	26	error	error	NOUN
ejpam-6803	124	27	,	,	PUNCT
ejpam-6803	124	28	and	and	CCONJ
ejpam-6803	124	29	their	their	PRON
ejpam-6803	124	30	cross	cross	NOUN
ejpam-6803	124	31	-	-	NOUN
ejpam-6803	124	32	section	section	NOUN
ejpam-6803	124	33	at	at	ADP
ejpam-6803	124	34	a	a	DET
ejpam-6803	124	35	given	give	VERB
ejpam-6803	124	36	time	time	NOUN
ejpam-6803	124	37	step	step	NOUN
ejpam-6803	124	38	(	(	PUNCT
ejpam-6803	124	39	β	β	NOUN
ejpam-6803	124	40	)	)	PUNCT
ejpam-6803	124	41	.	.	PUNCT
ejpam-6803	125	1	we	we	PRON
ejpam-6803	125	2	exploit	exploit	VERB
ejpam-6803	125	3	this	this	DET
ejpam-6803	125	4	setup	setup	NOUN
ejpam-6803	125	5	to	to	PART
ejpam-6803	125	6	investigate	investigate	VERB
ejpam-6803	125	7	the	the	DET
ejpam-6803	125	8	learning	learning	NOUN
ejpam-6803	125	9	dynamics	dynamic	NOUN
ejpam-6803	125	10	of	of	ADP
ejpam-6803	125	11	the	the	DET
ejpam-6803	125	12	model	model	NOUN
ejpam-6803	125	13	,	,	PUNCT
ejpam-6803	125	14	for	for	ADP
ejpam-6803	125	15	which	which	PRON
ejpam-6803	125	16	the	the	DET
ejpam-6803	125	17	dynamics	dynamic	NOUN
ejpam-6803	125	18	bbe	bbe	PROPN
ejpam-6803	125	19	systems	system	NOUN
ejpam-6803	125	20	are	be	AUX
ejpam-6803	125	21	accounted	account	VERB
ejpam-6803	125	22	for	for	ADP
ejpam-6803	125	23	numerically	numerically	ADV
ejpam-6803	125	24	with	with	ADP
ejpam-6803	125	25	high	high	ADJ
ejpam-6803	125	26	precision	precision	NOUN
ejpam-6803	125	27	and	and	CCONJ
ejpam-6803	125	28	consistency	consistency	NOUN
ejpam-6803	125	29	.	.	PUNCT
ejpam-6803	126	1	table	table	NOUN
ejpam-6803	126	2	2	2	NUM
ejpam-6803	126	3	summarizes	summarize	NOUN
ejpam-6803	126	4	the	the	DET
ejpam-6803	126	5	key	key	ADJ
ejpam-6803	126	6	parameters	parameter	NOUN
ejpam-6803	126	7	and	and	CCONJ
ejpam-6803	126	8	specifications	specification	NOUN
ejpam-6803	126	9	used	use	VERB
ejpam-6803	126	10	in	in	ADP
ejpam-6803	126	11	the	the	DET
ejpam-6803	126	12	implementation	implementation	NOUN
ejpam-6803	126	13	of	of	ADP
ejpam-6803	126	14	the	the	DET
ejpam-6803	126	15	pinn	pinn	NOUN
ejpam-6803	126	16	.	.	PUNCT
ejpam-6803	127	1	figure	figure	NOUN
ejpam-6803	127	2	2	2	NUM
ejpam-6803	127	3	:	:	PUNCT
ejpam-6803	127	4	neural	neural	ADJ
ejpam-6803	127	5	network	network	NOUN
ejpam-6803	127	6	weight	weight	NOUN
ejpam-6803	127	7	distribution	distribution	NOUN
ejpam-6803	127	8	and	and	CCONJ
ejpam-6803	127	9	adaptive	adaptive	ADJ
ejpam-6803	127	10	visualization	visualization	NOUN
ejpam-6803	127	11	.	.	PUNCT
ejpam-6803	128	1	a.	a.	NOUN
ejpam-6803	128	2	shafee	shafee	PROPN
ejpam-6803	128	3	et	et	PROPN
ejpam-6803	128	4	al	al	PROPN
ejpam-6803	128	5	.	.	PUNCT
ejpam-6803	128	6	/	/	SYM
ejpam-6803	128	7	eur	eur	PROPN
ejpam-6803	128	8	.	.	PUNCT
ejpam-6803	129	1	j.	j.	PROPN
ejpam-6803	129	2	pure	pure	PROPN
ejpam-6803	129	3	appl	appl	PROPN
ejpam-6803	129	4	.	.	PROPN
ejpam-6803	129	5	math	math	PROPN
ejpam-6803	129	6	,	,	PUNCT
ejpam-6803	129	7	18	18	NUM
ejpam-6803	129	8	(	(	PUNCT
ejpam-6803	129	9	4	4	NUM
ejpam-6803	129	10	)	)	PUNCT
ejpam-6803	129	11	(	(	PUNCT
ejpam-6803	129	12	2025	2025	NUM
ejpam-6803	129	13	)	)	PUNCT
ejpam-6803	129	14	,	,	PUNCT
ejpam-6803	129	15	6803	6803	NUM
ejpam-6803	129	16	8	8	NUM
ejpam-6803	129	17	of	of	ADP
ejpam-6803	129	18	18	18	NUM
ejpam-6803	129	19	table	table	NOUN
ejpam-6803	129	20	1	1	NUM
ejpam-6803	129	21	:	:	PUNCT
ejpam-6803	129	22	parameters	parameter	NOUN
ejpam-6803	129	23	and	and	CCONJ
ejpam-6803	129	24	specifications	specification	NOUN
ejpam-6803	129	25	of	of	ADP
ejpam-6803	129	26	the	the	DET
ejpam-6803	129	27	proposed	propose	VERB
ejpam-6803	129	28	pinn	pinn	NOUN
ejpam-6803	129	29	model	model	NOUN
ejpam-6803	129	30	.	.	PUNCT
ejpam-6803	130	1	parameters	parameter	NOUN
ejpam-6803	130	2	of	of	ADP
ejpam-6803	130	3	pinn	pinn	PROPN
ejpam-6803	130	4	specification	specification	NOUN
ejpam-6803	130	5	number	number	NOUN
ejpam-6803	130	6	of	of	ADP
ejpam-6803	130	7	hidden	hidden	ADJ
ejpam-6803	130	8	layers	layer	NOUN
ejpam-6803	130	9	5	5	NUM
ejpam-6803	130	10	number	number	NOUN
ejpam-6803	130	11	of	of	ADP
ejpam-6803	130	12	neurons	neuron	NOUN
ejpam-6803	130	13	per	per	ADP
ejpam-6803	130	14	hidden	hide	VERB
ejpam-6803	130	15	layer	layer	NOUN
ejpam-6803	130	16	128	128	NUM
ejpam-6803	130	17	activation	activation	NOUN
ejpam-6803	130	18	function	function	NOUN
ejpam-6803	130	19	tangent	tangent	NOUN
ejpam-6803	130	20	hyperbolic	hyperbolic	ADJ
ejpam-6803	130	21	(	(	PUNCT
ejpam-6803	130	22	tanh	tanh	NOUN
ejpam-6803	130	23	)	)	PUNCT
ejpam-6803	130	24	number	number	NOUN
ejpam-6803	130	25	of	of	ADP
ejpam-6803	130	26	epochs	epoch	NOUN
ejpam-6803	130	27	(	(	PUNCT
ejpam-6803	130	28	adam	adam	PROPN
ejpam-6803	130	29	)	)	PUNCT
ejpam-6803	130	30	500	500	NUM
ejpam-6803	130	31	optimizer	optimizer	NOUN
ejpam-6803	130	32	adam	adam	NOUN
ejpam-6803	130	33	learning	learning	PROPN
ejpam-6803	130	34	rate	rate	NOUN
ejpam-6803	130	35	(	(	PUNCT
ejpam-6803	130	36	adam	adam	PROPN
ejpam-6803	130	37	)	)	PUNCT
ejpam-6803	130	38	0.0001	0.0001	NUM
ejpam-6803	130	39	learning	learning	NOUN
ejpam-6803	130	40	rate	rate	NOUN
ejpam-6803	130	41	schedule	schedule	NOUN
ejpam-6803	130	42	fixed	fix	VERB
ejpam-6803	130	43	(	(	PUNCT
ejpam-6803	130	44	no	no	DET
ejpam-6803	130	45	decay	decay	NOUN
ejpam-6803	130	46	)	)	PUNCT
ejpam-6803	130	47	number	number	NOUN
ejpam-6803	130	48	of	of	ADP
ejpam-6803	130	49	ic	ic	PROPN
ejpam-6803	130	50	points	point	NOUN
ejpam-6803	130	51	(	(	PUNCT
ejpam-6803	130	52	ni	ni	NOUN
ejpam-6803	130	53	)	)	PUNCT
ejpam-6803	130	54	100	100	NUM
ejpam-6803	130	55	number	number	NOUN
ejpam-6803	130	56	of	of	ADP
ejpam-6803	130	57	collocation	collocation	NOUN
ejpam-6803	130	58	points	point	NOUN
ejpam-6803	130	59	(	(	PUNCT
ejpam-6803	130	60	nr	nr	NOUN
ejpam-6803	130	61	)	)	PUNCT
ejpam-6803	130	62	10,000	10,000	NUM
ejpam-6803	130	63	sampling	sample	VERB
ejpam-6803	130	64	strategy	strategy	NOUN
ejpam-6803	130	65	latin	latin	ADJ
ejpam-6803	130	66	hypercube	hypercube	NOUN
ejpam-6803	130	67	sampling	sample	VERB
ejpam-6803	130	68	(	(	PUNCT
ejpam-6803	130	69	lhs	lhs	PROPN
ejpam-6803	130	70	)	)	PUNCT
ejpam-6803	130	71	input	input	PROPN
ejpam-6803	130	72	normalization	normalization	PROPN
ejpam-6803	130	73	min	min	PROPN
ejpam-6803	130	74	–	–	PUNCT
ejpam-6803	130	75	max	max	NOUN
ejpam-6803	130	76	scaling	scaling	NOUN
ejpam-6803	130	77	to	to	ADP
ejpam-6803	130	78	[	[	X
ejpam-6803	130	79	−1	−1	NOUN
ejpam-6803	130	80	,	,	PUNCT
ejpam-6803	130	81	1	1	X
ejpam-6803	130	82	]	]	PUNCT
ejpam-6803	130	83	training	training	NOUN
ejpam-6803	130	84	time	time	NOUN
ejpam-6803	130	85	1216	1216	NUM
ejpam-6803	130	86	sec	sec	PROPN
ejpam-6803	130	87	average	average	ADJ
ejpam-6803	130	88	decision	decision	NOUN
ejpam-6803	130	89	time	time	NOUN
ejpam-6803	130	90	≤	≤	ADV
ejpam-6803	130	91	0.1	0.1	NUM
ejpam-6803	130	92	ms	ms	NOUN
ejpam-6803	130	93	per	per	ADP
ejpam-6803	130	94	point	point	NOUN
ejpam-6803	130	95	platform	platform	NOUN
ejpam-6803	130	96	google	google	PROPN
ejpam-6803	130	97	colab	colab	PROPN
ejpam-6803	130	98	programming	programming	PROPN
ejpam-6803	130	99	language	language	PROPN
ejpam-6803	130	100	python	python	NOUN
ejpam-6803	130	101	3	3	NUM
ejpam-6803	130	102	ram	ram	NOUN
ejpam-6803	130	103	12.67	12.67	NUM
ejpam-6803	130	104	gb	gb	ADP
ejpam-6803	130	105	3.1	3.1	NUM
ejpam-6803	130	106	.	.	PUNCT
ejpam-6803	131	1	model	model	NOUN
ejpam-6803	131	2	convergence	convergence	NOUN
ejpam-6803	131	3	analysis	analysis	NOUN
ejpam-6803	131	4	figure	figure	NOUN
ejpam-6803	131	5	3	3	NUM
ejpam-6803	131	6	shows	show	VERB
ejpam-6803	131	7	the	the	DET
ejpam-6803	131	8	total	total	ADJ
ejpam-6803	131	9	training	training	NOUN
ejpam-6803	131	10	loss	loss	NOUN
ejpam-6803	131	11	,	,	PUNCT
ejpam-6803	131	12	pde	pde	NOUN
ejpam-6803	131	13	residual	residual	ADJ
ejpam-6803	131	14	loss	loss	NOUN
ejpam-6803	131	15	and	and	CCONJ
ejpam-6803	131	16	the	the	DET
ejpam-6803	131	17	initial	initial	ADJ
ejpam-6803	131	18	condition	condition	NOUN
ejpam-6803	131	19	loss	loss	NOUN
ejpam-6803	131	20	during	during	ADP
ejpam-6803	131	21	500	500	NUM
ejpam-6803	131	22	epochs	epoch	NOUN
ejpam-6803	131	23	.	.	PUNCT
ejpam-6803	132	1	the	the	DET
ejpam-6803	132	2	losses	loss	NOUN
ejpam-6803	132	3	decrease	decrease	VERB
ejpam-6803	132	4	gradually	gradually	ADV
ejpam-6803	132	5	,	,	PUNCT
ejpam-6803	132	6	demonstrating	demonstrate	VERB
ejpam-6803	132	7	that	that	SCONJ
ejpam-6803	132	8	the	the	DET
ejpam-6803	132	9	model	model	NOUN
ejpam-6803	132	10	can	can	AUX
ejpam-6803	132	11	learn	learn	VERB
ejpam-6803	132	12	well	well	ADV
ejpam-6803	132	13	with	with	ADP
ejpam-6803	132	14	time	time	NOUN
ejpam-6803	132	15	.	.	PUNCT
ejpam-6803	133	1	the	the	DET
ejpam-6803	133	2	pinn	pinn	NOUN
ejpam-6803	133	3	can	can	AUX
ejpam-6803	133	4	effectively	effectively	ADV
ejpam-6803	133	5	minimize	minimize	VERB
ejpam-6803	133	6	the	the	DET
ejpam-6803	133	7	residuals	residual	NOUN
ejpam-6803	133	8	of	of	ADP
ejpam-6803	133	9	the	the	DET
ejpam-6803	133	10	governing	govern	VERB
ejpam-6803	133	11	equation	equation	NOUN
ejpam-6803	133	12	and	and	CCONJ
ejpam-6803	133	13	errors	error	NOUN
ejpam-6803	133	14	of	of	ADP
ejpam-6803	133	15	the	the	DET
ejpam-6803	133	16	initial	initial	ADJ
ejpam-6803	133	17	conditions	condition	NOUN
ejpam-6803	133	18	.	.	PUNCT
ejpam-6803	134	1	this	this	PRON
ejpam-6803	134	2	validates	validate	VERB
ejpam-6803	134	3	the	the	DET
ejpam-6803	134	4	convergent	convergent	NOUN
ejpam-6803	134	5	and	and	CCONJ
ejpam-6803	134	6	stable	stable	ADJ
ejpam-6803	134	7	training	training	NOUN
ejpam-6803	134	8	of	of	ADP
ejpam-6803	134	9	the	the	DET
ejpam-6803	134	10	model	model	NOUN
ejpam-6803	134	11	.	.	PUNCT
ejpam-6803	135	1	a.	a.	PROPN
ejpam-6803	135	2	shafee	shafee	PROPN
ejpam-6803	135	3	et	et	PROPN
ejpam-6803	135	4	al	al	PROPN
ejpam-6803	135	5	.	.	PUNCT
ejpam-6803	135	6	/	/	SYM
ejpam-6803	135	7	eur	eur	PROPN
ejpam-6803	135	8	.	.	PUNCT
ejpam-6803	136	1	j.	j.	PROPN
ejpam-6803	136	2	pure	pure	PROPN
ejpam-6803	136	3	appl	appl	PROPN
ejpam-6803	136	4	.	.	PROPN
ejpam-6803	136	5	math	math	PROPN
ejpam-6803	136	6	,	,	PUNCT
ejpam-6803	136	7	18	18	NUM
ejpam-6803	136	8	(	(	PUNCT
ejpam-6803	136	9	4	4	NUM
ejpam-6803	136	10	)	)	PUNCT
ejpam-6803	136	11	(	(	PUNCT
ejpam-6803	136	12	2025	2025	NUM
ejpam-6803	136	13	)	)	PUNCT
ejpam-6803	136	14	,	,	PUNCT
ejpam-6803	136	15	6803	6803	NUM
ejpam-6803	136	16	9	9	NUM
ejpam-6803	136	17	of	of	ADP
ejpam-6803	136	18	18	18	NUM
ejpam-6803	136	19	figure	figure	NOUN
ejpam-6803	136	20	3	3	NUM
ejpam-6803	136	21	:	:	PUNCT
ejpam-6803	136	22	training	train	VERB
ejpam-6803	136	23	loss	loss	NOUN
ejpam-6803	136	24	progression	progression	NOUN
ejpam-6803	136	25	with	with	ADP
ejpam-6803	136	26	smoothed	smoothed	ADJ
ejpam-6803	136	27	trends	trend	NOUN
ejpam-6803	136	28	.	.	PUNCT
ejpam-6803	137	1	3.2	3.2	NUM
ejpam-6803	137	2	.	.	PUNCT
ejpam-6803	138	1	surface	surface	NOUN
ejpam-6803	138	2	comparison	comparison	NOUN
ejpam-6803	138	3	with	with	ADP
ejpam-6803	138	4	exact	exact	ADJ
ejpam-6803	138	5	solutions	solution	NOUN
ejpam-6803	138	6	the	the	DET
ejpam-6803	138	7	predicted	predict	VERB
ejpam-6803	138	8	surfaces	surface	NOUN
ejpam-6803	138	9	for	for	ADP
ejpam-6803	138	10	ϕ(α	ϕ(α	PROPN
ejpam-6803	138	11	,	,	PUNCT
ejpam-6803	138	12	β	β	NOUN
ejpam-6803	138	13	)	)	PUNCT
ejpam-6803	138	14	and	and	CCONJ
ejpam-6803	138	15	ρ(α	ρ(α	NOUN
ejpam-6803	138	16	,	,	PUNCT
ejpam-6803	138	17	β	β	NOUN
ejpam-6803	138	18	)	)	PUNCT
ejpam-6803	138	19	are	be	AUX
ejpam-6803	138	20	in	in	ADP
ejpam-6803	138	21	closely	closely	ADV
ejpam-6803	138	22	match	match	NOUN
ejpam-6803	138	23	with	with	ADP
ejpam-6803	138	24	the	the	DET
ejpam-6803	138	25	exact	exact	ADJ
ejpam-6803	138	26	solutions	solution	NOUN
ejpam-6803	138	27	over	over	ADP
ejpam-6803	138	28	the	the	DET
ejpam-6803	138	29	complete	complete	ADJ
ejpam-6803	138	30	spatiotemporal	spatiotemporal	ADJ
ejpam-6803	138	31	region	region	NOUN
ejpam-6803	138	32	shown	show	VERB
ejpam-6803	138	33	in	in	ADP
ejpam-6803	138	34	figure	figure	NOUN
ejpam-6803	138	35	4	4	NUM
ejpam-6803	138	36	and	and	CCONJ
ejpam-6803	138	37	figure	figure	VERB
ejpam-6803	138	38	5	5	NUM
ejpam-6803	138	39	.	.	PUNCT
ejpam-6803	139	1	the	the	DET
ejpam-6803	139	2	similarity	similarity	NOUN
ejpam-6803	139	3	in	in	ADP
ejpam-6803	139	4	the	the	DET
ejpam-6803	139	5	surface	surface	NOUN
ejpam-6803	139	6	plots	plot	NOUN
ejpam-6803	139	7	shows	show	VERB
ejpam-6803	139	8	no	no	DET
ejpam-6803	139	9	visual	visual	ADJ
ejpam-6803	139	10	difference	difference	NOUN
ejpam-6803	139	11	.	.	PUNCT
ejpam-6803	140	1	the	the	DET
ejpam-6803	140	2	associated	associated	ADJ
ejpam-6803	140	3	absolute	absolute	ADJ
ejpam-6803	140	4	error	error	NOUN
ejpam-6803	140	5	surfaces	surface	NOUN
ejpam-6803	140	6	are	be	AUX
ejpam-6803	140	7	shown	show	VERB
ejpam-6803	140	8	in	in	ADP
ejpam-6803	140	9	figure	figure	NOUN
ejpam-6803	140	10	6	6	NUM
ejpam-6803	140	11	,	,	PUNCT
ejpam-6803	140	12	and	and	CCONJ
ejpam-6803	140	13	the	the	DET
ejpam-6803	140	14	error	error	NOUN
ejpam-6803	140	15	is	be	AUX
ejpam-6803	140	16	relatively	relatively	ADV
ejpam-6803	140	17	low	low	ADJ
ejpam-6803	140	18	throughout	throughout	ADP
ejpam-6803	140	19	the	the	DET
ejpam-6803	140	20	entire	entire	ADJ
ejpam-6803	140	21	domain	domain	NOUN
ejpam-6803	140	22	,	,	PUNCT
ejpam-6803	140	23	which	which	PRON
ejpam-6803	140	24	reflected	reflect	VERB
ejpam-6803	140	25	the	the	DET
ejpam-6803	140	26	strong	strong	ADJ
ejpam-6803	140	27	accuracy	accuracy	NOUN
ejpam-6803	140	28	of	of	ADP
ejpam-6803	140	29	the	the	DET
ejpam-6803	140	30	pinn	pinn	NOUN
ejpam-6803	140	31	predictions	prediction	NOUN
ejpam-6803	140	32	in	in	ADP
ejpam-6803	140	33	the	the	DET
ejpam-6803	140	34	overall	overall	NOUN
ejpam-6803	140	35	.	.	PUNCT
ejpam-6803	141	1	figure	figure	VERB
ejpam-6803	141	2	4	4	NUM
ejpam-6803	141	3	:	:	PUNCT
ejpam-6803	141	4	comparison	comparison	NOUN
ejpam-6803	141	5	of	of	ADP
ejpam-6803	141	6	the	the	DET
ejpam-6803	141	7	exact	exact	ADJ
ejpam-6803	141	8	solution	solution	NOUN
ejpam-6803	141	9	and	and	CCONJ
ejpam-6803	141	10	predicted	predict	VERB
ejpam-6803	141	11	solution	solution	NOUN
ejpam-6803	141	12	ϕ(α	ϕ(α	PROPN
ejpam-6803	141	13	,	,	PUNCT
ejpam-6803	141	14	β	β	NOUN
ejpam-6803	141	15	)	)	PUNCT
ejpam-6803	141	16	using	use	VERB
ejpam-6803	141	17	pinn	pinn	PROPN
ejpam-6803	141	18	.	.	PUNCT
ejpam-6803	142	1	a.	a.	PROPN
ejpam-6803	142	2	shafee	shafee	PROPN
ejpam-6803	142	3	et	et	PROPN
ejpam-6803	142	4	al	al	PROPN
ejpam-6803	142	5	.	.	PUNCT
ejpam-6803	142	6	/	/	SYM
ejpam-6803	142	7	eur	eur	PROPN
ejpam-6803	142	8	.	.	PUNCT
ejpam-6803	143	1	j.	j.	PROPN
ejpam-6803	143	2	pure	pure	PROPN
ejpam-6803	143	3	appl	appl	PROPN
ejpam-6803	143	4	.	.	PROPN
ejpam-6803	143	5	math	math	PROPN
ejpam-6803	143	6	,	,	PUNCT
ejpam-6803	143	7	18	18	NUM
ejpam-6803	143	8	(	(	PUNCT
ejpam-6803	143	9	4	4	NUM
ejpam-6803	143	10	)	)	PUNCT
ejpam-6803	143	11	(	(	PUNCT
ejpam-6803	143	12	2025	2025	NUM
ejpam-6803	143	13	)	)	PUNCT
ejpam-6803	143	14	,	,	PUNCT
ejpam-6803	143	15	6803	6803	NUM
ejpam-6803	143	16	10	10	NUM
ejpam-6803	143	17	of	of	ADP
ejpam-6803	143	18	18	18	NUM
ejpam-6803	143	19	figure	figure	NOUN
ejpam-6803	143	20	5	5	NUM
ejpam-6803	143	21	:	:	PUNCT
ejpam-6803	143	22	comparison	comparison	NOUN
ejpam-6803	143	23	of	of	ADP
ejpam-6803	143	24	the	the	DET
ejpam-6803	143	25	exact	exact	ADJ
ejpam-6803	143	26	solution	solution	NOUN
ejpam-6803	143	27	and	and	CCONJ
ejpam-6803	143	28	predicted	predict	VERB
ejpam-6803	143	29	solution	solution	NOUN
ejpam-6803	143	30	ρ(α	ρ(α	NOUN
ejpam-6803	143	31	,	,	PUNCT
ejpam-6803	143	32	β	β	X
ejpam-6803	143	33	)	)	PUNCT
ejpam-6803	143	34	using	use	VERB
ejpam-6803	143	35	pinn	pinn	PROPN
ejpam-6803	143	36	.	.	PUNCT
ejpam-6803	144	1	figure	figure	VERB
ejpam-6803	144	2	6	6	NUM
ejpam-6803	144	3	:	:	PUNCT
ejpam-6803	144	4	absolute	absolute	ADJ
ejpam-6803	144	5	error	error	NOUN
ejpam-6803	144	6	of	of	ADP
ejpam-6803	144	7	ϕ(α	ϕ(α	PROPN
ejpam-6803	144	8	,	,	PUNCT
ejpam-6803	144	9	β	β	NOUN
ejpam-6803	144	10	)	)	PUNCT
ejpam-6803	144	11	and	and	CCONJ
ejpam-6803	144	12	ρ(α	ρ(α	NOUN
ejpam-6803	144	13	,	,	PUNCT
ejpam-6803	144	14	β	β	NOUN
ejpam-6803	144	15	)	)	PUNCT
ejpam-6803	144	16	with	with	ADP
ejpam-6803	144	17	the	the	DET
ejpam-6803	144	18	exact	exact	ADJ
ejpam-6803	144	19	solution	solution	NOUN
ejpam-6803	144	20	.	.	PUNCT
ejpam-6803	145	1	3.3	3.3	NUM
ejpam-6803	145	2	.	.	PUNCT
ejpam-6803	145	3	parametric	parametric	ADJ
ejpam-6803	145	4	study	study	NOUN
ejpam-6803	145	5	for	for	ADP
ejpam-6803	145	6	β	β	PROPN
ejpam-6803	145	7	in	in	ADP
ejpam-6803	145	8	figures	figure	NOUN
ejpam-6803	145	9	7	7	NUM
ejpam-6803	145	10	and	and	CCONJ
ejpam-6803	145	11	8	8	NUM
ejpam-6803	145	12	solution	solution	NOUN
ejpam-6803	145	13	curves	curve	NOUN
ejpam-6803	145	14	for	for	ADP
ejpam-6803	145	15	various	various	ADJ
ejpam-6803	145	16	β	β	X
ejpam-6803	145	17	illustrate	illustrate	VERB
ejpam-6803	145	18	the	the	DET
ejpam-6803	145	19	capability	capability	NOUN
ejpam-6803	145	20	of	of	ADP
ejpam-6803	145	21	the	the	DET
ejpam-6803	145	22	proposed	propose	VERB
ejpam-6803	145	23	model	model	NOUN
ejpam-6803	145	24	to	to	PART
ejpam-6803	145	25	describe	describe	VERB
ejpam-6803	145	26	diverse	diverse	ADJ
ejpam-6803	145	27	dynamical	dynamical	ADJ
ejpam-6803	145	28	phenomena	phenomenon	NOUN
ejpam-6803	145	29	depending	depend	VERB
ejpam-6803	145	30	on	on	ADP
ejpam-6803	145	31	the	the	DET
ejpam-6803	145	32	nonlinear	nonlinear	ADJ
ejpam-6803	145	33	dispersion	dispersion	NOUN
ejpam-6803	145	34	for	for	ADP
ejpam-6803	145	35	ϕ(α	ϕ(α	PROPN
ejpam-6803	145	36	,	,	PUNCT
ejpam-6803	145	37	β	β	NOUN
ejpam-6803	145	38	)	)	PUNCT
ejpam-6803	145	39	and	and	CCONJ
ejpam-6803	145	40	ρ(α	ρ(α	NOUN
ejpam-6803	145	41	,	,	PUNCT
ejpam-6803	145	42	β	β	NOUN
ejpam-6803	145	43	)	)	PUNCT
ejpam-6803	145	44	.	.	PUNCT
ejpam-6803	146	1	the	the	DET
ejpam-6803	146	2	pinn	pinn	NOUN
ejpam-6803	146	3	also	also	ADV
ejpam-6803	146	4	closely	closely	ADV
ejpam-6803	146	5	follows	follow	VERB
ejpam-6803	146	6	all	all	DET
ejpam-6803	146	7	configurations	configuration	NOUN
ejpam-6803	146	8	while	while	SCONJ
ejpam-6803	146	9	maintaining	maintain	VERB
ejpam-6803	146	10	the	the	DET
ejpam-6803	146	11	general	general	ADJ
ejpam-6803	146	12	structure	structure	NOUN
ejpam-6803	146	13	and	and	CCONJ
ejpam-6803	146	14	stability	stability	NOUN
ejpam-6803	146	15	of	of	ADP
ejpam-6803	146	16	the	the	DET
ejpam-6803	146	17	solution	solution	NOUN
ejpam-6803	146	18	.	.	PUNCT
ejpam-6803	147	1	the	the	DET
ejpam-6803	147	2	absolute	absolute	ADJ
ejpam-6803	147	3	error	error	NOUN
ejpam-6803	147	4	among	among	ADP
ejpam-6803	147	5	these	these	DET
ejpam-6803	147	6	values	value	NOUN
ejpam-6803	147	7	of	of	ADP
ejpam-6803	147	8	β	β	PROPN
ejpam-6803	147	9	are	be	AUX
ejpam-6803	147	10	compared	compare	VERB
ejpam-6803	147	11	on	on	ADP
ejpam-6803	147	12	a	a	DET
ejpam-6803	147	13	bar	bar	NOUN
ejpam-6803	147	14	graph	graph	NOUN
ejpam-6803	147	15	in	in	ADP
ejpam-6803	147	16	figure	figure	NOUN
ejpam-6803	147	17	9	9	NUM
ejpam-6803	147	18	and	and	CCONJ
ejpam-6803	147	19	in	in	ADP
ejpam-6803	147	20	figure	figure	NOUN
ejpam-6803	147	21	10	10	NUM
ejpam-6803	147	22	.	.	PUNCT
ejpam-6803	148	1	while	while	SCONJ
ejpam-6803	148	2	some	some	DET
ejpam-6803	148	3	degree	degree	NOUN
ejpam-6803	148	4	of	of	ADP
ejpam-6803	148	5	variation	variation	NOUN
ejpam-6803	148	6	in	in	ADP
ejpam-6803	148	7	the	the	DET
ejpam-6803	148	8	amount	amount	NOUN
ejpam-6803	148	9	of	of	ADP
ejpam-6803	148	10	error	error	NOUN
ejpam-6803	148	11	is	be	AUX
ejpam-6803	148	12	evident	evident	ADJ
ejpam-6803	148	13	,	,	PUNCT
ejpam-6803	148	14	all	all	DET
ejpam-6803	148	15	output	output	NOUN
ejpam-6803	148	16	samples	sample	NOUN
ejpam-6803	148	17	show	show	VERB
ejpam-6803	148	18	acceptable	acceptable	ADJ
ejpam-6803	148	19	error	error	NOUN
ejpam-6803	148	20	values	value	NOUN
ejpam-6803	148	21	.	.	PUNCT
ejpam-6803	149	1	the	the	DET
ejpam-6803	149	2	robustness	robustness	NOUN
ejpam-6803	149	3	of	of	ADP
ejpam-6803	149	4	the	the	DET
ejpam-6803	149	5	model	model	NOUN
ejpam-6803	149	6	is	be	AUX
ejpam-6803	149	7	confirmed	confirm	VERB
ejpam-6803	149	8	by	by	ADP
ejpam-6803	149	9	its	its	PRON
ejpam-6803	149	10	consistent	consistent	ADJ
ejpam-6803	149	11	performance	performance	NOUN
ejpam-6803	149	12	across	across	ADP
ejpam-6803	149	13	values	value	NOUN
ejpam-6803	149	14	.	.	PUNCT
ejpam-6803	150	1	continuing	continue	VERB
ejpam-6803	150	2	to	to	PART
ejpam-6803	150	3	achieve	achieve	VERB
ejpam-6803	150	4	low	low	ADJ
ejpam-6803	150	5	errors	error	NOUN
ejpam-6803	150	6	in	in	ADP
ejpam-6803	150	7	the	the	DET
ejpam-6803	150	8	presence	presence	NOUN
ejpam-6803	150	9	of	of	ADP
ejpam-6803	150	10	varying	vary	VERB
ejpam-6803	150	11	nonlinear	nonlinear	ADJ
ejpam-6803	150	12	characteristics	characteristic	NOUN
ejpam-6803	150	13	provides	provide	VERB
ejpam-6803	150	14	further	further	ADJ
ejpam-6803	150	15	evidence	evidence	NOUN
ejpam-6803	150	16	to	to	ADP
ejpam-6803	150	17	the	the	DET
ejpam-6803	150	18	utility	utility	NOUN
ejpam-6803	150	19	of	of	ADP
ejpam-6803	150	20	the	the	DET
ejpam-6803	150	21	pinn	pinn	NOUN
ejpam-6803	150	22	approach	approach	NOUN
ejpam-6803	150	23	to	to	ADP
ejpam-6803	150	24	parameterized	parameterized	ADJ
ejpam-6803	150	25	pde	pde	NOUN
ejpam-6803	150	26	systems	system	NOUN
ejpam-6803	150	27	.	.	PUNCT
ejpam-6803	151	1	a.	a.	PROPN
ejpam-6803	151	2	shafee	shafee	PROPN
ejpam-6803	151	3	et	et	PROPN
ejpam-6803	151	4	al	al	PROPN
ejpam-6803	151	5	.	.	PUNCT
ejpam-6803	151	6	/	/	SYM
ejpam-6803	151	7	eur	eur	PROPN
ejpam-6803	151	8	.	.	PUNCT
ejpam-6803	152	1	j.	j.	PROPN
ejpam-6803	152	2	pure	pure	PROPN
ejpam-6803	152	3	appl	appl	PROPN
ejpam-6803	152	4	.	.	PROPN
ejpam-6803	152	5	math	math	PROPN
ejpam-6803	152	6	,	,	PUNCT
ejpam-6803	152	7	18	18	NUM
ejpam-6803	152	8	(	(	PUNCT
ejpam-6803	152	9	4	4	NUM
ejpam-6803	152	10	)	)	PUNCT
ejpam-6803	152	11	(	(	PUNCT
ejpam-6803	152	12	2025	2025	NUM
ejpam-6803	152	13	)	)	PUNCT
ejpam-6803	152	14	,	,	PUNCT
ejpam-6803	152	15	6803	6803	NUM
ejpam-6803	152	16	11	11	NUM
ejpam-6803	152	17	of	of	ADP
ejpam-6803	152	18	18	18	NUM
ejpam-6803	152	19	figure	figure	NOUN
ejpam-6803	152	20	7	7	NUM
ejpam-6803	152	21	:	:	PUNCT
ejpam-6803	152	22	exact	exact	ADJ
ejpam-6803	152	23	solution	solution	NOUN
ejpam-6803	152	24	and	and	CCONJ
ejpam-6803	152	25	pinn	pinn	NOUN
ejpam-6803	152	26	solution	solution	NOUN
ejpam-6803	152	27	ϕ(α	ϕ(α	PROPN
ejpam-6803	152	28	,	,	PUNCT
ejpam-6803	152	29	β	β	NOUN
ejpam-6803	152	30	)	)	PUNCT
ejpam-6803	152	31	at	at	ADP
ejpam-6803	152	32	specific	specific	ADJ
ejpam-6803	152	33	time	time	NOUN
ejpam-6803	152	34	values	value	NOUN
ejpam-6803	152	35	.	.	PUNCT
ejpam-6803	153	1	figure	figure	VERB
ejpam-6803	153	2	8	8	NUM
ejpam-6803	153	3	:	:	PUNCT
ejpam-6803	153	4	exact	exact	ADJ
ejpam-6803	153	5	solution	solution	NOUN
ejpam-6803	153	6	and	and	CCONJ
ejpam-6803	153	7	pinn	pinn	NOUN
ejpam-6803	153	8	solution	solution	NOUN
ejpam-6803	153	9	ρ(α	ρ(α	NOUN
ejpam-6803	153	10	,	,	PUNCT
ejpam-6803	153	11	β	β	NOUN
ejpam-6803	153	12	)	)	PUNCT
ejpam-6803	153	13	at	at	ADP
ejpam-6803	153	14	specific	specific	ADJ
ejpam-6803	153	15	time	time	NOUN
ejpam-6803	153	16	values	value	NOUN
ejpam-6803	153	17	.	.	PUNCT
ejpam-6803	154	1	a.	a.	NOUN
ejpam-6803	154	2	shafee	shafee	PROPN
ejpam-6803	154	3	et	et	PROPN
ejpam-6803	154	4	al	al	PROPN
ejpam-6803	154	5	.	.	PUNCT
ejpam-6803	154	6	/	/	SYM
ejpam-6803	154	7	eur	eur	PROPN
ejpam-6803	154	8	.	.	PUNCT
ejpam-6803	155	1	j.	j.	PROPN
ejpam-6803	155	2	pure	pure	PROPN
ejpam-6803	155	3	appl	appl	PROPN
ejpam-6803	155	4	.	.	PROPN
ejpam-6803	155	5	math	math	PROPN
ejpam-6803	155	6	,	,	PUNCT
ejpam-6803	155	7	18	18	NUM
ejpam-6803	155	8	(	(	PUNCT
ejpam-6803	155	9	4	4	NUM
ejpam-6803	155	10	)	)	PUNCT
ejpam-6803	155	11	(	(	PUNCT
ejpam-6803	155	12	2025	2025	NUM
ejpam-6803	155	13	)	)	PUNCT
ejpam-6803	155	14	,	,	PUNCT
ejpam-6803	155	15	6803	6803	NUM
ejpam-6803	155	16	12	12	NUM
ejpam-6803	155	17	of	of	ADP
ejpam-6803	155	18	18	18	NUM
ejpam-6803	155	19	figure	figure	NOUN
ejpam-6803	155	20	9	9	NUM
ejpam-6803	155	21	:	:	PUNCT
ejpam-6803	155	22	absolute	absolute	ADJ
ejpam-6803	155	23	error	error	NOUN
ejpam-6803	155	24	of	of	ADP
ejpam-6803	155	25	ϕ(α	ϕ(α	PROPN
ejpam-6803	155	26	,	,	PUNCT
ejpam-6803	155	27	β	β	NOUN
ejpam-6803	155	28	)	)	PUNCT
ejpam-6803	155	29	for	for	ADP
ejpam-6803	155	30	different	different	ADJ
ejpam-6803	155	31	time	time	NOUN
ejpam-6803	155	32	values	value	NOUN
ejpam-6803	155	33	.	.	PUNCT
ejpam-6803	156	1	figure	figure	VERB
ejpam-6803	156	2	10	10	NUM
ejpam-6803	156	3	:	:	PUNCT
ejpam-6803	156	4	absolute	absolute	ADJ
ejpam-6803	156	5	error	error	NOUN
ejpam-6803	156	6	of	of	ADP
ejpam-6803	156	7	ρ(α	ρ(α	NOUN
ejpam-6803	156	8	,	,	PUNCT
ejpam-6803	156	9	β	β	NOUN
ejpam-6803	156	10	)	)	PUNCT
ejpam-6803	156	11	for	for	ADP
ejpam-6803	156	12	different	different	ADJ
ejpam-6803	156	13	time	time	NOUN
ejpam-6803	156	14	values	value	NOUN
ejpam-6803	156	15	.	.	PUNCT
ejpam-6803	157	1	table	table	NOUN
ejpam-6803	157	2	2	2	NUM
ejpam-6803	157	3	:	:	PUNCT
ejpam-6803	157	4	l2	l2	NOUN
ejpam-6803	157	5	and	and	CCONJ
ejpam-6803	157	6	l∞	l∞	NOUN
ejpam-6803	157	7	error	error	NOUN
ejpam-6803	157	8	norms	norm	NOUN
ejpam-6803	157	9	for	for	ADP
ejpam-6803	157	10	ϕ	ϕ	NOUN
ejpam-6803	157	11	and	and	CCONJ
ejpam-6803	157	12	ρ	ρ	PROPN
ejpam-6803	157	13	,	,	PUNCT
ejpam-6803	157	14	with	with	ADP
ejpam-6803	157	15	comparison	comparison	NOUN
ejpam-6803	157	16	to	to	ADP
ejpam-6803	157	17	a	a	DET
ejpam-6803	157	18	finite	finite	ADJ
ejpam-6803	157	19	difference	difference	NOUN
ejpam-6803	157	20	(	(	PUNCT
ejpam-6803	157	21	fd	fd	NOUN
ejpam-6803	157	22	)	)	PUNCT
ejpam-6803	157	23	baseline	baseline	NOUN
ejpam-6803	157	24	.	.	PUNCT
ejpam-6803	158	1	pinn	pinn	PROPN
ejpam-6803	158	2	fd	fd	PROPN
ejpam-6803	158	3	baseline	baseline	PROPN
ejpam-6803	158	4	l2	l2	PROPN
ejpam-6803	158	5	l∞	l∞	NOUN
ejpam-6803	158	6	l2	l2	NOUN
ejpam-6803	158	7	l∞	l∞	NOUN
ejpam-6803	158	8	ϕ	ϕ	PROPN
ejpam-6803	158	9	1.21×	1.21×	NUM
ejpam-6803	158	10	10−3	10−3	NUM
ejpam-6803	158	11	2.29×	2.29×	NUM
ejpam-6803	158	12	10−3	10−3	NUM
ejpam-6803	158	13	8.74×	8.74×	NUM
ejpam-6803	158	14	10−4	10−4	NUM
ejpam-6803	158	15	1.95×	1.95×	NUM
ejpam-6803	158	16	10−3	10−3	NUM
ejpam-6803	158	17	ρ	ρ	PROPN
ejpam-6803	158	18	4.84×	4.84×	NUM
ejpam-6803	158	19	10−3	10−3	NUM
ejpam-6803	158	20	9.09×	9.09×	NUM
ejpam-6803	158	21	10−3	10−3	NUM
ejpam-6803	158	22	3.97×	3.97×	NUM
ejpam-6803	158	23	10−3	10−3	NUM
ejpam-6803	158	24	7.82×	7.82×	NUM
ejpam-6803	158	25	10−3	10−3	NUM
ejpam-6803	158	26	table	table	NOUN
ejpam-6803	158	27	2	2	NUM
ejpam-6803	158	28	reports	report	VERB
ejpam-6803	158	29	the	the	DET
ejpam-6803	158	30	l2	l2	NOUN
ejpam-6803	158	31	and	and	CCONJ
ejpam-6803	158	32	l∞	l∞	NOUN
ejpam-6803	158	33	error	error	NOUN
ejpam-6803	158	34	norms	norm	NOUN
ejpam-6803	158	35	for	for	ADP
ejpam-6803	158	36	the	the	DET
ejpam-6803	158	37	predicted	predict	VERB
ejpam-6803	158	38	variables	variables	PROPN
ejpam-6803	158	39	ϕ	ϕ	PROPN
ejpam-6803	158	40	and	and	CCONJ
ejpam-6803	158	41	ρ	ρ	PROPN
ejpam-6803	158	42	,	,	PUNCT
ejpam-6803	158	43	a.	a.	NOUN
ejpam-6803	158	44	shafee	shafee	PROPN
ejpam-6803	158	45	et	et	PROPN
ejpam-6803	158	46	al	al	PROPN
ejpam-6803	158	47	.	.	PUNCT
ejpam-6803	158	48	/	/	SYM
ejpam-6803	158	49	eur	eur	PROPN
ejpam-6803	158	50	.	.	PUNCT
ejpam-6803	159	1	j.	j.	PROPN
ejpam-6803	159	2	pure	pure	PROPN
ejpam-6803	159	3	appl	appl	PROPN
ejpam-6803	159	4	.	.	PROPN
ejpam-6803	159	5	math	math	PROPN
ejpam-6803	159	6	,	,	PUNCT
ejpam-6803	159	7	18	18	NUM
ejpam-6803	159	8	(	(	PUNCT
ejpam-6803	159	9	4	4	NUM
ejpam-6803	159	10	)	)	PUNCT
ejpam-6803	159	11	(	(	PUNCT
ejpam-6803	159	12	2025	2025	NUM
ejpam-6803	159	13	)	)	PUNCT
ejpam-6803	159	14	,	,	PUNCT
ejpam-6803	159	15	6803	6803	NUM
ejpam-6803	159	16	13	13	NUM
ejpam-6803	159	17	of	of	ADP
ejpam-6803	159	18	18	18	NUM
ejpam-6803	159	19	evaluated	evaluate	VERB
ejpam-6803	159	20	over	over	ADP
ejpam-6803	159	21	a	a	DET
ejpam-6803	159	22	uniform	uniform	ADJ
ejpam-6803	159	23	256×	256×	NOUN
ejpam-6803	159	24	256	256	NUM
ejpam-6803	159	25	grid	grid	NOUN
ejpam-6803	159	26	on	on	ADP
ejpam-6803	159	27	the	the	DET
ejpam-6803	159	28	domain	domain	NOUN
ejpam-6803	159	29	ω	ω	NOUN
ejpam-6803	159	30	=	=	PUNCT
ejpam-6803	160	1	[	[	X
ejpam-6803	160	2	0	0	NUM
ejpam-6803	160	3	,	,	PUNCT
ejpam-6803	160	4	1]×	1]×	NUM
ejpam-6803	160	5	[	[	X
ejpam-6803	160	6	0	0	NUM
ejpam-6803	160	7	,	,	PUNCT
ejpam-6803	160	8	1	1	NUM
ejpam-6803	160	9	]	]	PUNCT
ejpam-6803	160	10	.	.	PUNCT
ejpam-6803	161	1	the	the	DET
ejpam-6803	161	2	errors	error	NOUN
ejpam-6803	161	3	were	be	AUX
ejpam-6803	161	4	computed	compute	VERB
ejpam-6803	161	5	by	by	ADP
ejpam-6803	161	6	comparing	compare	VERB
ejpam-6803	161	7	the	the	DET
ejpam-6803	161	8	pinn	pinn	NOUN
ejpam-6803	161	9	solution	solution	NOUN
ejpam-6803	161	10	against	against	ADP
ejpam-6803	161	11	a	a	DET
ejpam-6803	161	12	high	high	ADJ
ejpam-6803	161	13	-	-	PUNCT
ejpam-6803	161	14	fidelity	fidelity	NOUN
ejpam-6803	161	15	finite	finite	ADJ
ejpam-6803	161	16	difference	difference	NOUN
ejpam-6803	161	17	(	(	PUNCT
ejpam-6803	161	18	fd	fd	NOUN
ejpam-6803	161	19	)	)	PUNCT
ejpam-6803	161	20	reference	reference	NOUN
ejpam-6803	161	21	solution	solution	NOUN
ejpam-6803	161	22	under	under	ADP
ejpam-6803	161	23	the	the	DET
ejpam-6803	161	24	same	same	ADJ
ejpam-6803	161	25	setup	setup	NOUN
ejpam-6803	161	26	.	.	PUNCT
ejpam-6803	162	1	the	the	DET
ejpam-6803	162	2	results	result	NOUN
ejpam-6803	162	3	demonstrate	demonstrate	VERB
ejpam-6803	162	4	that	that	SCONJ
ejpam-6803	162	5	the	the	DET
ejpam-6803	162	6	proposed	propose	VERB
ejpam-6803	162	7	pinn	pinn	NOUN
ejpam-6803	162	8	achieves	achieve	VERB
ejpam-6803	162	9	low	low	ADJ
ejpam-6803	162	10	error	error	NOUN
ejpam-6803	162	11	magnitudes	magnitude	NOUN
ejpam-6803	162	12	,	,	PUNCT
ejpam-6803	162	13	comparable	comparable	ADJ
ejpam-6803	162	14	to	to	ADP
ejpam-6803	162	15	the	the	DET
ejpam-6803	162	16	baseline	baseline	NOUN
ejpam-6803	162	17	solver	solver	NOUN
ejpam-6803	162	18	,	,	PUNCT
ejpam-6803	162	19	confirming	confirm	VERB
ejpam-6803	162	20	its	its	PRON
ejpam-6803	162	21	accuracy	accuracy	NOUN
ejpam-6803	162	22	and	and	CCONJ
ejpam-6803	162	23	reliability	reliability	NOUN
ejpam-6803	162	24	.	.	PUNCT
ejpam-6803	163	1	despite	despite	SCONJ
ejpam-6803	163	2	the	the	DET
ejpam-6803	163	3	empirical	empirical	ADJ
ejpam-6803	163	4	outcomes	outcome	NOUN
ejpam-6803	163	5	that	that	PRON
ejpam-6803	163	6	prove	prove	VERB
ejpam-6803	163	7	the	the	DET
ejpam-6803	163	8	stability	stability	NOUN
ejpam-6803	163	9	and	and	CCONJ
ejpam-6803	163	10	accuracy	accuracy	NOUN
ejpam-6803	163	11	of	of	ADP
ejpam-6803	163	12	the	the	DET
ejpam-6803	163	13	proposed	propose	VERB
ejpam-6803	163	14	pinn	pinn	NOUN
ejpam-6803	163	15	framework	framework	NOUN
ejpam-6803	163	16	,	,	PUNCT
ejpam-6803	163	17	a	a	DET
ejpam-6803	163	18	rigorous	rigorous	ADJ
ejpam-6803	163	19	theoretical	theoretical	ADJ
ejpam-6803	163	20	convergence	convergence	NOUN
ejpam-6803	163	21	proof	proof	NOUN
ejpam-6803	163	22	of	of	ADP
ejpam-6803	163	23	pinns	pinns	ADJ
ejpam-6803	163	24	is	be	AUX
ejpam-6803	163	25	still	still	ADV
ejpam-6803	163	26	an	an	DET
ejpam-6803	163	27	open	open	ADJ
ejpam-6803	163	28	problem	problem	NOUN
ejpam-6803	163	29	.	.	PUNCT
ejpam-6803	164	1	this	this	DET
ejpam-6803	164	2	challenge	challenge	NOUN
ejpam-6803	164	3	is	be	AUX
ejpam-6803	164	4	due	due	ADJ
ejpam-6803	164	5	to	to	ADP
ejpam-6803	164	6	the	the	DET
ejpam-6803	164	7	fact	fact	NOUN
ejpam-6803	164	8	that	that	SCONJ
ejpam-6803	164	9	the	the	DET
ejpam-6803	164	10	training	training	NOUN
ejpam-6803	164	11	process	process	NOUN
ejpam-6803	164	12	integrates	integrate	VERB
ejpam-6803	164	13	dynamics	dynamic	NOUN
ejpam-6803	164	14	of	of	ADP
ejpam-6803	164	15	optimization	optimization	NOUN
ejpam-6803	164	16	,	,	PUNCT
ejpam-6803	164	17	automatic	automatic	ADJ
ejpam-6803	164	18	differentiation	differentiation	NOUN
ejpam-6803	164	19	and	and	CCONJ
ejpam-6803	164	20	nonlinear	nonlinear	ADJ
ejpam-6803	164	21	activation	activation	NOUN
ejpam-6803	164	22	functions	function	NOUN
ejpam-6803	164	23	and	and	CCONJ
ejpam-6803	164	24	makes	make	VERB
ejpam-6803	164	25	it	it	PRON
ejpam-6803	164	26	difficult	difficult	ADJ
ejpam-6803	164	27	to	to	PART
ejpam-6803	164	28	derive	derive	VERB
ejpam-6803	164	29	explicit	explicit	ADJ
ejpam-6803	164	30	error	error	NOUN
ejpam-6803	164	31	bounds	bound	NOUN
ejpam-6803	164	32	.	.	PUNCT
ejpam-6803	165	1	a	a	DET
ejpam-6803	165	2	number	number	NOUN
ejpam-6803	165	3	of	of	ADP
ejpam-6803	165	4	recent	recent	ADJ
ejpam-6803	165	5	works	work	NOUN
ejpam-6803	165	6	have	have	AUX
ejpam-6803	165	7	tried	try	VERB
ejpam-6803	165	8	to	to	PART
ejpam-6803	165	9	derive	derive	VERB
ejpam-6803	165	10	preliminary	preliminary	ADJ
ejpam-6803	165	11	convergence	convergence	NOUN
ejpam-6803	165	12	results	result	NOUN
ejpam-6803	165	13	under	under	ADP
ejpam-6803	165	14	simplified	simplified	ADJ
ejpam-6803	165	15	models	model	NOUN
ejpam-6803	165	16	,	,	PUNCT
ejpam-6803	165	17	but	but	CCONJ
ejpam-6803	165	18	no	no	DET
ejpam-6803	165	19	general	general	ADJ
ejpam-6803	165	20	theory	theory	NOUN
ejpam-6803	165	21	exists	exist	VERB
ejpam-6803	165	22	.	.	PUNCT
ejpam-6803	166	1	our	our	PRON
ejpam-6803	166	2	results	result	NOUN
ejpam-6803	166	3	play	play	VERB
ejpam-6803	166	4	a	a	DET
ejpam-6803	166	5	part	part	NOUN
ejpam-6803	166	6	in	in	ADP
ejpam-6803	166	7	this	this	DET
ejpam-6803	166	8	continuing	continue	VERB
ejpam-6803	166	9	debate	debate	NOUN
ejpam-6803	166	10	by	by	ADP
ejpam-6803	166	11	providing	provide	VERB
ejpam-6803	166	12	empirical	empirical	ADJ
ejpam-6803	166	13	evidence	evidence	NOUN
ejpam-6803	166	14	of	of	ADP
ejpam-6803	166	15	convergence	convergence	NOUN
ejpam-6803	166	16	in	in	ADP
ejpam-6803	166	17	the	the	DET
ejpam-6803	166	18	form	form	NOUN
ejpam-6803	166	19	of	of	ADP
ejpam-6803	166	20	loss	loss	NOUN
ejpam-6803	166	21	function	function	NOUN
ejpam-6803	166	22	decay	decay	NOUN
ejpam-6803	166	23	,	,	PUNCT
ejpam-6803	166	24	error	error	NOUN
ejpam-6803	166	25	distributions	distribution	NOUN
ejpam-6803	166	26	and	and	CCONJ
ejpam-6803	166	27	comparisons	comparison	NOUN
ejpam-6803	166	28	with	with	ADP
ejpam-6803	166	29	exact	exact	ADJ
ejpam-6803	166	30	solutions	solution	NOUN
ejpam-6803	166	31	which	which	PRON
ejpam-6803	166	32	offer	offer	VERB
ejpam-6803	166	33	a	a	DET
ejpam-6803	166	34	practical	practical	ADJ
ejpam-6803	166	35	insight	insight	NOUN
ejpam-6803	166	36	to	to	ADP
ejpam-6803	166	37	the	the	DET
ejpam-6803	166	38	pinn	pinn	NOUN
ejpam-6803	166	39	convergence	convergence	NOUN
ejpam-6803	166	40	behavior	behavior	NOUN
ejpam-6803	166	41	.	.	PUNCT
ejpam-6803	167	1	we	we	PRON
ejpam-6803	167	2	summarize	summarize	VERB
ejpam-6803	167	3	the	the	DET
ejpam-6803	167	4	results	result	NOUN
ejpam-6803	167	5	for	for	ADP
ejpam-6803	167	6	different	different	ADJ
ejpam-6803	167	7	β	β	NOUN
ejpam-6803	167	8	in	in	ADP
ejpam-6803	167	9	table	table	NOUN
ejpam-6803	167	10	3	3	NUM
ejpam-6803	167	11	and	and	CCONJ
ejpam-6803	167	12	compare	compare	VERB
ejpam-6803	167	13	the	the	DET
ejpam-6803	167	14	exact	exact	ADJ
ejpam-6803	167	15	and	and	CCONJ
ejpam-6803	167	16	predicted	predict	VERB
ejpam-6803	167	17	results	result	NOUN
ejpam-6803	167	18	as	as	ADV
ejpam-6803	167	19	well	well	ADV
ejpam-6803	167	20	as	as	ADP
ejpam-6803	167	21	the	the	DET
ejpam-6803	167	22	absolute	absolute	ADJ
ejpam-6803	167	23	errors	error	NOUN
ejpam-6803	167	24	.	.	PUNCT
ejpam-6803	168	1	this	this	PRON
ejpam-6803	168	2	is	be	AUX
ejpam-6803	168	3	conducive	conducive	ADJ
ejpam-6803	168	4	to	to	ADP
ejpam-6803	168	5	the	the	DET
ejpam-6803	168	6	generalization	generalization	NOUN
ejpam-6803	168	7	ability	ability	NOUN
ejpam-6803	168	8	and	and	CCONJ
ejpam-6803	168	9	the	the	DET
ejpam-6803	168	10	performance	performance	NOUN
ejpam-6803	168	11	stability	stability	NOUN
ejpam-6803	168	12	of	of	ADP
ejpam-6803	168	13	the	the	DET
ejpam-6803	168	14	model	model	NOUN
ejpam-6803	168	15	.	.	PUNCT
ejpam-6803	169	1	a.	a.	PROPN
ejpam-6803	169	2	shafee	shafee	PROPN
ejpam-6803	169	3	et	et	PROPN
ejpam-6803	169	4	al	al	PROPN
ejpam-6803	169	5	.	.	PUNCT
ejpam-6803	169	6	/	/	SYM
ejpam-6803	169	7	eur	eur	PROPN
ejpam-6803	169	8	.	.	PUNCT
ejpam-6803	170	1	j.	j.	PROPN
ejpam-6803	170	2	pure	pure	PROPN
ejpam-6803	170	3	appl	appl	PROPN
ejpam-6803	170	4	.	.	PROPN
ejpam-6803	170	5	math	math	PROPN
ejpam-6803	170	6	,	,	PUNCT
ejpam-6803	170	7	18	18	NUM
ejpam-6803	170	8	(	(	PUNCT
ejpam-6803	170	9	4	4	NUM
ejpam-6803	170	10	)	)	PUNCT
ejpam-6803	170	11	(	(	PUNCT
ejpam-6803	170	12	2025	2025	NUM
ejpam-6803	170	13	)	)	PUNCT
ejpam-6803	170	14	,	,	PUNCT
ejpam-6803	170	15	6803	6803	NUM
ejpam-6803	170	16	14	14	NUM
ejpam-6803	170	17	of	of	ADP
ejpam-6803	170	18	18	18	NUM
ejpam-6803	170	19	table	table	NOUN
ejpam-6803	170	20	3	3	NUM
ejpam-6803	170	21	:	:	PUNCT
ejpam-6803	170	22	comparison	comparison	NOUN
ejpam-6803	170	23	of	of	ADP
ejpam-6803	170	24	exact	exact	ADJ
ejpam-6803	170	25	and	and	CCONJ
ejpam-6803	170	26	pinn	pinn	NOUN
ejpam-6803	170	27	solutions	solution	NOUN
ejpam-6803	170	28	for	for	ADP
ejpam-6803	170	29	ϕ	ϕ	PROPN
ejpam-6803	170	30	and	and	CCONJ
ejpam-6803	170	31	ρ	ρ	NOUN
ejpam-6803	170	32	with	with	ADP
ejpam-6803	170	33	errors	error	NOUN
ejpam-6803	170	34	.	.	PUNCT
ejpam-6803	171	1	β	β	X
ejpam-6803	171	2	α	α	X
ejpam-6803	171	3	ϕ	ϕ	PROPN
ejpam-6803	171	4	ρ	ρ	PROPN
ejpam-6803	171	5	exact	exact	ADJ
ejpam-6803	171	6	pinn	pinn	NOUN
ejpam-6803	171	7	error	error	NOUN
ejpam-6803	171	8	exact	exact	NOUN
ejpam-6803	171	9	pinn	pinn	NOUN
ejpam-6803	171	10	error	error	NOUN
ejpam-6803	171	11	0.25	0.25	NUM
ejpam-6803	171	12	-2	-2	NOUN
ejpam-6803	171	13	0.190699	0.190699	NUM
ejpam-6803	171	14	0.191580	0.191580	NUM
ejpam-6803	171	15	8.81e-4	8.81e-4	NOUN
ejpam-6803	171	16	0.172516	0.172516	NUM
ejpam-6803	171	17	0.167016	0.167016	NUM
ejpam-6803	171	18	5.50e-3	5.50e-3	NUM
ejpam-6803	171	19	-1	-1	NOUN
ejpam-6803	172	1	0.445400	0.445400	NUM
ejpam-6803	172	2	0.444955	0.444955	NUM
ejpam-6803	172	3	4.45e-4	4.45e-4	NOUN
ejpam-6803	172	4	0.346210	0.346210	NUM
ejpam-6803	172	5	0.342708	0.342708	NUM
ejpam-6803	172	6	3.50e-3	3.50e-3	NUM
ejpam-6803	172	7	0	0	NUM
ejpam-6803	172	8	0.875647	0.875647	NUM
ejpam-6803	172	9	0.875647	0.875647	NUM
ejpam-6803	172	10	0.00e0	0.00e0	NUM
ejpam-6803	172	11	0.492268	0.492268	NUM
ejpam-6803	172	12	0.500683	0.500683	NUM
ejpam-6803	172	13	8.42e-3	8.42e-3	NUM
ejpam-6803	172	14	1	1	NUM
ejpam-6803	172	15	1.358357	1.358357	NUM
ejpam-6803	172	16	1.358802	1.358802	NUM
ejpam-6803	172	17	4.45e-4	4.45e-4	NOUN
ejpam-6803	172	18	0.435790	0.435790	NUM
ejpam-6803	172	19	0.432288	0.432288	NUM
ejpam-6803	172	20	3.50e-3	3.50e-3	NUM
ejpam-6803	172	21	2	2	NUM
ejpam-6803	172	22	1.703906	1.703906	NUM
ejpam-6803	172	23	1.703025	1.703025	NUM
ejpam-6803	172	24	8.81e-4	8.81e-4	NOUN
ejpam-6803	172	25	0.252258	0.252258	NUM
ejpam-6803	172	26	0.246758	0.246758	NUM
ejpam-6803	172	27	5.50e-3	5.50e-3	NUM
ejpam-6803	172	28	0.50	0.50	NUM
ejpam-6803	172	29	-2	-2	NOUN
ejpam-6803	173	1	0.151716	0.151716	NUM
ejpam-6803	173	2	0.149478	0.149478	NUM
ejpam-6803	173	3	2.24e-3	2.24e-3	NUM
ejpam-6803	173	4	0.140207	0.140207	NUM
ejpam-6803	173	5	0.134264	0.134264	NUM
ejpam-6803	173	6	5.94e-3	5.94e-3	NUM
ejpam-6803	173	7	-1	-1	SYM
ejpam-6803	173	8	0.364851	0.364851	NUM
ejpam-6803	173	9	0.365982	0.365982	NUM
ejpam-6803	173	10	1.13e-3	1.13e-3	NUM
ejpam-6803	173	11	0.298293	0.298293	NUM
ejpam-6803	173	12	0.294509	0.294509	NUM
ejpam-6803	173	13	3.78e-3	3.78e-3	NUM
ejpam-6803	173	14	0	0	NUM
ejpam-6803	174	1	0.755081	0.755081	NUM
ejpam-6803	174	2	0.755081	0.755081	NUM
ejpam-6803	174	3	0.00e0	0.00e0	NUM
ejpam-6803	174	4	0.470007	0.470007	NUM
ejpam-6803	174	5	0.479100	0.479100	NUM
ejpam-6803	174	6	9.09e-3	9.09e-3	NUM
ejpam-6803	174	7	1	1	NUM
ejpam-6803	174	8	1.244919	1.244919	NUM
ejpam-6803	174	9	1.243788	1.243788	NUM
ejpam-6803	174	10	1.13e-3	1.13e-3	NUM
ejpam-6803	174	11	0.470007	0.470007	NUM
ejpam-6803	174	12	0.466223	0.466223	NUM
ejpam-6803	174	13	3.78e-3	3.78e-3	NUM
ejpam-6803	174	14	2	2	NUM
ejpam-6803	174	15	1.635149	1.635149	NUM
ejpam-6803	174	16	1.637387	1.637387	NUM
ejpam-6803	174	17	2.24e-3	2.24e-3	NUM
ejpam-6803	174	18	0.298293	0.298293	NUM
ejpam-6803	174	19	0.292349	0.292349	NUM
ejpam-6803	174	20	5.94e-3	5.94e-3	NUM
ejpam-6803	174	21	0.75	0.75	NUM
ejpam-6803	174	22	-2	-2	NOUN
ejpam-6803	174	23	0.120173	0.120173	NUM
ejpam-6803	174	24	0.117881	0.117881	NUM
ejpam-6803	174	25	2.29e-3	2.29e-3	NUM
ejpam-6803	174	26	0.112952	0.112952	NUM
ejpam-6803	174	27	0.112030	0.112030	NUM
ejpam-6803	174	28	9.22e-4	9.22e-4	NOUN
ejpam-6803	174	29	-1	-1	ADP
ejpam-6803	174	30	0.296094	0.296094	NUM
ejpam-6803	174	31	0.297252	0.297252	NUM
ejpam-6803	174	32	1.16e-3	1.16e-3	NUM
ejpam-6803	174	33	0.252258	0.252258	NUM
ejpam-6803	174	34	0.251671	0.251671	NUM
ejpam-6803	174	35	5.87e-4	5.87e-4	NOUN
ejpam-6803	174	36	0	0	NUM
ejpam-6803	174	37	0.641643	0.641643	NUM
ejpam-6803	174	38	0.641643	0.641643	NUM
ejpam-6803	174	39	0.00e0	0.00e0	NUM
ejpam-6803	174	40	0.435790	0.435790	NUM
ejpam-6803	174	41	0.437201	0.437201	NUM
ejpam-6803	174	42	1.41e-3	1.41e-3	NUM
ejpam-6803	174	43	1	1	NUM
ejpam-6803	174	44	1.124353	1.124353	NUM
ejpam-6803	174	45	1.123195	1.123195	NUM
ejpam-6803	174	46	1.16e-3	1.16e-3	NUM
ejpam-6803	174	47	0.492268	0.492268	NUM
ejpam-6803	174	48	0.491681	0.491681	NUM
ejpam-6803	174	49	5.87e-4	5.87e-4	NOUN
ejpam-6803	174	50	2	2	NUM
ejpam-6803	174	51	1.554600	1.554600	NUM
ejpam-6803	174	52	1.556892	1.556892	NUM
ejpam-6803	174	53	2.29e-3	2.29e-3	NOUN
ejpam-6803	174	54	0.346210	0.346210	NUM
ejpam-6803	174	55	0.345287	0.345287	NUM
ejpam-6803	174	56	9.22e-4	9.22e-4	NOUN
ejpam-6803	174	57	1.00	1.00	NUM
ejpam-6803	174	58	-2	-2	NOUN
ejpam-6803	174	59	0.094852	0.094852	NUM
ejpam-6803	174	60	0.095644	0.095644	NUM
ejpam-6803	174	61	7.93e-4	7.93e-4	NOUN
ejpam-6803	174	62	0.090353	0.090353	NUM
ejpam-6803	174	63	0.095300	0.095300	NUM
ejpam-6803	174	64	4.95e-3	4.95e-3	NUM
ejpam-6803	174	65	-1	-1	NOUN
ejpam-6803	174	66	0.238406	0.238406	NUM
ejpam-6803	174	67	0.238006	0.238006	NUM
ejpam-6803	174	68	4.00e-4	4.00e-4	NOUN
ejpam-6803	174	69	0.209987	0.209987	NUM
ejpam-6803	174	70	0.213137	0.213137	NUM
ejpam-6803	174	71	3.15e-3	3.15e-3	NUM
ejpam-6803	174	72	0	0	NUM
ejpam-6803	175	1	0.537883	0.537883	NUM
ejpam-6803	175	2	0.537883	0.537883	NUM
ejpam-6803	175	3	0.00e0	0.00e0	NUM
ejpam-6803	175	4	0.393224	0.393224	NUM
ejpam-6803	175	5	0.385656	0.385656	NUM
ejpam-6803	175	6	7.57e-3	7.57e-3	NUM
ejpam-6803	175	7	1	1	NUM
ejpam-6803	175	8	1.000000	1.000000	NUM
ejpam-6803	175	9	1.000400	1.000400	NUM
ejpam-6803	175	10	4.00e-4	4.00e-4	NOUN
ejpam-6803	175	11	0.500000	0.500000	NUM
ejpam-6803	175	12	0.503149	0.503149	NUM
ejpam-6803	175	13	3.15e-3	3.15e-3	NUM
ejpam-6803	175	14	2	2	NUM
ejpam-6803	175	15	1.462117	1.462117	NUM
ejpam-6803	175	16	1.461325	1.461325	NUM
ejpam-6803	175	17	7.93e-4	7.93e-4	NOUN
ejpam-6803	175	18	0.393224	0.393224	NUM
ejpam-6803	175	19	0.398171	0.398171	NUM
ejpam-6803	175	20	4.95e-3	4.95e-3	NUM
ejpam-6803	175	21	4	4	NUM
ejpam-6803	175	22	.	.	PUNCT
ejpam-6803	175	23	conclusion	conclusion	NOUN
ejpam-6803	175	24	in	in	ADP
ejpam-6803	175	25	this	this	DET
ejpam-6803	175	26	work	work	NOUN
ejpam-6803	175	27	,	,	PUNCT
ejpam-6803	175	28	we	we	PRON
ejpam-6803	175	29	used	use	VERB
ejpam-6803	175	30	pinns	pinn	NOUN
ejpam-6803	175	31	to	to	PART
ejpam-6803	175	32	solve	solve	VERB
ejpam-6803	175	33	the	the	DET
ejpam-6803	175	34	integer	integer	NOUN
ejpam-6803	175	35	-	-	PUNCT
ejpam-6803	175	36	order	order	NOUN
ejpam-6803	175	37	bbe	bbe	NOUN
ejpam-6803	175	38	system	system	NOUN
ejpam-6803	175	39	,	,	PUNCT
ejpam-6803	175	40	a	a	DET
ejpam-6803	175	41	system	system	NOUN
ejpam-6803	175	42	of	of	ADP
ejpam-6803	175	43	nonlinear	nonlinear	ADJ
ejpam-6803	175	44	coupled	couple	VERB
ejpam-6803	175	45	partial	partial	ADJ
ejpam-6803	175	46	differential	differential	NOUN
ejpam-6803	175	47	equations	equation	NOUN
ejpam-6803	175	48	that	that	PRON
ejpam-6803	175	49	govern	govern	VERB
ejpam-6803	175	50	the	the	DET
ejpam-6803	175	51	shallow	shallow	ADJ
ejpam-6803	175	52	water	water	NOUN
ejpam-6803	175	53	wave	wave	NOUN
ejpam-6803	175	54	dynamics	dynamic	NOUN
ejpam-6803	175	55	.	.	PUNCT
ejpam-6803	176	1	the	the	DET
ejpam-6803	176	2	pinn	pinn	NOUN
ejpam-6803	176	3	was	be	AUX
ejpam-6803	176	4	coded	code	VERB
ejpam-6803	176	5	in	in	ADP
ejpam-6803	176	6	python	python	NOUN
ejpam-6803	176	7	with	with	ADP
ejpam-6803	176	8	tensorflow	tensorflow	NOUN
ejpam-6803	176	9	and	and	CCONJ
ejpam-6803	176	10	trained	train	VERB
ejpam-6803	176	11	with	with	ADP
ejpam-6803	176	12	over	over	ADP
ejpam-6803	176	13	500	500	NUM
ejpam-6803	176	14	epochs	epoch	NOUN
ejpam-6803	176	15	of	of	ADP
ejpam-6803	176	16	training	training	NOUN
ejpam-6803	176	17	,	,	PUNCT
ejpam-6803	176	18	showing	show	VERB
ejpam-6803	176	19	consistent	consistent	ADJ
ejpam-6803	176	20	convergence	convergence	NOUN
ejpam-6803	176	21	by	by	ADP
ejpam-6803	176	22	decreasing	decrease	VERB
ejpam-6803	176	23	the	the	DET
ejpam-6803	176	24	loss	loss	NOUN
ejpam-6803	176	25	terms	term	NOUN
ejpam-6803	176	26	as	as	SCONJ
ejpam-6803	176	27	followed	follow	VERB
ejpam-6803	176	28	.	.	PUNCT
ejpam-6803	177	1	we	we	PRON
ejpam-6803	177	2	use	use	VERB
ejpam-6803	177	3	the	the	DET
ejpam-6803	177	4	dual	dual	ADJ
ejpam-6803	177	5	-	-	PUNCT
ejpam-6803	177	6	network	network	NOUN
ejpam-6803	177	7	architecture	architecture	NOUN
ejpam-6803	177	8	to	to	PART
ejpam-6803	177	9	learn	learn	VERB
ejpam-6803	177	10	the	the	DET
ejpam-6803	177	11	coupled	couple	VERB
ejpam-6803	177	12	variables	variable	NOUN
ejpam-6803	177	13	,	,	PUNCT
ejpam-6803	177	14	construct	construct	VERB
ejpam-6803	177	15	a	a	DET
ejpam-6803	177	16	loss	loss	NOUN
ejpam-6803	177	17	that	that	PRON
ejpam-6803	177	18	combines	combine	VERB
ejpam-6803	177	19	the	the	DET
ejpam-6803	177	20	pde	pde	NOUN
ejpam-6803	177	21	residuals	residual	NOUN
ejpam-6803	177	22	with	with	ADP
ejpam-6803	177	23	constants	constant	NOUN
ejpam-6803	177	24	and	and	CCONJ
ejpam-6803	177	25	use	use	VERB
ejpam-6803	177	26	activation	activation	NOUN
ejpam-6803	177	27	tuning	tuning	NOUN
ejpam-6803	177	28	and	and	CCONJ
ejpam-6803	177	29	gradient	gradient	NOUN
ejpam-6803	177	30	-	-	PUNCT
ejpam-6803	177	31	based	base	VERB
ejpam-6803	177	32	optimization	optimization	NOUN
ejpam-6803	177	33	to	to	PART
ejpam-6803	177	34	guarantee	guarantee	VERB
ejpam-6803	177	35	steady	steady	ADJ
ejpam-6803	177	36	convergence	convergence	NOUN
ejpam-6803	177	37	.	.	PUNCT
ejpam-6803	178	1	these	these	DET
ejpam-6803	178	2	innovations	innovation	NOUN
ejpam-6803	178	3	enable	enable	VERB
ejpam-6803	178	4	the	the	DET
ejpam-6803	178	5	proposed	propose	VERB
ejpam-6803	178	6	pinn	pinn	NOUN
ejpam-6803	178	7	framework	framework	NOUN
ejpam-6803	178	8	to	to	PART
ejpam-6803	178	9	obtain	obtain	VERB
ejpam-6803	178	10	high	high	ADJ
ejpam-6803	178	11	accuracy	accuracy	NOUN
ejpam-6803	178	12	with	with	ADP
ejpam-6803	178	13	low	low	ADJ
ejpam-6803	178	14	errors	error	NOUN
ejpam-6803	178	15	relative	relative	ADJ
ejpam-6803	178	16	to	to	ADP
ejpam-6803	178	17	exact	exact	ADJ
ejpam-6803	178	18	solutions	solution	NOUN
ejpam-6803	178	19	,	,	PUNCT
ejpam-6803	178	20	indicating	indicate	VERB
ejpam-6803	178	21	its	its	PRON
ejpam-6803	178	22	usefulness	usefulness	NOUN
ejpam-6803	178	23	in	in	ADP
ejpam-6803	178	24	the	the	DET
ejpam-6803	178	25	nonlinear	nonlinear	ADJ
ejpam-6803	178	26	wave	wave	NOUN
ejpam-6803	178	27	models	model	NOUN
ejpam-6803	178	28	and	and	CCONJ
ejpam-6803	178	29	its	its	PRON
ejpam-6803	178	30	possible	possible	ADJ
ejpam-6803	178	31	generalization	generalization	NOUN
ejpam-6803	178	32	to	to	ADP
ejpam-6803	178	33	systems	system	NOUN
ejpam-6803	178	34	of	of	ADP
ejpam-6803	178	35	fractional	fractional	ADJ
ejpam-6803	178	36	order	order	NOUN
ejpam-6803	178	37	.	.	PUNCT
ejpam-6803	179	1	visual	visual	ADJ
ejpam-6803	179	2	plots	plot	NOUN
ejpam-6803	179	3	of	of	ADP
ejpam-6803	179	4	exact	exact	ADJ
ejpam-6803	179	5	and	and	CCONJ
ejpam-6803	179	6	predicted	predict	VERB
ejpam-6803	179	7	solutions	solution	NOUN
ejpam-6803	179	8	matched	match	VERB
ejpam-6803	179	9	very	very	ADV
ejpam-6803	179	10	well	well	ADV
ejpam-6803	179	11	,	,	PUNCT
ejpam-6803	179	12	and	and	CCONJ
ejpam-6803	179	13	error	error	NOUN
ejpam-6803	179	14	surfaces	surface	NOUN
ejpam-6803	179	15	were	be	AUX
ejpam-6803	179	16	confirmed	confirm	VERB
ejpam-6803	179	17	very	very	ADV
ejpam-6803	179	18	accurate	accurate	ADJ
ejpam-6803	179	19	on	on	ADP
ejpam-6803	179	20	an	an	DET
ejpam-6803	179	21	absolute	absolute	ADJ
ejpam-6803	179	22	error	error	NOUN
ejpam-6803	179	23	basis	basis	NOUN
ejpam-6803	179	24	.	.	PUNCT
ejpam-6803	180	1	kde	kde	NOUN
ejpam-6803	180	2	plots	plot	NOUN
ejpam-6803	180	3	and	and	CCONJ
ejpam-6803	180	4	histograms	histogram	NOUN
ejpam-6803	180	5	were	be	AUX
ejpam-6803	180	6	used	use	VERB
ejpam-6803	180	7	to	to	PART
ejpam-6803	180	8	check	check	VERB
ejpam-6803	180	9	the	the	DET
ejpam-6803	180	10	statistical	statistical	ADJ
ejpam-6803	180	11	consistency	consistency	NOUN
ejpam-6803	180	12	of	of	ADP
ejpam-6803	180	13	the	the	DET
ejpam-6803	180	14	predictions	prediction	NOUN
ejpam-6803	180	15	.	.	PUNCT
ejpam-6803	181	1	the	the	DET
ejpam-6803	181	2	model	model	NOUN
ejpam-6803	181	3	was	be	AUX
ejpam-6803	181	4	also	also	ADV
ejpam-6803	181	5	stable	stable	ADJ
ejpam-6803	181	6	under	under	ADP
ejpam-6803	181	7	an	an	DET
ejpam-6803	181	8	alternating	alternate	VERB
ejpam-6803	181	9	set	set	NOUN
ejpam-6803	181	10	of	of	ADP
ejpam-6803	181	11	the	the	DET
ejpam-6803	181	12	values	value	NOUN
ejpam-6803	181	13	of	of	ADP
ejpam-6803	181	14	the	the	DET
ejpam-6803	181	15	parameter	parameter	NOUN
ejpam-6803	181	16	β	β	PROPN
ejpam-6803	181	17	,	,	PUNCT
ejpam-6803	181	18	leada	leada	PROPN
ejpam-6803	181	19	.	.	PUNCT
ejpam-6803	182	1	shafee	shafee	PROPN
ejpam-6803	182	2	et	et	PROPN
ejpam-6803	182	3	al	al	PROPN
ejpam-6803	182	4	.	.	PUNCT
ejpam-6803	182	5	/	/	SYM
ejpam-6803	182	6	eur	eur	PROPN
ejpam-6803	182	7	.	.	PUNCT
ejpam-6803	183	1	j.	j.	PROPN
ejpam-6803	183	2	pure	pure	PROPN
ejpam-6803	183	3	appl	appl	PROPN
ejpam-6803	183	4	.	.	PROPN
ejpam-6803	183	5	math	math	PROPN
ejpam-6803	183	6	,	,	PUNCT
ejpam-6803	183	7	18	18	NUM
ejpam-6803	183	8	(	(	PUNCT
ejpam-6803	183	9	4	4	NUM
ejpam-6803	183	10	)	)	PUNCT
ejpam-6803	183	11	(	(	PUNCT
ejpam-6803	183	12	2025	2025	NUM
ejpam-6803	183	13	)	)	PUNCT
ejpam-6803	183	14	,	,	PUNCT
ejpam-6803	183	15	6803	6803	NUM
ejpam-6803	183	16	15	15	NUM
ejpam-6803	183	17	of	of	ADP
ejpam-6803	183	18	18	18	NUM
ejpam-6803	183	19	ing	ing	NOUN
ejpam-6803	183	20	to	to	ADP
ejpam-6803	183	21	error	error	NOUN
ejpam-6803	183	22	of	of	ADP
ejpam-6803	183	23	the	the	DET
ejpam-6803	183	24	same	same	ADJ
ejpam-6803	183	25	low	low	ADJ
ejpam-6803	183	26	level	level	NOUN
ejpam-6803	183	27	in	in	ADP
ejpam-6803	183	28	all	all	DET
ejpam-6803	183	29	test	test	NOUN
ejpam-6803	183	30	cases	case	NOUN
ejpam-6803	183	31	.	.	PUNCT
ejpam-6803	184	1	the	the	DET
ejpam-6803	184	2	generalization	generalization	NOUN
ejpam-6803	184	3	of	of	ADP
ejpam-6803	184	4	the	the	DET
ejpam-6803	184	5	model	model	NOUN
ejpam-6803	184	6	was	be	AUX
ejpam-6803	184	7	explicitly	explicitly	ADV
ejpam-6803	184	8	demonstrated	demonstrate	VERB
ejpam-6803	184	9	with	with	ADP
ejpam-6803	184	10	the	the	DET
ejpam-6803	184	11	aid	aid	NOUN
ejpam-6803	184	12	of	of	ADP
ejpam-6803	184	13	surface	surface	NOUN
ejpam-6803	184	14	plots	plot	NOUN
ejpam-6803	184	15	,	,	PUNCT
ejpam-6803	184	16	cross	cross	ADJ
ejpam-6803	184	17	-	-	ADJ
ejpam-6803	184	18	section	section	NOUN
ejpam-6803	184	19	analysis	analysis	NOUN
ejpam-6803	184	20	and	and	CCONJ
ejpam-6803	184	21	a	a	DET
ejpam-6803	184	22	table	table	NOUN
ejpam-6803	184	23	summarizing	summarize	VERB
ejpam-6803	184	24	errors	error	NOUN
ejpam-6803	184	25	.	.	PUNCT
ejpam-6803	185	1	these	these	DET
ejpam-6803	185	2	observations	observation	NOUN
ejpam-6803	185	3	demonstrate	demonstrate	VERB
ejpam-6803	185	4	that	that	SCONJ
ejpam-6803	185	5	pinns	pinn	NOUN
ejpam-6803	185	6	are	be	AUX
ejpam-6803	185	7	an	an	DET
ejpam-6803	185	8	efficient	efficient	ADJ
ejpam-6803	185	9	tool	tool	NOUN
ejpam-6803	185	10	for	for	ADP
ejpam-6803	185	11	solving	solve	VERB
ejpam-6803	185	12	complicated	complicated	ADJ
ejpam-6803	185	13	nonlinear	nonlinear	ADJ
ejpam-6803	185	14	systems	system	NOUN
ejpam-6803	185	15	of	of	ADP
ejpam-6803	185	16	pdes	pde	NOUN
ejpam-6803	185	17	without	without	ADP
ejpam-6803	185	18	using	use	VERB
ejpam-6803	185	19	labeled	label	VERB
ejpam-6803	185	20	data	datum	NOUN
ejpam-6803	185	21	.	.	PUNCT
ejpam-6803	186	1	this	this	PRON
ejpam-6803	186	2	is	be	AUX
ejpam-6803	186	3	due	due	ADJ
ejpam-6803	186	4	to	to	ADP
ejpam-6803	186	5	the	the	DET
ejpam-6803	186	6	incorporation	incorporation	NOUN
ejpam-6803	186	7	of	of	ADP
ejpam-6803	186	8	physics	physics	NOUN
ejpam-6803	186	9	-	-	PUNCT
ejpam-6803	186	10	based	base	VERB
ejpam-6803	186	11	constraints	constraint	NOUN
ejpam-6803	186	12	in	in	ADP
ejpam-6803	186	13	the	the	DET
ejpam-6803	186	14	loss	loss	NOUN
ejpam-6803	186	15	function	function	NOUN
ejpam-6803	186	16	,	,	PUNCT
ejpam-6803	186	17	which	which	PRON
ejpam-6803	186	18	allows	allow	VERB
ejpam-6803	186	19	accurate	accurate	ADJ
ejpam-6803	186	20	learning	learning	NOUN
ejpam-6803	186	21	of	of	ADP
ejpam-6803	186	22	solution	solution	NOUN
ejpam-6803	186	23	dynamics	dynamic	NOUN
ejpam-6803	186	24	.	.	PUNCT
ejpam-6803	187	1	in	in	ADP
ejpam-6803	187	2	the	the	DET
ejpam-6803	187	3	future	future	NOUN
ejpam-6803	187	4	,	,	PUNCT
ejpam-6803	187	5	it	it	PRON
ejpam-6803	187	6	is	be	AUX
ejpam-6803	187	7	possible	possible	ADJ
ejpam-6803	187	8	to	to	PART
ejpam-6803	187	9	apply	apply	VERB
ejpam-6803	187	10	the	the	DET
ejpam-6803	187	11	framework	framework	NOUN
ejpam-6803	187	12	to	to	ADP
ejpam-6803	187	13	fractional	fractional	ADJ
ejpam-6803	187	14	-	-	PUNCT
ejpam-6803	187	15	order	order	NOUN
ejpam-6803	187	16	or	or	CCONJ
ejpam-6803	187	17	higher	high	ADJ
ejpam-6803	187	18	dimensional	dimensional	ADJ
ejpam-6803	187	19	pde	pde	NOUN
ejpam-6803	187	20	systems	system	NOUN
ejpam-6803	187	21	,	,	PUNCT
ejpam-6803	187	22	and	and	CCONJ
ejpam-6803	187	23	to	to	PART
ejpam-6803	187	24	consider	consider	VERB
ejpam-6803	187	25	optimal	optimal	ADJ
ejpam-6803	187	26	sampling	sampling	NOUN
ejpam-6803	187	27	selection	selection	NOUN
ejpam-6803	187	28	and	and	CCONJ
ejpam-6803	187	29	adaptive	adaptive	ADJ
ejpam-6803	187	30	strategy	strategy	NOUN
ejpam-6803	187	31	to	to	PART
ejpam-6803	187	32	further	far	ADV
ejpam-6803	187	33	enhance	enhance	VERB
ejpam-6803	187	34	the	the	DET
ejpam-6803	187	35	convergence	convergence	NOUN
ejpam-6803	187	36	performance	performance	NOUN
ejpam-6803	187	37	.	.	PUNCT
ejpam-6803	188	1	references	reference	NOUN
ejpam-6803	188	2	[	[	X
ejpam-6803	188	3	1	1	X
ejpam-6803	188	4	]	]	PUNCT
ejpam-6803	188	5	s.	s.	PROPN
ejpam-6803	188	6	noor	noor	PROPN
ejpam-6803	188	7	,	,	PUNCT
ejpam-6803	188	8	h.	h.	PROPN
ejpam-6803	188	9	a.	a.	PROPN
ejpam-6803	188	10	alyousef	alyousef	PROPN
ejpam-6803	188	11	,	,	PUNCT
ejpam-6803	188	12	a.	a.	NOUN
ejpam-6803	188	13	shafee	shafee	PROPN
ejpam-6803	188	14	,	,	PUNCT
ejpam-6803	188	15	r.	r.	PROPN
ejpam-6803	188	16	shah	shah	PROPN
ejpam-6803	188	17	,	,	PUNCT
ejpam-6803	188	18	and	and	CCONJ
ejpam-6803	189	1	s.	s.	PROPN
ejpam-6803	189	2	a.	a.	PROPN
ejpam-6803	189	3	el	el	PROPN
ejpam-6803	189	4	-	-	PUNCT
ejpam-6803	189	5	tantawy	tantawy	NOUN
ejpam-6803	189	6	.	.	PUNCT
ejpam-6803	190	1	a	a	DET
ejpam-6803	190	2	novel	novel	ADJ
ejpam-6803	190	3	analytical	analytical	ADJ
ejpam-6803	190	4	technique	technique	NOUN
ejpam-6803	190	5	for	for	ADP
ejpam-6803	190	6	analyzing	analyze	VERB
ejpam-6803	190	7	the	the	DET
ejpam-6803	190	8	(	(	PUNCT
ejpam-6803	190	9	3	3	NUM
ejpam-6803	190	10	+	+	NOUN
ejpam-6803	190	11	1)-dimensional	1)-dimensional	ADJ
ejpam-6803	190	12	fractional	fractional	ADJ
ejpam-6803	190	13	calogero	calogero	ADJ
ejpam-6803	190	14	-	-	PUNCT
ejpam-6803	190	15	bogoyavlenskiischiff	bogoyavlenskiischiff	NOUN
ejpam-6803	190	16	equation	equation	NOUN
ejpam-6803	190	17	:	:	PUNCT
ejpam-6803	190	18	investigating	investigate	VERB
ejpam-6803	190	19	solitary	solitary	ADJ
ejpam-6803	190	20	/	/	SYM
ejpam-6803	190	21	shock	shock	NOUN
ejpam-6803	190	22	waves	wave	NOUN
ejpam-6803	190	23	and	and	CCONJ
ejpam-6803	190	24	many	many	ADJ
ejpam-6803	190	25	others	other	NOUN
ejpam-6803	190	26	physical	physical	ADJ
ejpam-6803	190	27	phenomena	phenomenon	NOUN
ejpam-6803	190	28	.	.	PUNCT
ejpam-6803	191	1	physica	physica	PROPN
ejpam-6803	191	2	scripta	scripta	PROPN
ejpam-6803	191	3	,	,	PUNCT
ejpam-6803	191	4	99(6):065257	99(6):065257	NUM
ejpam-6803	191	5	,	,	PUNCT
ejpam-6803	191	6	2024	2024	NUM
ejpam-6803	191	7	.	.	PUNCT
ejpam-6803	192	1	[	[	X
ejpam-6803	192	2	2	2	NUM
ejpam-6803	192	3	]	]	X
ejpam-6803	192	4	n.	n.	NOUN
ejpam-6803	192	5	a.	a.	NOUN
ejpam-6803	192	6	shah	shah	PROPN
ejpam-6803	192	7	,	,	PUNCT
ejpam-6803	192	8	h.	h.	PROPN
ejpam-6803	192	9	a.	a.	PROPN
ejpam-6803	192	10	alyousef	alyousef	PROPN
ejpam-6803	192	11	,	,	PUNCT
ejpam-6803	192	12	s.	s.	PROPN
ejpam-6803	192	13	a.	a.	PROPN
ejpam-6803	192	14	el	el	PROPN
ejpam-6803	192	15	-	-	PUNCT
ejpam-6803	192	16	tantawy	tantawy	ADJ
ejpam-6803	192	17	,	,	PUNCT
ejpam-6803	192	18	and	and	CCONJ
ejpam-6803	192	19	j.	j.	PROPN
ejpam-6803	192	20	d.	d.	PROPN
ejpam-6803	192	21	chung	chung	PROPN
ejpam-6803	192	22	.	.	PUNCT
ejpam-6803	193	1	analytical	analytical	ADJ
ejpam-6803	193	2	investigation	investigation	NOUN
ejpam-6803	193	3	of	of	ADP
ejpam-6803	193	4	fractional	fractional	ADJ
ejpam-6803	193	5	-	-	PUNCT
ejpam-6803	193	6	order	order	NOUN
ejpam-6803	193	7	korteweg	korteweg	NOUN
ejpam-6803	193	8	-	-	PUNCT
ejpam-6803	193	9	de	de	NOUN
ejpam-6803	193	10	-	-	NOUN
ejpam-6803	193	11	vries	vries	NOUN
ejpam-6803	193	12	-	-	PUNCT
ejpam-6803	193	13	type	type	NOUN
ejpam-6803	193	14	equations	equation	NOUN
ejpam-6803	193	15	under	under	ADP
ejpam-6803	193	16	atangana	atangana	PROPN
ejpam-6803	193	17	-	-	PUNCT
ejpam-6803	193	18	baleanucaputo	baleanucaputo	NOUN
ejpam-6803	193	19	operator	operator	NOUN
ejpam-6803	193	20	:	:	PUNCT
ejpam-6803	193	21	modeling	model	VERB
ejpam-6803	193	22	nonlinear	nonlinear	ADJ
ejpam-6803	193	23	waves	wave	NOUN
ejpam-6803	193	24	in	in	ADP
ejpam-6803	193	25	a	a	DET
ejpam-6803	193	26	plasma	plasma	NOUN
ejpam-6803	193	27	and	and	CCONJ
ejpam-6803	193	28	fluid	fluid	NOUN
ejpam-6803	193	29	.	.	PUNCT
ejpam-6803	193	30	symmetry	symmetry	NOUN
ejpam-6803	193	31	,	,	PUNCT
ejpam-6803	193	32	14(4):739	14(4):739	NUM
ejpam-6803	193	33	,	,	PUNCT
ejpam-6803	193	34	2022	2022	NUM
ejpam-6803	193	35	.	.	PUNCT
ejpam-6803	194	1	[	[	X
ejpam-6803	194	2	3	3	X
ejpam-6803	194	3	]	]	X
ejpam-6803	194	4	h.	h.	PROPN
ejpam-6803	194	5	a.	a.	PROPN
ejpam-6803	194	6	alyousef	alyousef	PROPN
ejpam-6803	194	7	,	,	PUNCT
ejpam-6803	194	8	c.	c.	PROPN
ejpam-6803	194	9	g.	g.	PROPN
ejpam-6803	194	10	l.	l.	PROPN
ejpam-6803	194	11	tiofack	tiofack	PROPN
ejpam-6803	194	12	,	,	PUNCT
ejpam-6803	194	13	a.	a.	PROPN
ejpam-6803	194	14	h.	h.	PROPN
ejpam-6803	194	15	salas	salas	PROPN
ejpam-6803	194	16	,	,	PUNCT
ejpam-6803	194	17	w.	w.	PROPN
ejpam-6803	194	18	alhejaili	alhejaili	PROPN
ejpam-6803	194	19	,	,	PUNCT
ejpam-6803	194	20	s.	s.	PROPN
ejpam-6803	194	21	m.	m.	PROPN
ejpam-6803	194	22	ismaeel	ismaeel	PROPN
ejpam-6803	194	23	,	,	PUNCT
ejpam-6803	194	24	and	and	CCONJ
ejpam-6803	195	1	s.	s.	PROPN
ejpam-6803	195	2	a.	a.	PROPN
ejpam-6803	195	3	el	el	PROPN
ejpam-6803	195	4	-	-	PUNCT
ejpam-6803	195	5	tantawy	tantawy	NOUN
ejpam-6803	195	6	.	.	PUNCT
ejpam-6803	196	1	novel	novel	ADJ
ejpam-6803	196	2	approximations	approximation	NOUN
ejpam-6803	196	3	to	to	ADP
ejpam-6803	196	4	the	the	DET
ejpam-6803	196	5	third	third	ADJ
ejpam-6803	196	6	-	-	PUNCT
ejpam-6803	196	7	and	and	CCONJ
ejpam-6803	196	8	fifth	fifth	ADJ
ejpam-6803	196	9	-	-	PUNCT
ejpam-6803	196	10	order	order	NOUN
ejpam-6803	196	11	fractional	fractional	ADJ
ejpam-6803	196	12	kdv	kdv	NOUN
ejpam-6803	196	13	-	-	PUNCT
ejpam-6803	196	14	type	type	NOUN
ejpam-6803	196	15	equations	equation	NOUN
ejpam-6803	196	16	and	and	CCONJ
ejpam-6803	196	17	modeling	model	VERB
ejpam-6803	196	18	nonlinear	nonlinear	ADJ
ejpam-6803	196	19	structures	structure	NOUN
ejpam-6803	196	20	in	in	ADP
ejpam-6803	196	21	plasmas	plasma	NOUN
ejpam-6803	196	22	and	and	CCONJ
ejpam-6803	196	23	fluids	fluid	NOUN
ejpam-6803	196	24	.	.	PUNCT
ejpam-6803	197	1	brazilian	brazilian	ADJ
ejpam-6803	197	2	journal	journal	PROPN
ejpam-6803	197	3	of	of	ADP
ejpam-6803	197	4	physics	physics	PROPN
ejpam-6803	197	5	,	,	PUNCT
ejpam-6803	197	6	55(1):20	55(1):20	NUM
ejpam-6803	197	7	,	,	PUNCT
ejpam-6803	197	8	2025	2025	NUM
ejpam-6803	197	9	.	.	PUNCT
ejpam-6803	198	1	[	[	X
ejpam-6803	198	2	4	4	X
ejpam-6803	198	3	]	]	PUNCT
ejpam-6803	198	4	j.	j.	PROPN
ejpam-6803	198	5	lu	lu	PROPN
ejpam-6803	198	6	and	and	CCONJ
ejpam-6803	198	7	y.	y.	PROPN
ejpam-6803	198	8	sun	sun	PROPN
ejpam-6803	198	9	.	.	PUNCT
ejpam-6803	199	1	numerical	numerical	PROPN
ejpam-6803	199	2	approaches	approach	NOUN
ejpam-6803	199	3	to	to	ADP
ejpam-6803	199	4	time	time	NOUN
ejpam-6803	199	5	fractional	fractional	ADJ
ejpam-6803	199	6	boussinesq	boussinesq	ADJ
ejpam-6803	199	7	-	-	PUNCT
ejpam-6803	199	8	burgers	burger	NOUN
ejpam-6803	199	9	equations	equation	NOUN
ejpam-6803	199	10	.	.	PUNCT
ejpam-6803	200	1	fractals	fractal	NOUN
ejpam-6803	200	2	,	,	PUNCT
ejpam-6803	200	3	29(08):2150244	29(08):2150244	NUM
ejpam-6803	200	4	,	,	PUNCT
ejpam-6803	200	5	2021	2021	NUM
ejpam-6803	200	6	.	.	PUNCT
ejpam-6803	201	1	[	[	X
ejpam-6803	201	2	5	5	NUM
ejpam-6803	201	3	]	]	PUNCT
ejpam-6803	201	4	m.	m.	NOUN
ejpam-6803	201	5	rammane	rammane	PROPN
ejpam-6803	201	6	,	,	PUNCT
ejpam-6803	201	7	s.	s.	PROPN
ejpam-6803	201	8	mesmoudi	mesmoudi	PROPN
ejpam-6803	201	9	,	,	PUNCT
ejpam-6803	201	10	a.	a.	PROPN
ejpam-6803	201	11	tri	tri	PROPN
ejpam-6803	201	12	,	,	PUNCT
ejpam-6803	201	13	b.	b.	PROPN
ejpam-6803	201	14	braikat	braikat	PROPN
ejpam-6803	201	15	,	,	PUNCT
ejpam-6803	201	16	and	and	CCONJ
ejpam-6803	201	17	n.	n.	PROPN
ejpam-6803	201	18	damil	damil	PROPN
ejpam-6803	201	19	.	.	PUNCT
ejpam-6803	202	1	a	a	DET
ejpam-6803	202	2	dimensionless	dimensionless	NOUN
ejpam-6803	202	3	numerical	numerical	ADJ
ejpam-6803	202	4	mesh	mesh	NOUN
ejpam-6803	202	5	-	-	PUNCT
ejpam-6803	202	6	free	free	ADJ
ejpam-6803	202	7	model	model	NOUN
ejpam-6803	202	8	for	for	ADP
ejpam-6803	202	9	the	the	DET
ejpam-6803	202	10	compressible	compressible	ADJ
ejpam-6803	202	11	fluid	fluid	ADJ
ejpam-6803	202	12	flows	flow	NOUN
ejpam-6803	202	13	.	.	PUNCT
ejpam-6803	203	1	computers	computer	NOUN
ejpam-6803	203	2	and	and	CCONJ
ejpam-6803	203	3	fluids	fluid	NOUN
ejpam-6803	203	4	,	,	PUNCT
ejpam-6803	203	5	221:104845	221:104845	NUM
ejpam-6803	203	6	,	,	PUNCT
ejpam-6803	203	7	2021	2021	NUM
ejpam-6803	203	8	.	.	PUNCT
ejpam-6803	204	1	[	[	X
ejpam-6803	204	2	6	6	NUM
ejpam-6803	204	3	]	]	X
ejpam-6803	204	4	y.	y.	PROPN
ejpam-6803	204	5	s.	s.	PROPN
ejpam-6803	204	6	li	li	PROPN
ejpam-6803	204	7	and	and	CCONJ
ejpam-6803	204	8	j.	j.	PROPN
ejpam-6803	204	9	m.	m.	PROPN
ejpam-6803	204	10	zhan	zhan	PROPN
ejpam-6803	204	11	.	.	PUNCT
ejpam-6803	204	12	chebyshev	chebyshev	PROPN
ejpam-6803	204	13	finite	finite	ADJ
ejpam-6803	204	14	-	-	ADJ
ejpam-6803	204	15	spectral	spectral	ADJ
ejpam-6803	204	16	method	method	NOUN
ejpam-6803	204	17	for	for	ADP
ejpam-6803	204	18	1d	1d	NUM
ejpam-6803	204	19	boussinesqtype	boussinesqtype	ADJ
ejpam-6803	204	20	equations	equation	NOUN
ejpam-6803	204	21	.	.	PUNCT
ejpam-6803	205	1	journal	journal	PROPN
ejpam-6803	205	2	of	of	ADP
ejpam-6803	205	3	waterway	waterway	NOUN
ejpam-6803	205	4	,	,	PUNCT
ejpam-6803	205	5	port	port	NOUN
ejpam-6803	205	6	,	,	PUNCT
ejpam-6803	205	7	coastal	coastal	ADJ
ejpam-6803	205	8	,	,	PUNCT
ejpam-6803	205	9	and	and	CCONJ
ejpam-6803	205	10	ocean	ocean	PROPN
ejpam-6803	205	11	engineering	engineering	NOUN
ejpam-6803	205	12	,	,	PUNCT
ejpam-6803	205	13	132(3):212–223	132(3):212–223	NUM
ejpam-6803	205	14	,	,	PUNCT
ejpam-6803	205	15	2006	2006	NUM
ejpam-6803	205	16	.	.	PUNCT
ejpam-6803	206	1	[	[	X
ejpam-6803	206	2	7	7	X
ejpam-6803	206	3	]	]	X
ejpam-6803	206	4	j.	j.	PROPN
ejpam-6803	206	5	huang	huang	PROPN
ejpam-6803	206	6	,	,	PUNCT
ejpam-6803	206	7	l.	l.	PROPN
ejpam-6803	206	8	duan	duan	PROPN
ejpam-6803	206	9	,	,	PUNCT
ejpam-6803	206	10	and	and	CCONJ
ejpam-6803	206	11	m.	m.	NOUN
ejpam-6803	206	12	m.	m.	NOUN
ejpam-6803	206	13	choudhari	choudhari	PROPN
ejpam-6803	206	14	.	.	PUNCT
ejpam-6803	207	1	direct	direct	PROPN
ejpam-6803	207	2	numerical	numerical	PROPN
ejpam-6803	207	3	simulation	simulation	PROPN
ejpam-6803	207	4	of	of	ADP
ejpam-6803	207	5	hypersonic	hypersonic	ADJ
ejpam-6803	207	6	turbulent	turbulent	ADJ
ejpam-6803	207	7	boundary	boundary	ADJ
ejpam-6803	207	8	layers	layer	NOUN
ejpam-6803	207	9	:	:	PUNCT
ejpam-6803	207	10	effect	effect	NOUN
ejpam-6803	207	11	of	of	ADP
ejpam-6803	207	12	spatial	spatial	ADJ
ejpam-6803	207	13	evolution	evolution	NOUN
ejpam-6803	207	14	and	and	CCONJ
ejpam-6803	207	15	reynolds	reynolds	PROPN
ejpam-6803	207	16	number	number	PROPN
ejpam-6803	207	17	.	.	PUNCT
ejpam-6803	208	1	journal	journal	NOUN
ejpam-6803	208	2	of	of	ADP
ejpam-6803	208	3	fluid	fluid	ADJ
ejpam-6803	208	4	mechanics	mechanic	NOUN
ejpam-6803	208	5	,	,	PUNCT
ejpam-6803	208	6	937	937	NUM
ejpam-6803	208	7	:	:	PUNCT
ejpam-6803	208	8	a3	a3	NOUN
ejpam-6803	208	9	,	,	PUNCT
ejpam-6803	208	10	2022	2022	NUM
ejpam-6803	208	11	.	.	PUNCT
ejpam-6803	209	1	[	[	X
ejpam-6803	209	2	8	8	NUM
ejpam-6803	209	3	]	]	PUNCT
ejpam-6803	209	4	a.	a.	NOUN
ejpam-6803	209	5	manzoni	manzoni	NOUN
ejpam-6803	209	6	and	and	CCONJ
ejpam-6803	209	7	f.	f.	PROPN
ejpam-6803	209	8	negri	negri	PROPN
ejpam-6803	209	9	.	.	PUNCT
ejpam-6803	210	1	heuristic	heuristic	ADJ
ejpam-6803	210	2	strategies	strategy	NOUN
ejpam-6803	210	3	for	for	ADP
ejpam-6803	210	4	the	the	DET
ejpam-6803	210	5	approximation	approximation	NOUN
ejpam-6803	210	6	of	of	ADP
ejpam-6803	210	7	stability	stability	NOUN
ejpam-6803	210	8	factors	factor	NOUN
ejpam-6803	210	9	in	in	ADP
ejpam-6803	210	10	quadratically	quadratically	ADV
ejpam-6803	210	11	nonlinear	nonlinear	ADJ
ejpam-6803	210	12	parametrized	parametrized	ADJ
ejpam-6803	210	13	pdes	pde	NOUN
ejpam-6803	210	14	.	.	PUNCT
ejpam-6803	211	1	advances	advance	NOUN
ejpam-6803	211	2	in	in	ADP
ejpam-6803	211	3	computational	computational	ADJ
ejpam-6803	211	4	mathematics	mathematic	NOUN
ejpam-6803	211	5	,	,	PUNCT
ejpam-6803	211	6	41:1255–1288	41:1255–1288	NUM
ejpam-6803	211	7	,	,	PUNCT
ejpam-6803	211	8	2015	2015	NUM
ejpam-6803	211	9	.	.	PUNCT
ejpam-6803	212	1	[	[	X
ejpam-6803	212	2	9	9	NUM
ejpam-6803	212	3	]	]	PUNCT
ejpam-6803	212	4	m.	m.	NOUN
ejpam-6803	212	5	j.	j.	PROPN
ejpam-6803	212	6	martinez	martinez	PROPN
ejpam-6803	212	7	.	.	PUNCT
ejpam-6803	212	8	analysis	analysis	NOUN
ejpam-6803	212	9	of	of	ADP
ejpam-6803	212	10	anelastic	anelastic	ADJ
ejpam-6803	212	11	flow	flow	NOUN
ejpam-6803	212	12	and	and	CCONJ
ejpam-6803	212	13	numerical	numerical	ADJ
ejpam-6803	212	14	treatment	treatment	NOUN
ejpam-6803	212	15	via	via	ADP
ejpam-6803	212	16	finite	finite	ADJ
ejpam-6803	212	17	elements	element	NOUN
ejpam-6803	212	18	.	.	PUNCT
ejpam-6803	213	1	technical	technical	ADJ
ejpam-6803	213	2	report	report	PROPN
ejpam-6803	213	3	sand-94	sand-94	PROPN
ejpam-6803	213	4	-	-	PUNCT
ejpam-6803	213	5	0320	0320	NUM
ejpam-6803	213	6	,	,	PUNCT
ejpam-6803	213	7	sandia	sandia	PROPN
ejpam-6803	213	8	national	national	PROPN
ejpam-6803	213	9	lab	lab	PROPN
ejpam-6803	214	1	.	.	PUNCT
ejpam-6803	215	1	(	(	PUNCT
ejpam-6803	215	2	snl	snl	PROPN
ejpam-6803	215	3	-	-	PUNCT
ejpam-6803	215	4	nm	nm	NOUN
ejpam-6803	215	5	)	)	PUNCT
ejpam-6803	215	6	,	,	PUNCT
ejpam-6803	215	7	albuquerque	albuquerque	PROPN
ejpam-6803	215	8	,	,	PUNCT
ejpam-6803	215	9	nm	nm	PROPN
ejpam-6803	215	10	,	,	PUNCT
ejpam-6803	215	11	united	united	PROPN
ejpam-6803	215	12	states	states	PROPN
ejpam-6803	215	13	,	,	PUNCT
ejpam-6803	215	14	1994	1994	NUM
ejpam-6803	215	15	.	.	PUNCT
ejpam-6803	216	1	[	[	X
ejpam-6803	216	2	10	10	NUM
ejpam-6803	216	3	]	]	PUNCT
ejpam-6803	216	4	m.	m.	NOUN
ejpam-6803	216	5	adel	adel	PROPN
ejpam-6803	216	6	,	,	PUNCT
ejpam-6803	216	7	h.	h.	PROPN
ejpam-6803	216	8	m.	m.	PROPN
ejpam-6803	216	9	srivastava	srivastava	PROPN
ejpam-6803	216	10	,	,	PUNCT
ejpam-6803	216	11	and	and	CCONJ
ejpam-6803	216	12	m.	m.	NOUN
ejpam-6803	216	13	m.	m.	NOUN
ejpam-6803	216	14	khader	khader	PROPN
ejpam-6803	216	15	.	.	PUNCT
ejpam-6803	217	1	implementation	implementation	NOUN
ejpam-6803	217	2	of	of	ADP
ejpam-6803	217	3	an	an	DET
ejpam-6803	217	4	accurate	accurate	ADJ
ejpam-6803	217	5	method	method	NOUN
ejpam-6803	217	6	a.	a.	NOUN
ejpam-6803	217	7	shafee	shafee	PROPN
ejpam-6803	217	8	et	et	PROPN
ejpam-6803	217	9	al	al	PROPN
ejpam-6803	217	10	.	.	PUNCT
ejpam-6803	217	11	/	/	SYM
ejpam-6803	217	12	eur	eur	PROPN
ejpam-6803	217	13	.	.	PUNCT
ejpam-6803	218	1	j.	j.	PROPN
ejpam-6803	218	2	pure	pure	PROPN
ejpam-6803	218	3	appl	appl	PROPN
ejpam-6803	218	4	.	.	PROPN
ejpam-6803	218	5	math	math	PROPN
ejpam-6803	218	6	,	,	PUNCT
ejpam-6803	218	7	18	18	NUM
ejpam-6803	218	8	(	(	PUNCT
ejpam-6803	218	9	4	4	NUM
ejpam-6803	218	10	)	)	PUNCT
ejpam-6803	218	11	(	(	PUNCT
ejpam-6803	218	12	2025	2025	NUM
ejpam-6803	218	13	)	)	PUNCT
ejpam-6803	218	14	,	,	PUNCT
ejpam-6803	218	15	6803	6803	NUM
ejpam-6803	218	16	16	16	NUM
ejpam-6803	218	17	of	of	ADP
ejpam-6803	218	18	18	18	NUM
ejpam-6803	218	19	for	for	ADP
ejpam-6803	218	20	the	the	DET
ejpam-6803	218	21	analysis	analysis	NOUN
ejpam-6803	218	22	and	and	CCONJ
ejpam-6803	218	23	simulation	simulation	NOUN
ejpam-6803	218	24	of	of	ADP
ejpam-6803	218	25	electrical	electrical	ADJ
ejpam-6803	218	26	r	r	NOUN
ejpam-6803	218	27	-	-	PUNCT
ejpam-6803	218	28	l	l	NOUN
ejpam-6803	218	29	circuits	circuit	NOUN
ejpam-6803	218	30	.	.	PUNCT
ejpam-6803	219	1	mathematical	mathematical	ADJ
ejpam-6803	219	2	methods	method	NOUN
ejpam-6803	219	3	in	in	ADP
ejpam-6803	219	4	the	the	DET
ejpam-6803	219	5	applied	apply	VERB
ejpam-6803	219	6	sciences	science	NOUN
ejpam-6803	219	7	,	,	PUNCT
ejpam-6803	219	8	46(7):8362–8371	46(7):8362–8371	NUM
ejpam-6803	219	9	,	,	PUNCT
ejpam-6803	219	10	2023	2023	NUM
ejpam-6803	219	11	.	.	PUNCT
ejpam-6803	220	1	[	[	X
ejpam-6803	220	2	11	11	NUM
ejpam-6803	220	3	]	]	PUNCT
ejpam-6803	220	4	m.	m.	NOUN
ejpam-6803	220	5	m.	m.	NOUN
ejpam-6803	220	6	khader	khader	PROPN
ejpam-6803	220	7	,	,	PUNCT
ejpam-6803	220	8	j.	j.	PROPN
ejpam-6803	220	9	f.	f.	PROPN
ejpam-6803	220	10	gomez	gomez	PROPN
ejpam-6803	220	11	-	-	PUNCT
ejpam-6803	220	12	aguilar	aguilar	PROPN
ejpam-6803	220	13	,	,	PUNCT
ejpam-6803	220	14	and	and	CCONJ
ejpam-6803	220	15	m.	m.	PROPN
ejpam-6803	220	16	adel	adel	PROPN
ejpam-6803	220	17	.	.	PUNCT
ejpam-6803	221	1	numerical	numerical	PROPN
ejpam-6803	221	2	study	study	PROPN
ejpam-6803	221	3	for	for	ADP
ejpam-6803	221	4	the	the	DET
ejpam-6803	221	5	fractional	fractional	PROPN
ejpam-6803	221	6	rl	rl	PROPN
ejpam-6803	221	7	,	,	PUNCT
ejpam-6803	221	8	rc	rc	PROPN
ejpam-6803	221	9	,	,	PUNCT
ejpam-6803	221	10	and	and	CCONJ
ejpam-6803	221	11	rlc	rlc	PROPN
ejpam-6803	221	12	electrical	electrical	ADJ
ejpam-6803	221	13	circuits	circuit	NOUN
ejpam-6803	221	14	using	use	VERB
ejpam-6803	221	15	legendre	legendre	PROPN
ejpam-6803	221	16	pseudo	pseudo	NOUN
ejpam-6803	221	17	-	-	ADJ
ejpam-6803	221	18	spectral	spectral	ADJ
ejpam-6803	221	19	method	method	NOUN
ejpam-6803	221	20	.	.	PUNCT
ejpam-6803	222	1	international	international	ADJ
ejpam-6803	222	2	journal	journal	PROPN
ejpam-6803	222	3	of	of	ADP
ejpam-6803	222	4	circuit	circuit	NOUN
ejpam-6803	222	5	theory	theory	NOUN
ejpam-6803	222	6	and	and	CCONJ
ejpam-6803	222	7	applications	application	NOUN
ejpam-6803	222	8	,	,	PUNCT
ejpam-6803	222	9	49(10):3266–3285	49(10):3266–3285	NUM
ejpam-6803	222	10	,	,	PUNCT
ejpam-6803	222	11	2021	2021	NUM
ejpam-6803	222	12	.	.	PUNCT
ejpam-6803	223	1	[	[	X
ejpam-6803	223	2	12	12	NUM
ejpam-6803	223	3	]	]	PUNCT
ejpam-6803	223	4	m.	m.	NOUN
ejpam-6803	223	5	adel	adel	PROPN
ejpam-6803	223	6	,	,	PUNCT
ejpam-6803	223	7	n.	n.	PROPN
ejpam-6803	223	8	h.	h.	PROPN
ejpam-6803	223	9	sweilam	sweilam	PROPN
ejpam-6803	223	10	,	,	PUNCT
ejpam-6803	223	11	m.	m.	NOUN
ejpam-6803	223	12	m.	m.	NOUN
ejpam-6803	223	13	khader	khader	PROPN
ejpam-6803	223	14	,	,	PUNCT
ejpam-6803	223	15	s.	s.	PROPN
ejpam-6803	223	16	m.	m.	PROPN
ejpam-6803	223	17	ahmed	ahmed	PROPN
ejpam-6803	223	18	,	,	PUNCT
ejpam-6803	223	19	h.	h.	PROPN
ejpam-6803	223	20	ahmad	ahmad	PROPN
ejpam-6803	223	21	,	,	PUNCT
ejpam-6803	223	22	and	and	CCONJ
ejpam-6803	223	23	t.	t.	NOUN
ejpam-6803	223	24	botmart	botmart	NOUN
ejpam-6803	223	25	.	.	PUNCT
ejpam-6803	224	1	numerical	numerical	PROPN
ejpam-6803	224	2	simulation	simulation	PROPN
ejpam-6803	224	3	using	use	VERB
ejpam-6803	224	4	the	the	DET
ejpam-6803	224	5	non	non	ADJ
ejpam-6803	224	6	-	-	ADJ
ejpam-6803	224	7	standard	standard	ADJ
ejpam-6803	224	8	weighted	weight	VERB
ejpam-6803	224	9	average	average	ADJ
ejpam-6803	224	10	fdm	fdm	NOUN
ejpam-6803	224	11	for	for	ADP
ejpam-6803	224	12	2dim	2dim	PROPN
ejpam-6803	224	13	variableorder	variableorder	NOUN
ejpam-6803	224	14	cable	cable	NOUN
ejpam-6803	224	15	equation	equation	NOUN
ejpam-6803	224	16	.	.	PUNCT
ejpam-6803	225	1	results	result	NOUN
ejpam-6803	225	2	in	in	ADP
ejpam-6803	225	3	physics	physics	NOUN
ejpam-6803	225	4	,	,	PUNCT
ejpam-6803	225	5	39:105682	39:105682	NOUN
ejpam-6803	225	6	,	,	PUNCT
ejpam-6803	225	7	2022	2022	NUM
ejpam-6803	225	8	.	.	PUNCT
ejpam-6803	226	1	[	[	X
ejpam-6803	226	2	13	13	NUM
ejpam-6803	226	3	]	]	X
ejpam-6803	226	4	n.	n.	PROPN
ejpam-6803	226	5	h.	h.	PROPN
ejpam-6803	226	6	sweilam	sweilam	PROPN
ejpam-6803	226	7	,	,	PUNCT
ejpam-6803	226	8	m.	m.	NOUN
ejpam-6803	226	9	m.	m.	NOUN
ejpam-6803	226	10	khader	khader	PROPN
ejpam-6803	226	11	,	,	PUNCT
ejpam-6803	226	12	and	and	CCONJ
ejpam-6803	226	13	m.	m.	PROPN
ejpam-6803	226	14	adel	adel	PROPN
ejpam-6803	226	15	.	.	PROPN
ejpam-6803	226	16	numerical	numerical	PROPN
ejpam-6803	226	17	simulation	simulation	PROPN
ejpam-6803	226	18	of	of	ADP
ejpam-6803	226	19	fractional	fractional	ADJ
ejpam-6803	226	20	cable	cable	NOUN
ejpam-6803	226	21	equation	equation	NOUN
ejpam-6803	226	22	of	of	ADP
ejpam-6803	226	23	spiny	spiny	ADJ
ejpam-6803	226	24	neuronal	neuronal	ADJ
ejpam-6803	226	25	dendrites	dendrite	NOUN
ejpam-6803	226	26	.	.	PUNCT
ejpam-6803	227	1	journal	journal	NOUN
ejpam-6803	227	2	of	of	ADP
ejpam-6803	227	3	advanced	advanced	ADJ
ejpam-6803	227	4	research	research	NOUN
ejpam-6803	227	5	,	,	PUNCT
ejpam-6803	227	6	5(2):253–259	5(2):253–259	NOUN
ejpam-6803	227	7	,	,	PUNCT
ejpam-6803	227	8	2014	2014	NUM
ejpam-6803	227	9	.	.	PUNCT
ejpam-6803	228	1	[	[	X
ejpam-6803	228	2	14	14	NUM
ejpam-6803	228	3	]	]	PUNCT
ejpam-6803	228	4	m.	m.	NOUN
ejpam-6803	228	5	m.	m.	NOUN
ejpam-6803	228	6	khader	khader	PROPN
ejpam-6803	228	7	and	and	CCONJ
ejpam-6803	228	8	m.	m.	PROPN
ejpam-6803	228	9	h.	h.	PROPN
ejpam-6803	228	10	adel	adel	PROPN
ejpam-6803	228	11	.	.	PUNCT
ejpam-6803	229	1	numerical	numerical	PROPN
ejpam-6803	229	2	solutions	solution	NOUN
ejpam-6803	229	3	of	of	ADP
ejpam-6803	229	4	fractional	fractional	ADJ
ejpam-6803	229	5	wave	wave	NOUN
ejpam-6803	229	6	equations	equation	NOUN
ejpam-6803	229	7	using	use	VERB
ejpam-6803	229	8	an	an	DET
ejpam-6803	229	9	efficient	efficient	ADJ
ejpam-6803	229	10	class	class	NOUN
ejpam-6803	229	11	of	of	ADP
ejpam-6803	229	12	fdm	fdm	NOUN
ejpam-6803	229	13	based	base	VERB
ejpam-6803	229	14	on	on	ADP
ejpam-6803	229	15	the	the	DET
ejpam-6803	229	16	hermite	hermite	ADJ
ejpam-6803	229	17	formula	formula	NOUN
ejpam-6803	229	18	.	.	PUNCT
ejpam-6803	230	1	advances	advance	NOUN
ejpam-6803	230	2	in	in	ADP
ejpam-6803	230	3	difference	difference	NOUN
ejpam-6803	230	4	equations	equation	NOUN
ejpam-6803	230	5	,	,	PUNCT
ejpam-6803	230	6	2016(1):34	2016(1):34	NUM
ejpam-6803	230	7	,	,	PUNCT
ejpam-6803	230	8	2016	2016	NUM
ejpam-6803	230	9	.	.	PUNCT
ejpam-6803	231	1	[	[	X
ejpam-6803	231	2	15	15	NUM
ejpam-6803	231	3	]	]	X
ejpam-6803	231	4	m.	m.	NOUN
ejpam-6803	231	5	m.	m.	NOUN
ejpam-6803	231	6	khader	khader	PROPN
ejpam-6803	231	7	and	and	CCONJ
ejpam-6803	231	8	m.	m.	PROPN
ejpam-6803	231	9	adel	adel	PROPN
ejpam-6803	231	10	.	.	PUNCT
ejpam-6803	232	1	analytical	analytical	ADJ
ejpam-6803	232	2	and	and	CCONJ
ejpam-6803	232	3	numerical	numerical	ADJ
ejpam-6803	232	4	validation	validation	NOUN
ejpam-6803	232	5	for	for	ADP
ejpam-6803	232	6	solving	solve	VERB
ejpam-6803	232	7	the	the	DET
ejpam-6803	232	8	fractional	fractional	PROPN
ejpam-6803	232	9	klein	klein	PROPN
ejpam-6803	232	10	-	-	PUNCT
ejpam-6803	232	11	gordon	gordon	PROPN
ejpam-6803	232	12	equation	equation	NOUN
ejpam-6803	232	13	using	use	VERB
ejpam-6803	232	14	the	the	DET
ejpam-6803	232	15	fractional	fractional	ADJ
ejpam-6803	232	16	complex	complex	ADJ
ejpam-6803	232	17	transform	transform	NOUN
ejpam-6803	232	18	and	and	CCONJ
ejpam-6803	232	19	variational	variational	ADJ
ejpam-6803	232	20	iteration	iteration	NOUN
ejpam-6803	232	21	methods	method	NOUN
ejpam-6803	232	22	.	.	PUNCT
ejpam-6803	233	1	nonlinear	nonlinear	ADJ
ejpam-6803	233	2	engineering	engineering	NOUN
ejpam-6803	233	3	,	,	PUNCT
ejpam-6803	233	4	5(3):141–145	5(3):141–145	NUM
ejpam-6803	233	5	,	,	PUNCT
ejpam-6803	233	6	2016	2016	NUM
ejpam-6803	233	7	.	.	PUNCT
ejpam-6803	234	1	[	[	X
ejpam-6803	234	2	16	16	NUM
ejpam-6803	234	3	]	]	X
ejpam-6803	234	4	c.	c.	PROPN
ejpam-6803	234	5	beck	beck	PROPN
ejpam-6803	234	6	,	,	PUNCT
ejpam-6803	234	7	m.	m.	NOUN
ejpam-6803	234	8	hutzenthaler	hutzenthaler	PROPN
ejpam-6803	234	9	,	,	PUNCT
ejpam-6803	234	10	a.	a.	NOUN
ejpam-6803	234	11	jentzen	jentzen	NOUN
ejpam-6803	234	12	,	,	PUNCT
ejpam-6803	234	13	and	and	CCONJ
ejpam-6803	234	14	b.	b.	PROPN
ejpam-6803	234	15	kuckuck	kuckuck	PROPN
ejpam-6803	234	16	.	.	PUNCT
ejpam-6803	235	1	an	an	DET
ejpam-6803	235	2	overview	overview	NOUN
ejpam-6803	235	3	on	on	ADP
ejpam-6803	235	4	deep	deep	ADJ
ejpam-6803	235	5	learning	learning	NOUN
ejpam-6803	235	6	-	-	PUNCT
ejpam-6803	235	7	based	base	VERB
ejpam-6803	235	8	approximation	approximation	NOUN
ejpam-6803	235	9	methods	method	NOUN
ejpam-6803	235	10	for	for	ADP
ejpam-6803	235	11	partial	partial	ADJ
ejpam-6803	235	12	differential	differential	NOUN
ejpam-6803	235	13	equations	equation	NOUN
ejpam-6803	235	14	,	,	PUNCT
ejpam-6803	235	15	2020	2020	NUM
ejpam-6803	235	16	.	.	PUNCT
ejpam-6803	236	1	arxiv:2012.12348	arxiv:2012.12348	VERB
ejpam-6803	236	2	.	.	PUNCT
ejpam-6803	237	1	[	[	X
ejpam-6803	237	2	17	17	NUM
ejpam-6803	237	3	]	]	X
ejpam-6803	237	4	j.	j.	PROPN
ejpam-6803	237	5	han	han	PROPN
ejpam-6803	237	6	,	,	PUNCT
ejpam-6803	237	7	a.	a.	NOUN
ejpam-6803	237	8	jentzen	jentzen	NOUN
ejpam-6803	237	9	,	,	PUNCT
ejpam-6803	237	10	and	and	CCONJ
ejpam-6803	237	11	w.	w.	PROPN
ejpam-6803	237	12	e.	e.	PROPN
ejpam-6803	237	13	solving	solve	VERB
ejpam-6803	237	14	high	high	ADJ
ejpam-6803	237	15	-	-	PUNCT
ejpam-6803	237	16	dimensional	dimensional	ADJ
ejpam-6803	237	17	partial	partial	ADJ
ejpam-6803	237	18	differential	differential	NOUN
ejpam-6803	237	19	equations	equation	NOUN
ejpam-6803	237	20	using	use	VERB
ejpam-6803	237	21	deep	deep	ADJ
ejpam-6803	237	22	learning	learning	NOUN
ejpam-6803	237	23	.	.	PUNCT
ejpam-6803	238	1	proceedings	proceeding	NOUN
ejpam-6803	238	2	of	of	ADP
ejpam-6803	238	3	the	the	DET
ejpam-6803	238	4	national	national	PROPN
ejpam-6803	238	5	academy	academy	PROPN
ejpam-6803	238	6	of	of	ADP
ejpam-6803	238	7	sciences	sciences	PROPN
ejpam-6803	238	8	,	,	PUNCT
ejpam-6803	238	9	115(34):8505–8510	115(34):8505–8510	NUM
ejpam-6803	238	10	,	,	PUNCT
ejpam-6803	238	11	2018	2018	NUM
ejpam-6803	238	12	.	.	PUNCT
ejpam-6803	239	1	[	[	X
ejpam-6803	239	2	18	18	NUM
ejpam-6803	239	3	]	]	X
ejpam-6803	239	4	y.	y.	PROPN
ejpam-6803	239	5	guo	guo	PROPN
ejpam-6803	239	6	,	,	PUNCT
ejpam-6803	239	7	x.	x.	PROPN
ejpam-6803	239	8	cao	cao	PROPN
ejpam-6803	239	9	,	,	PUNCT
ejpam-6803	239	10	b.	b.	PROPN
ejpam-6803	239	11	liu	liu	PROPN
ejpam-6803	239	12	,	,	PUNCT
ejpam-6803	239	13	and	and	CCONJ
ejpam-6803	239	14	m.	m.	PROPN
ejpam-6803	239	15	gao	gao	PROPN
ejpam-6803	239	16	.	.	PUNCT
ejpam-6803	240	1	solving	solve	VERB
ejpam-6803	240	2	partial	partial	ADJ
ejpam-6803	240	3	differential	differential	ADJ
ejpam-6803	240	4	equations	equation	NOUN
ejpam-6803	240	5	using	use	VERB
ejpam-6803	240	6	deep	deep	ADJ
ejpam-6803	240	7	learning	learning	NOUN
ejpam-6803	240	8	and	and	CCONJ
ejpam-6803	240	9	physical	physical	ADJ
ejpam-6803	240	10	constraints	constraint	NOUN
ejpam-6803	240	11	.	.	PUNCT
ejpam-6803	241	1	applied	apply	VERB
ejpam-6803	241	2	sciences	science	NOUN
ejpam-6803	241	3	,	,	PUNCT
ejpam-6803	241	4	10(17):5917	10(17):5917	NUM
ejpam-6803	241	5	,	,	PUNCT
ejpam-6803	241	6	2020	2020	NUM
ejpam-6803	241	7	.	.	PUNCT
ejpam-6803	242	1	[	[	X
ejpam-6803	242	2	19	19	NUM
ejpam-6803	242	3	]	]	X
ejpam-6803	242	4	g.	g.	PROPN
ejpam-6803	242	5	cybenko	cybenko	PROPN
ejpam-6803	242	6	.	.	PUNCT
ejpam-6803	243	1	approximation	approximation	NOUN
ejpam-6803	243	2	by	by	ADP
ejpam-6803	243	3	superpositions	superposition	NOUN
ejpam-6803	243	4	of	of	ADP
ejpam-6803	243	5	a	a	DET
ejpam-6803	243	6	sigmoidal	sigmoidal	NOUN
ejpam-6803	243	7	function	function	NOUN
ejpam-6803	243	8	.	.	PUNCT
ejpam-6803	244	1	mathematics	mathematic	NOUN
ejpam-6803	244	2	of	of	ADP
ejpam-6803	244	3	control	control	NOUN
ejpam-6803	244	4	,	,	PUNCT
ejpam-6803	244	5	signals	signal	NOUN
ejpam-6803	244	6	and	and	CCONJ
ejpam-6803	244	7	systems	system	NOUN
ejpam-6803	244	8	,	,	PUNCT
ejpam-6803	244	9	2(4):303–314	2(4):303–314	NUM
ejpam-6803	244	10	,	,	PUNCT
ejpam-6803	244	11	1989	1989	NUM
ejpam-6803	244	12	.	.	PUNCT
ejpam-6803	245	1	[	[	X
ejpam-6803	245	2	20	20	NUM
ejpam-6803	245	3	]	]	PUNCT
ejpam-6803	245	4	k.	k.	PROPN
ejpam-6803	245	5	hornik	hornik	PROPN
ejpam-6803	245	6	,	,	PUNCT
ejpam-6803	245	7	m.	m.	NOUN
ejpam-6803	245	8	stinchcombe	stinchcombe	PROPN
ejpam-6803	245	9	,	,	PUNCT
ejpam-6803	245	10	and	and	CCONJ
ejpam-6803	245	11	h.	h.	PROPN
ejpam-6803	245	12	white	white	PROPN
ejpam-6803	245	13	.	.	PUNCT
ejpam-6803	246	1	multilayer	multilayer	ADJ
ejpam-6803	246	2	feedforward	feedforward	NOUN
ejpam-6803	246	3	networks	network	NOUN
ejpam-6803	246	4	are	be	AUX
ejpam-6803	246	5	universal	universal	ADJ
ejpam-6803	246	6	approximators	approximator	NOUN
ejpam-6803	246	7	.	.	PUNCT
ejpam-6803	247	1	neural	neural	ADJ
ejpam-6803	247	2	networks	network	NOUN
ejpam-6803	247	3	,	,	PUNCT
ejpam-6803	247	4	2(5):359–366	2(5):359–366	NUM
ejpam-6803	247	5	,	,	PUNCT
ejpam-6803	247	6	1989	1989	NUM
ejpam-6803	247	7	.	.	PUNCT
ejpam-6803	248	1	[	[	X
ejpam-6803	248	2	21	21	NUM
ejpam-6803	248	3	]	]	X
ejpam-6803	248	4	r.	r.	PROPN
ejpam-6803	248	5	t.	t.	PROPN
ejpam-6803	248	6	chen	chen	PROPN
ejpam-6803	248	7	,	,	PUNCT
ejpam-6803	248	8	y.	y.	PROPN
ejpam-6803	248	9	rubanova	rubanova	PROPN
ejpam-6803	248	10	,	,	PUNCT
ejpam-6803	248	11	j.	j.	PROPN
ejpam-6803	248	12	bettencourt	bettencourt	PROPN
ejpam-6803	248	13	,	,	PUNCT
ejpam-6803	248	14	and	and	CCONJ
ejpam-6803	248	15	d.	d.	PROPN
ejpam-6803	248	16	k.	k.	PROPN
ejpam-6803	248	17	duvenaud	duvenaud	PROPN
ejpam-6803	248	18	.	.	PUNCT
ejpam-6803	249	1	neural	neural	ADJ
ejpam-6803	249	2	ordinary	ordinary	ADJ
ejpam-6803	249	3	differential	differential	ADJ
ejpam-6803	249	4	equations	equation	NOUN
ejpam-6803	249	5	.	.	PUNCT
ejpam-6803	250	1	advances	advance	NOUN
ejpam-6803	250	2	in	in	ADP
ejpam-6803	250	3	neural	neural	ADJ
ejpam-6803	250	4	information	information	NOUN
ejpam-6803	250	5	processing	processing	NOUN
ejpam-6803	250	6	systems	system	NOUN
ejpam-6803	250	7	,	,	PUNCT
ejpam-6803	250	8	31	31	NUM
ejpam-6803	250	9	,	,	PUNCT
ejpam-6803	250	10	2018	2018	NUM
ejpam-6803	250	11	.	.	PUNCT
ejpam-6803	251	1	[	[	X
ejpam-6803	251	2	22	22	NUM
ejpam-6803	251	3	]	]	PUNCT
ejpam-6803	251	4	j.	j.	PROPN
ejpam-6803	251	5	sirignano	sirignano	PROPN
ejpam-6803	251	6	and	and	CCONJ
ejpam-6803	251	7	k.	k.	PROPN
ejpam-6803	251	8	spiliopoulos	spiliopoulos	PROPN
ejpam-6803	251	9	.	.	PUNCT
ejpam-6803	252	1	dgm	dgm	PROPN
ejpam-6803	252	2	:	:	PUNCT
ejpam-6803	252	3	a	a	DET
ejpam-6803	252	4	deep	deep	ADJ
ejpam-6803	252	5	learning	learning	NOUN
ejpam-6803	252	6	algorithm	algorithm	NOUN
ejpam-6803	252	7	for	for	ADP
ejpam-6803	252	8	solving	solve	VERB
ejpam-6803	252	9	partial	partial	ADJ
ejpam-6803	252	10	differential	differential	ADJ
ejpam-6803	252	11	equations	equation	NOUN
ejpam-6803	252	12	.	.	PUNCT
ejpam-6803	253	1	journal	journal	NOUN
ejpam-6803	253	2	of	of	ADP
ejpam-6803	253	3	computational	computational	ADJ
ejpam-6803	253	4	physics	physics	NOUN
ejpam-6803	253	5	,	,	PUNCT
ejpam-6803	253	6	375:1339–1364	375:1339–1364	NUM
ejpam-6803	253	7	,	,	PUNCT
ejpam-6803	253	8	2018	2018	NUM
ejpam-6803	253	9	.	.	PUNCT
ejpam-6803	254	1	[	[	X
ejpam-6803	254	2	23	23	NUM
ejpam-6803	254	3	]	]	PUNCT
ejpam-6803	254	4	j.	j.	PROPN
ejpam-6803	254	5	han	han	PROPN
ejpam-6803	254	6	and	and	CCONJ
ejpam-6803	254	7	j.	j.	PROPN
ejpam-6803	254	8	long	long	PROPN
ejpam-6803	254	9	.	.	PUNCT
ejpam-6803	255	1	convergence	convergence	NOUN
ejpam-6803	255	2	of	of	ADP
ejpam-6803	255	3	the	the	DET
ejpam-6803	255	4	deep	deep	ADJ
ejpam-6803	255	5	bsde	bsde	NOUN
ejpam-6803	255	6	method	method	NOUN
ejpam-6803	255	7	for	for	ADP
ejpam-6803	255	8	coupled	couple	VERB
ejpam-6803	255	9	fbsdes	fbsde	NOUN
ejpam-6803	255	10	.	.	PUNCT
ejpam-6803	256	1	probability	probability	NOUN
ejpam-6803	256	2	,	,	PUNCT
ejpam-6803	256	3	uncertainty	uncertainty	NOUN
ejpam-6803	256	4	and	and	CCONJ
ejpam-6803	256	5	quantitative	quantitative	ADJ
ejpam-6803	256	6	risk	risk	NOUN
ejpam-6803	256	7	,	,	PUNCT
ejpam-6803	256	8	5(1):5	5(1):5	NUM
ejpam-6803	256	9	,	,	PUNCT
ejpam-6803	256	10	2020	2020	NUM
ejpam-6803	256	11	.	.	PUNCT
ejpam-6803	257	1	[	[	X
ejpam-6803	257	2	24	24	NUM
ejpam-6803	257	3	]	]	PUNCT
ejpam-6803	257	4	m.	m.	NOUN
ejpam-6803	257	5	raissi	raissi	NOUN
ejpam-6803	257	6	,	,	PUNCT
ejpam-6803	257	7	p.	p.	NOUN
ejpam-6803	257	8	perdikaris	perdikaris	NOUN
ejpam-6803	257	9	,	,	PUNCT
ejpam-6803	257	10	and	and	CCONJ
ejpam-6803	257	11	g.	g.	PROPN
ejpam-6803	257	12	e.	e.	PROPN
ejpam-6803	257	13	karniadakis	karniadakis	PROPN
ejpam-6803	257	14	.	.	PUNCT
ejpam-6803	258	1	physics	physics	NOUN
ejpam-6803	258	2	-	-	PUNCT
ejpam-6803	258	3	informed	inform	VERB
ejpam-6803	258	4	neural	neural	ADJ
ejpam-6803	258	5	networks	network	NOUN
ejpam-6803	258	6	:	:	PUNCT
ejpam-6803	258	7	a	a	DET
ejpam-6803	258	8	deep	deep	ADJ
ejpam-6803	258	9	learning	learning	NOUN
ejpam-6803	258	10	framework	framework	NOUN
ejpam-6803	258	11	for	for	ADP
ejpam-6803	258	12	solving	solve	VERB
ejpam-6803	258	13	forward	forward	ADV
ejpam-6803	258	14	and	and	CCONJ
ejpam-6803	258	15	inverse	inverse	NOUN
ejpam-6803	258	16	problems	problem	NOUN
ejpam-6803	258	17	involving	involve	VERB
ejpam-6803	258	18	nonlinear	nonlinear	ADJ
ejpam-6803	258	19	partial	partial	ADJ
ejpam-6803	258	20	differential	differential	NOUN
ejpam-6803	258	21	equations	equation	NOUN
ejpam-6803	258	22	.	.	PUNCT
ejpam-6803	259	1	journal	journal	NOUN
ejpam-6803	259	2	of	of	ADP
ejpam-6803	259	3	computational	computational	ADJ
ejpam-6803	259	4	physics	physics	NOUN
ejpam-6803	259	5	,	,	PUNCT
ejpam-6803	259	6	378:686–707	378:686–707	NUM
ejpam-6803	259	7	,	,	PUNCT
ejpam-6803	259	8	2019	2019	NUM
ejpam-6803	259	9	.	.	PUNCT
ejpam-6803	260	1	[	[	X
ejpam-6803	260	2	25	25	NUM
ejpam-6803	260	3	]	]	PUNCT
ejpam-6803	260	4	l.	l.	PROPN
ejpam-6803	260	5	lu	lu	PROPN
ejpam-6803	260	6	,	,	PUNCT
ejpam-6803	260	7	x.	x.	PROPN
ejpam-6803	260	8	meng	meng	PROPN
ejpam-6803	260	9	,	,	PUNCT
ejpam-6803	260	10	z.	z.	PROPN
ejpam-6803	260	11	mao	mao	PROPN
ejpam-6803	260	12	,	,	PUNCT
ejpam-6803	260	13	and	and	CCONJ
ejpam-6803	260	14	g.	g.	PROPN
ejpam-6803	260	15	e.	e.	PROPN
ejpam-6803	260	16	karniadakis	karniadakis	PROPN
ejpam-6803	260	17	.	.	PUNCT
ejpam-6803	261	1	deepxde	deepxde	NOUN
ejpam-6803	261	2	:	:	PUNCT
ejpam-6803	261	3	a	a	DET
ejpam-6803	261	4	deep	deep	ADJ
ejpam-6803	261	5	learning	learning	NOUN
ejpam-6803	261	6	library	library	NOUN
ejpam-6803	261	7	for	for	ADP
ejpam-6803	261	8	solving	solve	VERB
ejpam-6803	261	9	differential	differential	ADJ
ejpam-6803	261	10	equations	equation	NOUN
ejpam-6803	261	11	.	.	PUNCT
ejpam-6803	262	1	siam	siam	PROPN
ejpam-6803	262	2	review	review	PROPN
ejpam-6803	262	3	,	,	PUNCT
ejpam-6803	262	4	63(1):208–228	63(1):208–228	PROPN
ejpam-6803	262	5	,	,	PUNCT
ejpam-6803	262	6	2021	2021	NUM
ejpam-6803	262	7	.	.	PUNCT
ejpam-6803	263	1	[	[	X
ejpam-6803	263	2	26	26	NUM
ejpam-6803	263	3	]	]	PUNCT
ejpam-6803	263	4	h.	h.	PROPN
ejpam-6803	263	5	eivazi	eivazi	PROPN
ejpam-6803	263	6	,	,	PUNCT
ejpam-6803	263	7	m.	m.	NOUN
ejpam-6803	263	8	tahani	tahani	PROPN
ejpam-6803	263	9	,	,	PUNCT
ejpam-6803	263	10	p.	p.	NOUN
ejpam-6803	263	11	schlatter	schlatter	PROPN
ejpam-6803	263	12	,	,	PUNCT
ejpam-6803	263	13	and	and	CCONJ
ejpam-6803	263	14	r.	r.	PROPN
ejpam-6803	263	15	vinuesa	vinuesa	PROPN
ejpam-6803	263	16	.	.	PUNCT
ejpam-6803	264	1	physics	physics	NOUN
ejpam-6803	264	2	-	-	PUNCT
ejpam-6803	264	3	informed	inform	VERB
ejpam-6803	264	4	neural	neural	ADJ
ejpam-6803	264	5	networks	network	NOUN
ejpam-6803	264	6	for	for	ADP
ejpam-6803	264	7	solving	solve	VERB
ejpam-6803	264	8	reynolds	reynold	NOUN
ejpam-6803	264	9	-	-	PUNCT
ejpam-6803	264	10	averaged	average	VERB
ejpam-6803	264	11	navier	navier	NOUN
ejpam-6803	264	12	-	-	PUNCT
ejpam-6803	264	13	stokes	stoke	NOUN
ejpam-6803	264	14	equations	equation	NOUN
ejpam-6803	264	15	.	.	PUNCT
ejpam-6803	265	1	physics	physics	PROPN
ejpam-6803	265	2	of	of	ADP
ejpam-6803	265	3	fluids	fluid	NOUN
ejpam-6803	265	4	,	,	PUNCT
ejpam-6803	265	5	34(7	34(7	NUM
ejpam-6803	265	6	)	)	PUNCT
ejpam-6803	265	7	,	,	PUNCT
ejpam-6803	265	8	2022	2022	NUM
ejpam-6803	265	9	.	.	PUNCT
ejpam-6803	266	1	[	[	X
ejpam-6803	266	2	27	27	NUM
ejpam-6803	266	3	]	]	X
ejpam-6803	266	4	r.	r.	PROPN
ejpam-6803	266	5	d.	d.	PROPN
ejpam-6803	266	6	ortiz	ortiz	PROPN
ejpam-6803	266	7	ortiz	ortiz	PROPN
ejpam-6803	266	8	,	,	PUNCT
ejpam-6803	266	9	o.	o.	PROPN
ejpam-6803	266	10	martinez	martinez	PROPN
ejpam-6803	266	11	nunez	nunez	PROPN
ejpam-6803	266	12	,	,	PUNCT
ejpam-6803	266	13	and	and	CCONJ
ejpam-6803	266	14	a.	a.	NOUN
ejpam-6803	266	15	m.	m.	NOUN
ejpam-6803	266	16	marin	marin	PROPN
ejpam-6803	266	17	ramirz	ramirz	PROPN
ejpam-6803	266	18	.	.	PUNCT
ejpam-6803	267	1	solving	solve	VERB
ejpam-6803	267	2	viscous	viscous	ADJ
ejpam-6803	267	3	a.	a.	NOUN
ejpam-6803	267	4	shafee	shafee	PROPN
ejpam-6803	267	5	et	et	PROPN
ejpam-6803	267	6	al	al	PROPN
ejpam-6803	267	7	.	.	PUNCT
ejpam-6803	267	8	/	/	SYM
ejpam-6803	267	9	eur	eur	PROPN
ejpam-6803	267	10	.	.	PUNCT
ejpam-6803	268	1	j.	j.	PROPN
ejpam-6803	268	2	pure	pure	PROPN
ejpam-6803	268	3	appl	appl	PROPN
ejpam-6803	268	4	.	.	PROPN
ejpam-6803	268	5	math	math	PROPN
ejpam-6803	268	6	,	,	PUNCT
ejpam-6803	268	7	18	18	NUM
ejpam-6803	268	8	(	(	PUNCT
ejpam-6803	268	9	4	4	NUM
ejpam-6803	268	10	)	)	PUNCT
ejpam-6803	268	11	(	(	PUNCT
ejpam-6803	268	12	2025	2025	NUM
ejpam-6803	268	13	)	)	PUNCT
ejpam-6803	268	14	,	,	PUNCT
ejpam-6803	268	15	6803	6803	NUM
ejpam-6803	268	16	17	17	NUM
ejpam-6803	268	17	of	of	ADP
ejpam-6803	268	18	18	18	NUM
ejpam-6803	268	19	burgers	burger	NOUN
ejpam-6803	268	20	’	'	PUNCT
ejpam-6803	268	21	equation	equation	NOUN
ejpam-6803	268	22	:	:	PUNCT
ejpam-6803	268	23	hybrid	hybrid	ADJ
ejpam-6803	268	24	approach	approach	NOUN
ejpam-6803	268	25	combining	combine	VERB
ejpam-6803	268	26	boundary	boundary	ADJ
ejpam-6803	268	27	layer	layer	NOUN
ejpam-6803	268	28	theory	theory	NOUN
ejpam-6803	268	29	and	and	CCONJ
ejpam-6803	268	30	physicsinformed	physicsinforme	VERB
ejpam-6803	268	31	neural	neural	ADJ
ejpam-6803	268	32	networks	network	NOUN
ejpam-6803	268	33	.	.	PUNCT
ejpam-6803	269	1	mathematics	mathematic	NOUN
ejpam-6803	269	2	,	,	PUNCT
ejpam-6803	269	3	12(21):3430	12(21):3430	NUM
ejpam-6803	269	4	,	,	PUNCT
ejpam-6803	269	5	2024	2024	NUM
ejpam-6803	269	6	.	.	PUNCT
ejpam-6803	270	1	[	[	X
ejpam-6803	270	2	28	28	NUM
ejpam-6803	270	3	]	]	X
ejpam-6803	270	4	m.	m.	NOUN
ejpam-6803	270	5	raissi	raissi	PROPN
ejpam-6803	270	6	and	and	CCONJ
ejpam-6803	270	7	g.	g.	PROPN
ejpam-6803	270	8	e.	e.	PROPN
ejpam-6803	270	9	karniadakis	karniadakis	PROPN
ejpam-6803	270	10	.	.	PUNCT
ejpam-6803	271	1	hidden	hide	VERB
ejpam-6803	271	2	physics	physics	NOUN
ejpam-6803	271	3	models	model	NOUN
ejpam-6803	271	4	:	:	PUNCT
ejpam-6803	271	5	machine	machine	NOUN
ejpam-6803	271	6	learning	learning	NOUN
ejpam-6803	271	7	of	of	ADP
ejpam-6803	271	8	nonlinear	nonlinear	ADJ
ejpam-6803	271	9	partial	partial	ADJ
ejpam-6803	271	10	differential	differential	NOUN
ejpam-6803	271	11	equations	equation	NOUN
ejpam-6803	271	12	.	.	PUNCT
ejpam-6803	272	1	journal	journal	NOUN
ejpam-6803	272	2	of	of	ADP
ejpam-6803	272	3	computational	computational	ADJ
ejpam-6803	272	4	physics	physics	NOUN
ejpam-6803	272	5	,	,	PUNCT
ejpam-6803	272	6	357:125–141	357:125–141	NUM
ejpam-6803	272	7	,	,	PUNCT
ejpam-6803	272	8	2018	2018	NUM
ejpam-6803	272	9	.	.	PUNCT
ejpam-6803	273	1	[	[	X
ejpam-6803	273	2	29	29	NUM
ejpam-6803	273	3	]	]	X
ejpam-6803	273	4	r.	r.	PROPN
ejpam-6803	273	5	gao	gao	PROPN
ejpam-6803	273	6	,	,	PUNCT
ejpam-6803	273	7	w.	w.	PROPN
ejpam-6803	273	8	hu	hu	PROPN
ejpam-6803	273	9	,	,	PUNCT
ejpam-6803	273	10	j.	j.	PROPN
ejpam-6803	273	11	fei	fei	PROPN
ejpam-6803	273	12	,	,	PUNCT
ejpam-6803	273	13	and	and	CCONJ
ejpam-6803	273	14	h.	h.	PROPN
ejpam-6803	273	15	wu	wu	PROPN
ejpam-6803	273	16	.	.	PUNCT
ejpam-6803	274	1	boussinesq	boussinesq	ADJ
ejpam-6803	274	2	equation	equation	NOUN
ejpam-6803	274	3	solved	solve	VERB
ejpam-6803	274	4	by	by	ADP
ejpam-6803	274	5	the	the	DET
ejpam-6803	274	6	physics	physics	NOUN
ejpam-6803	274	7	-	-	PUNCT
ejpam-6803	274	8	informed	inform	VERB
ejpam-6803	274	9	neural	neural	ADJ
ejpam-6803	274	10	networks	network	NOUN
ejpam-6803	274	11	.	.	PUNCT
ejpam-6803	275	1	nonlinear	nonlinear	ADJ
ejpam-6803	275	2	dynamics	dynamic	NOUN
ejpam-6803	275	3	,	,	PUNCT
ejpam-6803	275	4	111(16):15279–15291	111(16):15279–15291	NUM
ejpam-6803	275	5	,	,	PUNCT
ejpam-6803	275	6	2023	2023	NUM
ejpam-6803	275	7	.	.	PUNCT
ejpam-6803	276	1	[	[	X
ejpam-6803	276	2	30	30	NUM
ejpam-6803	276	3	]	]	X
ejpam-6803	276	4	g.	g.	PROPN
ejpam-6803	276	5	pang	pang	PROPN
ejpam-6803	276	6	,	,	PUNCT
ejpam-6803	276	7	l.	l.	PROPN
ejpam-6803	276	8	lu	lu	PROPN
ejpam-6803	276	9	,	,	PUNCT
ejpam-6803	276	10	and	and	CCONJ
ejpam-6803	276	11	g.	g.	PROPN
ejpam-6803	276	12	e.	e.	PROPN
ejpam-6803	276	13	karniadakis	karniadakis	PROPN
ejpam-6803	276	14	.	.	PUNCT
ejpam-6803	277	1	fpinns	fpinns	PROPN
ejpam-6803	277	2	:	:	PUNCT
ejpam-6803	277	3	fractional	fractional	ADJ
ejpam-6803	277	4	physics	physics	NOUN
ejpam-6803	277	5	-	-	PUNCT
ejpam-6803	277	6	informed	inform	VERB
ejpam-6803	277	7	neural	neural	ADJ
ejpam-6803	277	8	networks	network	NOUN
ejpam-6803	277	9	.	.	PUNCT
ejpam-6803	278	1	siam	siam	PROPN
ejpam-6803	278	2	journal	journal	PROPN
ejpam-6803	278	3	on	on	ADP
ejpam-6803	278	4	scientific	scientific	ADJ
ejpam-6803	278	5	computing	computing	NOUN
ejpam-6803	278	6	,	,	PUNCT
ejpam-6803	278	7	41(4):a2603	41(4):a2603	PROPN
ejpam-6803	278	8	–	–	PUNCT
ejpam-6803	278	9	a2626	a2626	PROPN
ejpam-6803	278	10	,	,	PUNCT
ejpam-6803	278	11	2019	2019	NUM
ejpam-6803	278	12	.	.	PUNCT
ejpam-6803	279	1	[	[	X
ejpam-6803	279	2	31	31	NUM
ejpam-6803	279	3	]	]	PUNCT
ejpam-6803	279	4	h.	h.	PROPN
ejpam-6803	279	5	pandey	pandey	PROPN
ejpam-6803	279	6	,	,	PUNCT
ejpam-6803	279	7	a.	a.	PROPN
ejpam-6803	279	8	singh	singh	PROPN
ejpam-6803	279	9	,	,	PUNCT
ejpam-6803	279	10	and	and	CCONJ
ejpam-6803	279	11	r.	r.	PROPN
ejpam-6803	279	12	behera	behera	PROPN
ejpam-6803	279	13	.	.	PUNCT
ejpam-6803	280	1	an	an	DET
ejpam-6803	280	2	efficient	efficient	ADJ
ejpam-6803	280	3	wavelet	wavelet	NOUN
ejpam-6803	280	4	-	-	PUNCT
ejpam-6803	280	5	based	base	VERB
ejpam-6803	280	6	physics	physics	NOUN
ejpam-6803	280	7	-	-	PUNCT
ejpam-6803	280	8	informed	inform	VERB
ejpam-6803	280	9	neural	neural	ADJ
ejpam-6803	280	10	networks	network	NOUN
ejpam-6803	280	11	for	for	ADP
ejpam-6803	280	12	singularly	singularly	ADV
ejpam-6803	280	13	perturbed	perturb	VERB
ejpam-6803	280	14	problems	problem	NOUN
ejpam-6803	280	15	,	,	PUNCT
ejpam-6803	280	16	2024	2024	NUM
ejpam-6803	280	17	.	.	PUNCT
ejpam-6803	280	18	arxiv:2409.11847	arxiv:2409.11847	NOUN
ejpam-6803	280	19	.	.	PUNCT
ejpam-6803	281	1	[	[	X
ejpam-6803	281	2	32	32	NUM
ejpam-6803	281	3	]	]	PUNCT
ejpam-6803	281	4	h.	h.	PROPN
ejpam-6803	281	5	zhang	zhang	PROPN
ejpam-6803	281	6	,	,	PUNCT
ejpam-6803	281	7	d.	d.	PROPN
ejpam-6803	281	8	yu	yu	PROPN
ejpam-6803	281	9	,	,	PUNCT
ejpam-6803	281	10	m.	m.	NOUN
ejpam-6803	281	11	yi	yi	PROPN
ejpam-6803	281	12	,	,	PUNCT
ejpam-6803	281	13	w.	w.	PROPN
ejpam-6803	281	14	chen	chen	PROPN
ejpam-6803	281	15	,	,	PUNCT
ejpam-6803	281	16	and	and	CCONJ
ejpam-6803	281	17	t.	t.	PROPN
ejpam-6803	281	18	y.	y.	PROPN
ejpam-6803	281	19	liu	liu	PROPN
ejpam-6803	281	20	.	.	PUNCT
ejpam-6803	282	1	stability	stability	NOUN
ejpam-6803	282	2	and	and	CCONJ
ejpam-6803	282	3	convergence	convergence	NOUN
ejpam-6803	282	4	theory	theory	NOUN
ejpam-6803	282	5	for	for	ADP
ejpam-6803	282	6	learning	learn	VERB
ejpam-6803	282	7	resnet	resnet	NOUN
ejpam-6803	282	8	:	:	PUNCT
ejpam-6803	282	9	a	a	DET
ejpam-6803	282	10	full	full	ADJ
ejpam-6803	282	11	characterization	characterization	NOUN
ejpam-6803	282	12	.	.	PUNCT
ejpam-6803	283	1	2019	2019	NUM
ejpam-6803	283	2	.	.	PUNCT
ejpam-6803	284	1	[	[	X
ejpam-6803	284	2	33	33	NUM
ejpam-6803	284	3	]	]	X
ejpam-6803	284	4	y.	y.	PROPN
ejpam-6803	284	5	wang	wang	PROPN
ejpam-6803	284	6	and	and	CCONJ
ejpam-6803	284	7	l.	l.	PROPN
ejpam-6803	284	8	zhong	zhong	PROPN
ejpam-6803	284	9	.	.	PUNCT
ejpam-6803	285	1	nas	nas	PROPN
ejpam-6803	285	2	-	-	PUNCT
ejpam-6803	285	3	pinn	pinn	NOUN
ejpam-6803	285	4	:	:	PUNCT
ejpam-6803	285	5	neural	neural	ADJ
ejpam-6803	285	6	architecture	architecture	NOUN
ejpam-6803	285	7	search	search	NOUN
ejpam-6803	285	8	-	-	PUNCT
ejpam-6803	285	9	guided	guide	VERB
ejpam-6803	285	10	physics	physics	NOUN
ejpam-6803	285	11	-	-	PUNCT
ejpam-6803	285	12	informed	inform	VERB
ejpam-6803	285	13	neural	neural	ADJ
ejpam-6803	285	14	network	network	NOUN
ejpam-6803	285	15	for	for	ADP
ejpam-6803	285	16	solving	solve	VERB
ejpam-6803	285	17	pdes	pde	NOUN
ejpam-6803	285	18	.	.	PUNCT
ejpam-6803	286	1	journal	journal	NOUN
ejpam-6803	286	2	of	of	ADP
ejpam-6803	286	3	computational	computational	ADJ
ejpam-6803	286	4	physics	physics	NOUN
ejpam-6803	286	5	,	,	PUNCT
ejpam-6803	286	6	496:112603	496:112603	PROPN
ejpam-6803	286	7	,	,	PUNCT
ejpam-6803	286	8	2024	2024	NUM
ejpam-6803	286	9	.	.	PUNCT
ejpam-6803	287	1	[	[	X
ejpam-6803	287	2	34	34	NUM
ejpam-6803	287	3	]	]	PUNCT
ejpam-6803	287	4	a.	a.	NOUN
ejpam-6803	287	5	tanvir	tanvir	PROPN
ejpam-6803	287	6	.	.	PUNCT
ejpam-6803	288	1	reconstruction	reconstruction	NOUN
ejpam-6803	288	2	of	of	ADP
ejpam-6803	288	3	super	super	ADJ
ejpam-6803	288	4	-	-	ADJ
ejpam-6803	288	5	resolution	resolution	ADJ
ejpam-6803	288	6	image	image	NOUN
ejpam-6803	288	7	using	use	VERB
ejpam-6803	288	8	wavelet	wavelet	NOUN
ejpam-6803	288	9	residual	residual	ADJ
ejpam-6803	288	10	convolutional	convolutional	ADJ
ejpam-6803	288	11	neural	neural	ADJ
ejpam-6803	288	12	networks	network	NOUN
ejpam-6803	288	13	.	.	PUNCT
ejpam-6803	289	1	2023	2023	NUM
ejpam-6803	289	2	.	.	PUNCT
ejpam-6803	290	1	[	[	X
ejpam-6803	290	2	35	35	NUM
ejpam-6803	290	3	]	]	PUNCT
ejpam-6803	290	4	z.	z.	PROPN
ejpam-6803	290	5	li	li	PROPN
ejpam-6803	290	6	,	,	PUNCT
ejpam-6803	290	7	n.	n.	PROPN
ejpam-6803	290	8	kovachki	kovachki	PROPN
ejpam-6803	290	9	,	,	PUNCT
ejpam-6803	290	10	k.	k.	PROPN
ejpam-6803	290	11	azizzadenesheli	azizzadenesheli	PROPN
ejpam-6803	290	12	,	,	PUNCT
ejpam-6803	290	13	b.	b.	PROPN
ejpam-6803	290	14	liu	liu	PROPN
ejpam-6803	290	15	,	,	PUNCT
ejpam-6803	290	16	k.	k.	PROPN
ejpam-6803	290	17	bhattacharya	bhattacharya	PROPN
ejpam-6803	290	18	,	,	PUNCT
ejpam-6803	290	19	a.	a.	PROPN
ejpam-6803	290	20	stuart	stuart	PROPN
ejpam-6803	290	21	,	,	PUNCT
ejpam-6803	290	22	and	and	CCONJ
ejpam-6803	290	23	a.	a.	NOUN
ejpam-6803	290	24	anandkumar	anandkumar	PROPN
ejpam-6803	290	25	.	.	PUNCT
ejpam-6803	291	1	fourier	fourier	PROPN
ejpam-6803	291	2	neural	neural	ADJ
ejpam-6803	291	3	operator	operator	NOUN
ejpam-6803	291	4	for	for	ADP
ejpam-6803	291	5	parametric	parametric	ADJ
ejpam-6803	291	6	partial	partial	ADJ
ejpam-6803	291	7	differential	differential	NOUN
ejpam-6803	291	8	equations	equation	NOUN
ejpam-6803	291	9	,	,	PUNCT
ejpam-6803	291	10	2020	2020	NUM
ejpam-6803	291	11	.	.	PUNCT
ejpam-6803	292	1	arxiv:2010.08895	arxiv:2010.08895	VERB
ejpam-6803	292	2	.	.	PUNCT
ejpam-6803	293	1	[	[	X
ejpam-6803	293	2	36	36	NUM
ejpam-6803	293	3	]	]	X
ejpam-6803	293	4	y.	y.	PROPN
ejpam-6803	293	5	dai	dai	PROPN
ejpam-6803	293	6	,	,	PUNCT
ejpam-6803	293	7	y.	y.	PROPN
ejpam-6803	293	8	an	an	PROPN
ejpam-6803	293	9	,	,	PUNCT
ejpam-6803	293	10	z.	z.	PROPN
ejpam-6803	293	11	li	li	PROPN
ejpam-6803	293	12	,	,	PUNCT
ejpam-6803	293	13	j.	j.	PROPN
ejpam-6803	293	14	zhang	zhang	PROPN
ejpam-6803	293	15	,	,	PUNCT
ejpam-6803	293	16	and	and	CCONJ
ejpam-6803	293	17	c.	c.	PROPN
ejpam-6803	293	18	yu	yu	PROPN
ejpam-6803	293	19	.	.	PROPN
ejpam-6803	294	1	fourier	fourier	PROPN
ejpam-6803	294	2	neural	neural	ADJ
ejpam-6803	294	3	operator	operator	NOUN
ejpam-6803	294	4	with	with	ADP
ejpam-6803	294	5	boundary	boundary	ADJ
ejpam-6803	294	6	conditions	condition	NOUN
ejpam-6803	294	7	for	for	ADP
ejpam-6803	294	8	efficient	efficient	ADJ
ejpam-6803	294	9	prediction	prediction	NOUN
ejpam-6803	294	10	of	of	ADP
ejpam-6803	294	11	steady	steady	ADJ
ejpam-6803	294	12	airfoil	airfoil	NOUN
ejpam-6803	294	13	flows	flow	NOUN
ejpam-6803	294	14	.	.	PUNCT
ejpam-6803	295	1	applied	apply	VERB
ejpam-6803	295	2	mathematics	mathematic	NOUN
ejpam-6803	295	3	and	and	CCONJ
ejpam-6803	295	4	mechanics	mechanic	NOUN
ejpam-6803	295	5	,	,	PUNCT
ejpam-6803	295	6	44(11):2019–2038	44(11):2019–2038	NUM
ejpam-6803	295	7	,	,	PUNCT
ejpam-6803	295	8	2023	2023	NUM
ejpam-6803	295	9	.	.	PUNCT
ejpam-6803	296	1	[	[	X
ejpam-6803	296	2	37	37	NUM
ejpam-6803	296	3	]	]	PUNCT
ejpam-6803	296	4	s.	s.	PROPN
ejpam-6803	296	5	chen	chen	PROPN
ejpam-6803	296	6	,	,	PUNCT
ejpam-6803	296	7	p.	p.	PROPN
ejpam-6803	296	8	givi	givi	PROPN
ejpam-6803	296	9	,	,	PUNCT
ejpam-6803	296	10	c.	c.	PROPN
ejpam-6803	296	11	zheng	zheng	PROPN
ejpam-6803	296	12	,	,	PUNCT
ejpam-6803	296	13	and	and	CCONJ
ejpam-6803	296	14	x.	x.	PROPN
ejpam-6803	296	15	jia	jia	PROPN
ejpam-6803	296	16	.	.	PROPN
ejpam-6803	296	17	physics	physics	NOUN
ejpam-6803	296	18	-	-	PUNCT
ejpam-6803	296	19	enhanced	enhance	VERB
ejpam-6803	296	20	neural	neural	ADJ
ejpam-6803	296	21	operator	operator	NOUN
ejpam-6803	296	22	for	for	ADP
ejpam-6803	296	23	simulating	simulate	VERB
ejpam-6803	296	24	turbulent	turbulent	ADJ
ejpam-6803	296	25	transport	transport	NOUN
ejpam-6803	296	26	,	,	PUNCT
ejpam-6803	296	27	2024	2024	NUM
ejpam-6803	296	28	.	.	PUNCT
ejpam-6803	297	1	arxiv:2406.04367	arxiv:2406.04367	PROPN
ejpam-6803	297	2	.	.	PUNCT
ejpam-6803	298	1	[	[	X
ejpam-6803	298	2	38	38	NUM
ejpam-6803	298	3	]	]	PUNCT
ejpam-6803	299	1	z.	z.	PROPN
ejpam-6803	299	2	li	li	PROPN
ejpam-6803	299	3	,	,	PUNCT
ejpam-6803	299	4	n.	n.	PROPN
ejpam-6803	299	5	kovachki	kovachki	PROPN
ejpam-6803	299	6	,	,	PUNCT
ejpam-6803	299	7	c.	c.	PROPN
ejpam-6803	299	8	choy	choy	PROPN
ejpam-6803	299	9	,	,	PUNCT
ejpam-6803	299	10	b.	b.	PROPN
ejpam-6803	299	11	li	li	PROPN
ejpam-6803	299	12	,	,	PUNCT
ejpam-6803	299	13	j.	j.	PROPN
ejpam-6803	299	14	kossaifi	kossaifi	PROPN
ejpam-6803	299	15	,	,	PUNCT
ejpam-6803	299	16	s.	s.	PROPN
ejpam-6803	299	17	otta	otta	PROPN
ejpam-6803	299	18	,	,	PUNCT
ejpam-6803	299	19	m.	m.	NOUN
ejpam-6803	299	20	a.	a.	NOUN
ejpam-6803	299	21	nabian	nabian	PROPN
ejpam-6803	299	22	,	,	PUNCT
ejpam-6803	299	23	m.	m.	NOUN
ejpam-6803	299	24	stadler	stadler	NOUN
ejpam-6803	299	25	,	,	PUNCT
ejpam-6803	299	26	c.	c.	PROPN
ejpam-6803	299	27	hundt	hundt	PROPN
ejpam-6803	299	28	,	,	PUNCT
ejpam-6803	299	29	k.	k.	PROPN
ejpam-6803	299	30	azizzadenesheli	azizzadenesheli	PROPN
ejpam-6803	299	31	,	,	PUNCT
ejpam-6803	299	32	and	and	CCONJ
ejpam-6803	299	33	a.	a.	NOUN
ejpam-6803	299	34	anandkumar	anandkumar	PROPN
ejpam-6803	299	35	.	.	PUNCT
ejpam-6803	300	1	geometry	geometry	NOUN
ejpam-6803	300	2	-	-	PUNCT
ejpam-6803	300	3	informed	inform	VERB
ejpam-6803	300	4	neural	neural	ADJ
ejpam-6803	300	5	operator	operator	NOUN
ejpam-6803	300	6	for	for	ADP
ejpam-6803	300	7	large	large	ADJ
ejpam-6803	300	8	-	-	PUNCT
ejpam-6803	300	9	scale	scale	NOUN
ejpam-6803	300	10	3d	3d	NUM
ejpam-6803	300	11	pdes	pde	NOUN
ejpam-6803	300	12	.	.	PUNCT
ejpam-6803	301	1	advances	advance	NOUN
ejpam-6803	301	2	in	in	ADP
ejpam-6803	301	3	neural	neural	ADJ
ejpam-6803	301	4	information	information	NOUN
ejpam-6803	301	5	processing	processing	NOUN
ejpam-6803	301	6	systems	system	NOUN
ejpam-6803	301	7	,	,	PUNCT
ejpam-6803	301	8	36:35836–35854	36:35836–35854	NUM
ejpam-6803	301	9	,	,	PUNCT
ejpam-6803	301	10	2023	2023	NUM
ejpam-6803	301	11	.	.	PUNCT
ejpam-6803	302	1	[	[	X
ejpam-6803	302	2	39	39	NUM
ejpam-6803	302	3	]	]	PUNCT
ejpam-6803	302	4	j.	j.	PROPN
ejpam-6803	302	5	sanders	sanders	PROPN
ejpam-6803	302	6	and	and	CCONJ
ejpam-6803	302	7	e.	e.	PROPN
ejpam-6803	302	8	kandrot	kandrot	PROPN
ejpam-6803	302	9	.	.	PUNCT
ejpam-6803	303	1	cuda	cuda	NOUN
ejpam-6803	303	2	by	by	ADP
ejpam-6803	303	3	example	example	NOUN
ejpam-6803	303	4	:	:	PUNCT
ejpam-6803	303	5	an	an	DET
ejpam-6803	303	6	introduction	introduction	NOUN
ejpam-6803	303	7	to	to	ADP
ejpam-6803	303	8	general	general	ADJ
ejpam-6803	303	9	-	-	PUNCT
ejpam-6803	303	10	purpose	purpose	NOUN
ejpam-6803	303	11	gpu	gpu	NOUN
ejpam-6803	303	12	programming	programming	NOUN
ejpam-6803	303	13	.	.	PUNCT
ejpam-6803	304	1	addison	addison	PROPN
ejpam-6803	304	2	-	-	PUNCT
ejpam-6803	304	3	wesley	wesley	PROPN
ejpam-6803	304	4	professional	professional	NOUN
ejpam-6803	304	5	,	,	PUNCT
ejpam-6803	304	6	2010	2010	NUM
ejpam-6803	304	7	.	.	PUNCT
ejpam-6803	305	1	[	[	X
ejpam-6803	305	2	40	40	NUM
ejpam-6803	305	3	]	]	X
ejpam-6803	305	4	n.	n.	PROPN
ejpam-6803	305	5	s.	s.	PROPN
ejpam-6803	305	6	keskar	keskar	PROPN
ejpam-6803	305	7	and	and	CCONJ
ejpam-6803	305	8	a.	a.	PROPN
ejpam-6803	305	9	s.	s.	PROPN
ejpam-6803	305	10	berahas	berahas	PROPN
ejpam-6803	305	11	.	.	PUNCT
ejpam-6803	306	1	adaqn	adaqn	NOUN
ejpam-6803	306	2	:	:	PUNCT
ejpam-6803	306	3	an	an	DET
ejpam-6803	306	4	adaptive	adaptive	ADJ
ejpam-6803	306	5	quasi	quasi	NOUN
ejpam-6803	306	6	-	-	ADJ
ejpam-6803	306	7	newton	newton	PROPN
ejpam-6803	306	8	algorithm	algorithm	NOUN
ejpam-6803	306	9	for	for	ADP
ejpam-6803	306	10	training	training	NOUN
ejpam-6803	306	11	rnns	rnn	NOUN
ejpam-6803	306	12	.	.	PUNCT
ejpam-6803	307	1	in	in	ADP
ejpam-6803	307	2	machine	machine	NOUN
ejpam-6803	307	3	learning	learning	NOUN
ejpam-6803	307	4	and	and	CCONJ
ejpam-6803	307	5	knowledge	knowledge	NOUN
ejpam-6803	307	6	discovery	discovery	NOUN
ejpam-6803	307	7	in	in	ADP
ejpam-6803	307	8	databases	database	NOUN
ejpam-6803	307	9	:	:	PUNCT
ejpam-6803	307	10	european	european	ADJ
ejpam-6803	307	11	conference	conference	NOUN
ejpam-6803	307	12	,	,	PUNCT
ejpam-6803	307	13	ecml	ecml	PROPN
ejpam-6803	307	14	pkdd	pkdd	NOUN
ejpam-6803	307	15	2016	2016	NUM
ejpam-6803	307	16	,	,	PUNCT
ejpam-6803	307	17	riva	riva	PROPN
ejpam-6803	307	18	del	del	PROPN
ejpam-6803	307	19	garda	garda	PROPN
ejpam-6803	307	20	,	,	PUNCT
ejpam-6803	307	21	italy	italy	PROPN
ejpam-6803	307	22	,	,	PUNCT
ejpam-6803	307	23	september	september	PROPN
ejpam-6803	307	24	19	19	NUM
ejpam-6803	307	25	-	-	SYM
ejpam-6803	307	26	23	23	NUM
ejpam-6803	307	27	,	,	PUNCT
ejpam-6803	307	28	2016	2016	NUM
ejpam-6803	307	29	,	,	PUNCT
ejpam-6803	307	30	proceedings	proceeding	NOUN
ejpam-6803	307	31	,	,	PUNCT
ejpam-6803	307	32	part	part	NOUN
ejpam-6803	307	33	i	i	PRON
ejpam-6803	307	34	16	16	NUM
ejpam-6803	307	35	,	,	PUNCT
ejpam-6803	307	36	pages	page	VERB
ejpam-6803	307	37	1–16	1–16	PROPN
ejpam-6803	307	38	.	.	PUNCT
ejpam-6803	308	1	springer	springer	NOUN
ejpam-6803	308	2	international	international	ADJ
ejpam-6803	308	3	publishing	publishing	NOUN
ejpam-6803	308	4	,	,	PUNCT
ejpam-6803	308	5	2016	2016	NUM
ejpam-6803	308	6	.	.	PUNCT
ejpam-6803	309	1	[	[	X
ejpam-6803	309	2	41	41	NUM
ejpam-6803	309	3	]	]	X
ejpam-6803	309	4	n.	n.	PROPN
ejpam-6803	309	5	iqbal	iqbal	PROPN
ejpam-6803	309	6	,	,	PUNCT
ejpam-6803	309	7	s.	s.	PROPN
ejpam-6803	309	8	mukhtar	mukhtar	PROPN
ejpam-6803	309	9	,	,	PUNCT
ejpam-6803	309	10	a.	a.	PROPN
ejpam-6803	309	11	mohammed	mohammed	PROPN
ejpam-6803	309	12	saeed	saeed	PROPN
ejpam-6803	309	13	,	,	PUNCT
ejpam-6803	309	14	r.	r.	PROPN
ejpam-6803	309	15	shah	shah	PROPN
ejpam-6803	309	16	,	,	PUNCT
ejpam-6803	309	17	and	and	CCONJ
ejpam-6803	309	18	s.	s.	PROPN
ejpam-6803	309	19	hussain	hussain	PROPN
ejpam-6803	309	20	.	.	PUNCT
ejpam-6803	310	1	new	new	ADJ
ejpam-6803	310	2	solitary	solitary	ADJ
ejpam-6803	310	3	and	and	CCONJ
ejpam-6803	310	4	soliton	soliton	NOUN
ejpam-6803	310	5	wave	wave	NOUN
ejpam-6803	310	6	solutions	solution	NOUN
ejpam-6803	310	7	of	of	ADP
ejpam-6803	310	8	the	the	DET
ejpam-6803	310	9	fractional	fractional	ADJ
ejpam-6803	310	10	higgs	higgs	NOUN
ejpam-6803	310	11	system	system	NOUN
ejpam-6803	310	12	using	use	VERB
ejpam-6803	310	13	a	a	DET
ejpam-6803	310	14	riccati	riccati	NOUN
ejpam-6803	310	15	-	-	PUNCT
ejpam-6803	310	16	bernoulli	bernoulli	PROPN
ejpam-6803	310	17	and	and	CCONJ
ejpam-6803	310	18	backlund	backlund	PROPN
ejpam-6803	310	19	framework	framework	PROPN
ejpam-6803	310	20	.	.	PUNCT
ejpam-6803	311	1	nonlinear	nonlinear	ADJ
ejpam-6803	311	2	dynamics	dynamic	NOUN
ejpam-6803	311	3	,	,	PUNCT
ejpam-6803	311	4	pages	page	NOUN
ejpam-6803	311	5	1–15	1–15	PROPN
ejpam-6803	311	6	,	,	PUNCT
ejpam-6803	311	7	2025	2025	NUM
ejpam-6803	311	8	.	.	PUNCT
ejpam-6803	312	1	[	[	X
ejpam-6803	312	2	42	42	NUM
ejpam-6803	312	3	]	]	PUNCT
ejpam-6803	312	4	a.	a.	NOUN
ejpam-6803	312	5	s.	s.	PROPN
ejpam-6803	312	6	alshehry	alshehry	PROPN
ejpam-6803	312	7	and	and	CCONJ
ejpam-6803	312	8	r.	r.	PROPN
ejpam-6803	312	9	shah	shah	PROPN
ejpam-6803	312	10	.	.	PUNCT
ejpam-6803	313	1	exploring	explore	VERB
ejpam-6803	313	2	fractional	fractional	ADJ
ejpam-6803	313	3	damped	damp	VERB
ejpam-6803	313	4	burgers	burger	NOUN
ejpam-6803	313	5	’	'	PUNCT
ejpam-6803	313	6	equation	equation	NOUN
ejpam-6803	313	7	:	:	PUNCT
ejpam-6803	313	8	a	a	DET
ejpam-6803	313	9	comparative	comparative	ADJ
ejpam-6803	313	10	analysis	analysis	NOUN
ejpam-6803	313	11	of	of	ADP
ejpam-6803	313	12	analytical	analytical	ADJ
ejpam-6803	313	13	methods	method	NOUN
ejpam-6803	313	14	.	.	PUNCT
ejpam-6803	314	1	fractal	fractal	PROPN
ejpam-6803	314	2	&	&	CCONJ
ejpam-6803	314	3	fractional	fractional	ADJ
ejpam-6803	314	4	,	,	PUNCT
ejpam-6803	314	5	9(2	9(2	NUM
ejpam-6803	314	6	)	)	PUNCT
ejpam-6803	314	7	,	,	PUNCT
ejpam-6803	314	8	2025	2025	NUM
ejpam-6803	314	9	.	.	PUNCT
ejpam-6803	315	1	[	[	X
ejpam-6803	315	2	43	43	NUM
ejpam-6803	315	3	]	]	PUNCT
ejpam-6803	315	4	m.	m.	NOUN
ejpam-6803	315	5	naeem	naeem	PROPN
ejpam-6803	315	6	,	,	PUNCT
ejpam-6803	315	7	h.	h.	PROPN
ejpam-6803	315	8	yasmin	yasmin	PROPN
ejpam-6803	315	9	,	,	PUNCT
ejpam-6803	315	10	r.	r.	PROPN
ejpam-6803	315	11	shah	shah	PROPN
ejpam-6803	315	12	,	,	PUNCT
ejpam-6803	315	13	n.	n.	NOUN
ejpam-6803	315	14	a.	a.	NOUN
ejpam-6803	315	15	shah	shah	PROPN
ejpam-6803	315	16	,	,	PUNCT
ejpam-6803	315	17	and	and	CCONJ
ejpam-6803	315	18	k.	k.	PROPN
ejpam-6803	315	19	nonlaopon	nonlaopon	PROPN
ejpam-6803	315	20	.	.	PUNCT
ejpam-6803	316	1	investigation	investigation	NOUN
ejpam-6803	316	2	of	of	ADP
ejpam-6803	316	3	fractional	fractional	ADJ
ejpam-6803	316	4	nonlinear	nonlinear	ADJ
ejpam-6803	316	5	regularized	regularize	VERB
ejpam-6803	316	6	long	long	ADJ
ejpam-6803	316	7	-	-	PUNCT
ejpam-6803	316	8	wave	wave	NOUN
ejpam-6803	316	9	models	model	NOUN
ejpam-6803	316	10	via	via	ADP
ejpam-6803	316	11	novel	novel	ADJ
ejpam-6803	316	12	techniques	technique	NOUN
ejpam-6803	316	13	.	.	PUNCT
ejpam-6803	317	1	symmetry	symmetry	NOUN
ejpam-6803	317	2	,	,	PUNCT
ejpam-6803	317	3	15(1):220	15(1):220	NUM
ejpam-6803	317	4	,	,	PUNCT
ejpam-6803	317	5	2023	2023	NUM
ejpam-6803	317	6	.	.	PUNCT
ejpam-6803	318	1	a.	a.	NOUN
ejpam-6803	318	2	shafee	shafee	PROPN
ejpam-6803	318	3	et	et	PROPN
ejpam-6803	318	4	al	al	PROPN
ejpam-6803	318	5	.	.	PUNCT
ejpam-6803	318	6	/	/	SYM
ejpam-6803	318	7	eur	eur	PROPN
ejpam-6803	318	8	.	.	PUNCT
ejpam-6803	319	1	j.	j.	PROPN
ejpam-6803	319	2	pure	pure	PROPN
ejpam-6803	319	3	appl	appl	PROPN
ejpam-6803	319	4	.	.	PROPN
ejpam-6803	319	5	math	math	PROPN
ejpam-6803	319	6	,	,	PUNCT
ejpam-6803	319	7	18	18	NUM
ejpam-6803	319	8	(	(	PUNCT
ejpam-6803	319	9	4	4	NUM
ejpam-6803	319	10	)	)	PUNCT
ejpam-6803	319	11	(	(	PUNCT
ejpam-6803	319	12	2025	2025	NUM
ejpam-6803	319	13	)	)	PUNCT
ejpam-6803	319	14	,	,	PUNCT
ejpam-6803	319	15	6803	6803	NUM
ejpam-6803	319	16	18	18	NUM
ejpam-6803	319	17	of	of	ADP
ejpam-6803	319	18	18	18	NUM
ejpam-6803	319	19	[	[	SYM
ejpam-6803	319	20	44	44	NUM
ejpam-6803	319	21	]	]	PUNCT
ejpam-6803	319	22	s.	s.	PROPN
ejpam-6803	319	23	noor	noor	PROPN
ejpam-6803	319	24	,	,	PUNCT
ejpam-6803	319	25	a.	a.	PROPN
ejpam-6803	319	26	s.	s.	PROPN
ejpam-6803	319	27	alshehry	alshehry	PROPN
ejpam-6803	319	28	,	,	PUNCT
ejpam-6803	319	29	h.	h.	PROPN
ejpam-6803	319	30	m.	m.	PROPN
ejpam-6803	319	31	dutt	dutt	PROPN
ejpam-6803	319	32	,	,	PUNCT
ejpam-6803	319	33	r.	r.	PROPN
ejpam-6803	319	34	nazir	nazir	PROPN
ejpam-6803	319	35	,	,	PUNCT
ejpam-6803	319	36	and	and	CCONJ
ejpam-6803	319	37	a.	a.	PROPN
ejpam-6803	319	38	khan	khan	PROPN
ejpam-6803	319	39	.	.	PUNCT
ejpam-6803	320	1	investigating	investigate	VERB
ejpam-6803	320	2	the	the	DET
ejpam-6803	320	3	dynamics	dynamic	NOUN
ejpam-6803	320	4	of	of	ADP
ejpam-6803	320	5	time	time	NOUN
ejpam-6803	320	6	-	-	PUNCT
ejpam-6803	320	7	fractional	fractional	ADJ
ejpam-6803	320	8	drinfeld	drinfeld	VERB
ejpam-6803	320	9	-	-	PUNCT
ejpam-6803	320	10	sokolov	sokolov	NOUN
ejpam-6803	320	11	-	-	PUNCT
ejpam-6803	320	12	wilson	wilson	NOUN
ejpam-6803	320	13	system	system	NOUN
ejpam-6803	320	14	through	through	ADP
ejpam-6803	320	15	analytical	analytical	ADJ
ejpam-6803	320	16	solutions	solution	NOUN
ejpam-6803	320	17	.	.	PUNCT
ejpam-6803	321	1	symmetry	symmetry	NOUN
ejpam-6803	321	2	,	,	PUNCT
ejpam-6803	321	3	15(3):703	15(3):703	NUM
ejpam-6803	321	4	,	,	PUNCT
ejpam-6803	321	5	2023	2023	NUM
ejpam-6803	321	6	.	.	PUNCT
ejpam-6803	322	1	[	[	X
ejpam-6803	322	2	45	45	NUM
ejpam-6803	322	3	]	]	X
ejpam-6803	322	4	n.	n.	PROPN
ejpam-6803	322	5	iqbal	iqbal	PROPN
ejpam-6803	322	6	,	,	PUNCT
ejpam-6803	322	7	w.	w.	PROPN
ejpam-6803	322	8	w.	w.	PROPN
ejpam-6803	322	9	mohammed	mohammed	PROPN
ejpam-6803	322	10	,	,	PUNCT
ejpam-6803	322	11	a.	a.	PROPN
ejpam-6803	322	12	e.	e.	PROPN
ejpam-6803	322	13	hamza	hamza	PROPN
ejpam-6803	322	14	,	,	PUNCT
ejpam-6803	322	15	s.	s.	PROPN
ejpam-6803	322	16	hussain	hussain	PROPN
ejpam-6803	322	17	,	,	PUNCT
ejpam-6803	322	18	y.	y.	PROPN
ejpam-6803	322	19	jawarneh	jawarneh	PROPN
ejpam-6803	322	20	,	,	PUNCT
ejpam-6803	322	21	and	and	CCONJ
ejpam-6803	322	22	r.	r.	PROPN
ejpam-6803	322	23	shah	shah	PROPN
ejpam-6803	322	24	.	.	PUNCT
ejpam-6803	323	1	fractals	fractal	NOUN
ejpam-6803	323	2	and	and	CCONJ
ejpam-6803	323	3	chaotic	chaotic	ADJ
ejpam-6803	323	4	solitons	soliton	NOUN
ejpam-6803	323	5	phenomena	phenomenon	NOUN
ejpam-6803	323	6	in	in	ADP
ejpam-6803	323	7	conformable	conformable	ADJ
ejpam-6803	323	8	coupled	couple	VERB
ejpam-6803	323	9	higgs	higgs	NOUN
ejpam-6803	323	10	system	system	NOUN
ejpam-6803	323	11	.	.	PUNCT
ejpam-6803	324	1	discrete	discrete	ADJ
ejpam-6803	324	2	dynamics	dynamic	NOUN
ejpam-6803	324	3	in	in	ADP
ejpam-6803	324	4	nature	nature	NOUN
ejpam-6803	324	5	and	and	CCONJ
ejpam-6803	324	6	society	society	NOUN
ejpam-6803	324	7	,	,	PUNCT
ejpam-6803	324	8	2025(1):8384630	2025(1):8384630	NOUN
ejpam-6803	324	9	,	,	PUNCT
ejpam-6803	324	10	2025	2025	NUM
ejpam-6803	324	11	.	.	PUNCT
ejpam-6803	325	1	[	[	X
ejpam-6803	325	2	46	46	NUM
ejpam-6803	325	3	]	]	X
ejpam-6803	325	4	d.	d.	PROPN
ejpam-6803	325	5	e.	e.	PROPN
ejpam-6803	325	6	rumelhart	rumelhart	PROPN
ejpam-6803	325	7	,	,	PUNCT
ejpam-6803	325	8	g.	g.	PROPN
ejpam-6803	325	9	e.	e.	PROPN
ejpam-6803	325	10	hinton	hinton	PROPN
ejpam-6803	325	11	,	,	PUNCT
ejpam-6803	325	12	and	and	CCONJ
ejpam-6803	325	13	r.	r.	PROPN
ejpam-6803	325	14	j.	j.	PROPN
ejpam-6803	325	15	williams	williams	PROPN
ejpam-6803	325	16	.	.	PUNCT
ejpam-6803	326	1	learning	learn	VERB
ejpam-6803	326	2	internal	internal	ADJ
ejpam-6803	326	3	representations	representation	NOUN
ejpam-6803	326	4	by	by	ADP
ejpam-6803	326	5	error	error	NOUN
ejpam-6803	326	6	propagation	propagation	NOUN
ejpam-6803	326	7	.	.	PUNCT
ejpam-6803	327	1	in	in	ADP
ejpam-6803	327	2	d.	d.	PROPN
ejpam-6803	327	3	e.	e.	PROPN
ejpam-6803	327	4	rumelhart	rumelhart	PROPN
ejpam-6803	327	5	and	and	CCONJ
ejpam-6803	327	6	j.	j.	PROPN
ejpam-6803	327	7	l.	l.	PROPN
ejpam-6803	327	8	mcclelland	mcclelland	PROPN
ejpam-6803	327	9	,	,	PUNCT
ejpam-6803	327	10	editors	editor	NOUN
ejpam-6803	327	11	,	,	PUNCT
ejpam-6803	327	12	parallel	parallel	ADJ
ejpam-6803	327	13	distributed	distribute	VERB
ejpam-6803	327	14	processing	processing	NOUN
ejpam-6803	327	15	:	:	PUNCT
ejpam-6803	327	16	explorations	exploration	NOUN
ejpam-6803	327	17	in	in	ADP
ejpam-6803	327	18	the	the	DET
ejpam-6803	327	19	microstructures	microstructure	NOUN
ejpam-6803	327	20	of	of	ADP
ejpam-6803	327	21	cognition	cognition	NOUN
ejpam-6803	327	22	,	,	PUNCT
ejpam-6803	327	23	volume	volume	NOUN
ejpam-6803	327	24	1	1	NUM
ejpam-6803	327	25	,	,	PUNCT
ejpam-6803	327	26	pages	page	NOUN
ejpam-6803	327	27	318–362	318–362	NUM
ejpam-6803	327	28	.	.	PUNCT
ejpam-6803	327	29	mit	mit	PROPN
ejpam-6803	327	30	press	press	NOUN
ejpam-6803	327	31	,	,	PUNCT
ejpam-6803	327	32	1986	1986	NUM
ejpam-6803	327	33	.	.	PUNCT