id	sid	tid	token	lemma	pos
ajpdis-580	1	1	126	126	NUM
ajpdis-580	1	2	american	american	ADJ
ajpdis-580	1	3	journal	journal	PROPN
ajpdis-580	1	4	of	of	ADP
ajpdis-580	1	5	public	public	ADJ
ajpdis-580	1	6	diplomacy	diplomacy	NOUN
ajpdis-580	1	7	and	and	CCONJ
ajpdis-580	1	8	international	international	ADJ
ajpdis-580	1	9	studies	study	NOUN
ajpdis-580	1	10	www	www	PROPN
ajpdis-580	1	11	.	.	PROPN
ajpdis-580	2	1	grnjournal.us	grnjournal.us	PROPN
ajpdis-580	2	2	american	american	PROPN
ajpdis-580	2	3	journal	journal	PROPN
ajpdis-580	2	4	of	of	ADP
ajpdis-580	2	5	public	public	ADJ
ajpdis-580	2	6	diplomacy	diplomacy	NOUN
ajpdis-580	2	7	and	and	CCONJ
ajpdis-580	2	8	international	international	ADJ
ajpdis-580	2	9	studies	study	NOUN
ajpdis-580	2	10	volume	volume	NOUN
ajpdis-580	2	11	01	01	NUM
ajpdis-580	2	12	,	,	PUNCT
ajpdis-580	2	13	issue	issue	NOUN
ajpdis-580	2	14	06	06	NUM
ajpdis-580	2	15	,	,	PUNCT
ajpdis-580	2	16	2023	2023	NUM
ajpdis-580	2	17	issn	issn	X
ajpdis-580	2	18	(	(	PUNCT
ajpdis-580	2	19	e	e	NOUN
ajpdis-580	2	20	):	):	PUNCT
ajpdis-580	2	21	2993	2993	NUM
ajpdis-580	2	22	-	-	SYM
ajpdis-580	2	23	2157	2157	NUM
ajpdis-580	2	24	numerical	numerical	ADJ
ajpdis-580	2	25	methods	method	NOUN
ajpdis-580	2	26	in	in	ADP
ajpdis-580	2	27	mathematics	mathematic	NOUN
ajpdis-580	2	28	and	and	CCONJ
ajpdis-580	2	29	informatics	informatic	NOUN
ajpdis-580	2	30	:	:	PUNCT
ajpdis-580	2	31	bridging	bridge	VERB
ajpdis-580	2	32	theory	theory	NOUN
ajpdis-580	2	33	and	and	CCONJ
ajpdis-580	2	34	computation	computation	NOUN
ajpdis-580	2	35	turganbaeva	turganbaeva	PROPN
ajpdis-580	2	36	ramiza	ramiza	PROPN
ajpdis-580	2	37	tolibaevna	tolibaevna	NOUN
ajpdis-580	2	38	,	,	PUNCT
ajpdis-580	2	39	qa’llibekov	qa’llibekov	PROPN
ajpdis-580	2	40	u’mitbek	u’mitbek	PROPN
ajpdis-580	2	41	o’serbay	o’serbay	PROPN
ajpdis-580	2	42	uli	uli	PROPN
ajpdis-580	2	43	,	,	PUNCT
ajpdis-580	2	44	abatbaev	abatbaev	PROPN
ajpdis-580	2	45	rasulbek	rasulbek	PROPN
ajpdis-580	2	46	nietbay	nietbay	PROPN
ajpdis-580	2	47	uli	uli	PROPN
ajpdis-580	2	48	,	,	PUNCT
ajpdis-580	2	49	mnajatdinov	mnajatdinov	PROPN
ajpdis-580	2	50	atabek	atabek	PROPN
ajpdis-580	2	51	rafatdin	rafatdin	VERB
ajpdis-580	2	52	uli	uli	PROPN
ajpdis-580	2	53	a	a	DET
ajpdis-580	2	54	student	student	NOUN
ajpdis-580	2	55	of	of	ADP
ajpdis-580	2	56	the	the	DET
ajpdis-580	2	57	faculty	faculty	NOUN
ajpdis-580	2	58	of	of	ADP
ajpdis-580	2	59	mathematics	mathematic	NOUN
ajpdis-580	2	60	of	of	ADP
ajpdis-580	2	61	ksu	ksu	PROPN
ajpdis-580	2	62	abstract	abstract	PROPN
ajpdis-580	2	63	:	:	PUNCT
ajpdis-580	2	64	numerical	numerical	ADJ
ajpdis-580	2	65	methods	method	NOUN
ajpdis-580	2	66	play	play	VERB
ajpdis-580	2	67	a	a	DET
ajpdis-580	2	68	pivotal	pivotal	ADJ
ajpdis-580	2	69	role	role	NOUN
ajpdis-580	2	70	in	in	ADP
ajpdis-580	2	71	the	the	DET
ajpdis-580	2	72	fields	field	NOUN
ajpdis-580	2	73	of	of	ADP
ajpdis-580	2	74	mathematics	mathematic	NOUN
ajpdis-580	2	75	and	and	CCONJ
ajpdis-580	2	76	informatics	informatic	NOUN
ajpdis-580	2	77	by	by	ADP
ajpdis-580	2	78	providing	provide	VERB
ajpdis-580	2	79	powerful	powerful	ADJ
ajpdis-580	2	80	tools	tool	NOUN
ajpdis-580	2	81	for	for	ADP
ajpdis-580	2	82	solving	solve	VERB
ajpdis-580	2	83	complex	complex	ADJ
ajpdis-580	2	84	mathematical	mathematical	ADJ
ajpdis-580	2	85	problems	problem	NOUN
ajpdis-580	2	86	that	that	PRON
ajpdis-580	2	87	are	be	AUX
ajpdis-580	2	88	often	often	ADV
ajpdis-580	2	89	intractable	intractable	ADJ
ajpdis-580	2	90	through	through	ADP
ajpdis-580	2	91	analytical	analytical	ADJ
ajpdis-580	2	92	methods	method	NOUN
ajpdis-580	2	93	alone	alone	ADV
ajpdis-580	2	94	.	.	PUNCT
ajpdis-580	3	1	this	this	DET
ajpdis-580	3	2	article	article	NOUN
ajpdis-580	3	3	explores	explore	VERB
ajpdis-580	3	4	the	the	DET
ajpdis-580	3	5	fundamental	fundamental	ADJ
ajpdis-580	3	6	concepts	concept	NOUN
ajpdis-580	3	7	,	,	PUNCT
ajpdis-580	3	8	applications	application	NOUN
ajpdis-580	3	9	,	,	PUNCT
ajpdis-580	3	10	and	and	CCONJ
ajpdis-580	3	11	advancements	advancement	NOUN
ajpdis-580	3	12	in	in	ADP
ajpdis-580	3	13	numerical	numerical	ADJ
ajpdis-580	3	14	methods	method	NOUN
ajpdis-580	3	15	,	,	PUNCT
ajpdis-580	3	16	highlighting	highlight	VERB
ajpdis-580	3	17	their	their	PRON
ajpdis-580	3	18	significance	significance	NOUN
ajpdis-580	3	19	in	in	ADP
ajpdis-580	3	20	both	both	CCONJ
ajpdis-580	3	21	theoretical	theoretical	ADJ
ajpdis-580	3	22	research	research	NOUN
ajpdis-580	3	23	and	and	CCONJ
ajpdis-580	3	24	practical	practical	ADJ
ajpdis-580	3	25	computational	computational	ADJ
ajpdis-580	3	26	tasks	task	NOUN
ajpdis-580	3	27	.	.	PUNCT
ajpdis-580	4	1	we	we	PRON
ajpdis-580	4	2	delve	delve	VERB
ajpdis-580	4	3	into	into	ADP
ajpdis-580	4	4	various	various	ADJ
ajpdis-580	4	5	numerical	numerical	ADJ
ajpdis-580	4	6	techniques	technique	NOUN
ajpdis-580	4	7	,	,	PUNCT
ajpdis-580	4	8	their	their	PRON
ajpdis-580	4	9	underlying	underlie	VERB
ajpdis-580	4	10	principles	principle	NOUN
ajpdis-580	4	11	,	,	PUNCT
ajpdis-580	4	12	and	and	CCONJ
ajpdis-580	4	13	their	their	PRON
ajpdis-580	4	14	applications	application	NOUN
ajpdis-580	4	15	across	across	ADP
ajpdis-580	4	16	different	different	ADJ
ajpdis-580	4	17	branches	branch	NOUN
ajpdis-580	4	18	of	of	ADP
ajpdis-580	4	19	mathematics	mathematic	NOUN
ajpdis-580	4	20	and	and	CCONJ
ajpdis-580	4	21	informatics	informatic	NOUN
ajpdis-580	4	22	.	.	PUNCT
ajpdis-580	5	1	keywords	keyword	NOUN
ajpdis-580	5	2	:	:	PUNCT
ajpdis-580	5	3	numerical	numerical	ADJ
ajpdis-580	5	4	methods	method	NOUN
ajpdis-580	5	5	,	,	PUNCT
ajpdis-580	5	6	mathematics	mathematic	NOUN
ajpdis-580	5	7	,	,	PUNCT
ajpdis-580	5	8	informatics	informatic	NOUN
ajpdis-580	5	9	,	,	PUNCT
ajpdis-580	5	10	root	root	NOUN
ajpdis-580	5	11	finding	finding	NOUN
ajpdis-580	5	12	,	,	PUNCT
ajpdis-580	5	13	optimization	optimization	NOUN
ajpdis-580	5	14	,	,	PUNCT
ajpdis-580	5	15	numerical	numerical	ADJ
ajpdis-580	5	16	integration	integration	NOUN
ajpdis-580	5	17	,	,	PUNCT
ajpdis-580	5	18	numerical	numerical	ADJ
ajpdis-580	5	19	differentiation	differentiation	NOUN
ajpdis-580	5	20	,	,	PUNCT
ajpdis-580	5	21	differential	differential	ADJ
ajpdis-580	5	22	equations	equation	NOUN
ajpdis-580	5	23	,	,	PUNCT
ajpdis-580	5	24	linear	linear	PROPN
ajpdis-580	5	25	algebra	algebra	NOUN
ajpdis-580	5	26	,	,	PUNCT
ajpdis-580	5	27	machine	machine	NOUN
ajpdis-580	5	28	learning	learning	NOUN
ajpdis-580	5	29	,	,	PUNCT
ajpdis-580	5	30	simulation	simulation	NOUN
ajpdis-580	5	31	,	,	PUNCT
ajpdis-580	5	32	modeling	modeling	NOUN
ajpdis-580	5	33	.	.	PUNCT
ajpdis-580	6	1	numerical	numerical	ADJ
ajpdis-580	6	2	methods	method	NOUN
ajpdis-580	6	3	encompass	encompass	VERB
ajpdis-580	6	4	a	a	DET
ajpdis-580	6	5	wide	wide	ADJ
ajpdis-580	6	6	range	range	NOUN
ajpdis-580	6	7	of	of	ADP
ajpdis-580	6	8	techniques	technique	NOUN
ajpdis-580	6	9	used	use	VERB
ajpdis-580	6	10	to	to	PART
ajpdis-580	6	11	approximate	approximate	VERB
ajpdis-580	6	12	solutions	solution	NOUN
ajpdis-580	6	13	to	to	ADP
ajpdis-580	6	14	mathematical	mathematical	ADJ
ajpdis-580	6	15	problems	problem	NOUN
ajpdis-580	6	16	,	,	PUNCT
ajpdis-580	6	17	where	where	SCONJ
ajpdis-580	6	18	analytical	analytical	ADJ
ajpdis-580	6	19	solutions	solution	NOUN
ajpdis-580	6	20	may	may	AUX
ajpdis-580	6	21	be	be	AUX
ajpdis-580	6	22	elusive	elusive	ADJ
ajpdis-580	6	23	or	or	CCONJ
ajpdis-580	6	24	computationally	computationally	ADV
ajpdis-580	6	25	expensive	expensive	ADJ
ajpdis-580	6	26	.	.	PUNCT
ajpdis-580	7	1	these	these	DET
ajpdis-580	7	2	methods	method	NOUN
ajpdis-580	7	3	bridge	bridge	VERB
ajpdis-580	7	4	the	the	DET
ajpdis-580	7	5	gap	gap	NOUN
ajpdis-580	7	6	between	between	ADP
ajpdis-580	7	7	mathematical	mathematical	ADJ
ajpdis-580	7	8	theory	theory	NOUN
ajpdis-580	7	9	and	and	CCONJ
ajpdis-580	7	10	computational	computational	ADJ
ajpdis-580	7	11	implementation	implementation	NOUN
ajpdis-580	7	12	,	,	PUNCT
ajpdis-580	7	13	enabling	enable	VERB
ajpdis-580	7	14	researchers	researcher	NOUN
ajpdis-580	7	15	and	and	CCONJ
ajpdis-580	7	16	practitioners	practitioner	NOUN
ajpdis-580	7	17	to	to	PART
ajpdis-580	7	18	tackle	tackle	VERB
ajpdis-580	7	19	problems	problem	NOUN
ajpdis-580	7	20	that	that	PRON
ajpdis-580	7	21	arise	arise	VERB
ajpdis-580	7	22	in	in	ADP
ajpdis-580	7	23	diverse	diverse	ADJ
ajpdis-580	7	24	fields	field	NOUN
ajpdis-580	7	25	such	such	ADJ
ajpdis-580	7	26	as	as	ADP
ajpdis-580	7	27	physics	physics	NOUN
ajpdis-580	7	28	,	,	PUNCT
ajpdis-580	7	29	engineering	engineering	NOUN
ajpdis-580	7	30	,	,	PUNCT
ajpdis-580	7	31	economics	economic	NOUN
ajpdis-580	7	32	,	,	PUNCT
ajpdis-580	7	33	and	and	CCONJ
ajpdis-580	7	34	computer	computer	NOUN
ajpdis-580	7	35	science	science	NOUN
ajpdis-580	7	36	.	.	PUNCT
ajpdis-580	8	1	numerical	numerical	ADJ
ajpdis-580	8	2	methods	method	NOUN
ajpdis-580	8	3	for	for	ADP
ajpdis-580	8	4	root	root	NOUN
ajpdis-580	8	5	finding	finding	NOUN
ajpdis-580	8	6	,	,	PUNCT
ajpdis-580	8	7	such	such	ADJ
ajpdis-580	8	8	as	as	ADP
ajpdis-580	8	9	the	the	DET
ajpdis-580	8	10	newton	newton	PROPN
ajpdis-580	8	11	-	-	PUNCT
ajpdis-580	8	12	raphson	raphson	PROPN
ajpdis-580	8	13	method	method	NOUN
ajpdis-580	8	14	and	and	CCONJ
ajpdis-580	8	15	the	the	DET
ajpdis-580	8	16	bisection	bisection	NOUN
ajpdis-580	8	17	method	method	NOUN
ajpdis-580	8	18	,	,	PUNCT
ajpdis-580	8	19	play	play	VERB
ajpdis-580	8	20	a	a	DET
ajpdis-580	8	21	crucial	crucial	ADJ
ajpdis-580	8	22	role	role	NOUN
ajpdis-580	8	23	in	in	ADP
ajpdis-580	8	24	finding	find	VERB
ajpdis-580	8	25	solutions	solution	NOUN
ajpdis-580	8	26	to	to	ADP
ajpdis-580	8	27	equations	equation	NOUN
ajpdis-580	8	28	that	that	PRON
ajpdis-580	8	29	can	can	AUX
ajpdis-580	8	30	not	not	PART
ajpdis-580	8	31	be	be	AUX
ajpdis-580	8	32	solved	solve	VERB
ajpdis-580	8	33	explicitly	explicitly	ADV
ajpdis-580	8	34	.	.	PUNCT
ajpdis-580	9	1	optimization	optimization	NOUN
ajpdis-580	9	2	techniques	technique	NOUN
ajpdis-580	9	3	like	like	ADP
ajpdis-580	9	4	gradient	gradient	ADJ
ajpdis-580	9	5	descent	descent	NOUN
ajpdis-580	9	6	and	and	CCONJ
ajpdis-580	9	7	simulated	simulate	VERB
ajpdis-580	9	8	annealing	annealing	NOUN
ajpdis-580	9	9	are	be	AUX
ajpdis-580	9	10	fundamental	fundamental	ADJ
ajpdis-580	9	11	tools	tool	NOUN
ajpdis-580	9	12	for	for	ADP
ajpdis-580	9	13	finding	find	VERB
ajpdis-580	9	14	optimal	optimal	ADJ
ajpdis-580	9	15	solutions	solution	NOUN
ajpdis-580	9	16	in	in	ADP
ajpdis-580	9	17	a	a	DET
ajpdis-580	9	18	wide	wide	ADJ
ajpdis-580	9	19	range	range	NOUN
ajpdis-580	9	20	of	of	ADP
ajpdis-580	9	21	applications	application	NOUN
ajpdis-580	9	22	.	.	PUNCT
ajpdis-580	10	1	numerical	numerical	ADJ
ajpdis-580	10	2	integration	integration	NOUN
ajpdis-580	10	3	techniques	technique	NOUN
ajpdis-580	10	4	,	,	PUNCT
ajpdis-580	10	5	including	include	VERB
ajpdis-580	10	6	the	the	DET
ajpdis-580	10	7	trapezoidal	trapezoidal	ADJ
ajpdis-580	10	8	rule	rule	NOUN
ajpdis-580	10	9	and	and	CCONJ
ajpdis-580	10	10	simpson	simpson	PROPN
ajpdis-580	10	11	's	's	PART
ajpdis-580	10	12	rule	rule	NOUN
ajpdis-580	10	13	,	,	PUNCT
ajpdis-580	10	14	enable	enable	VERB
ajpdis-580	10	15	the	the	DET
ajpdis-580	10	16	approximation	approximation	NOUN
ajpdis-580	10	17	of	of	ADP
ajpdis-580	10	18	definite	definite	ADJ
ajpdis-580	10	19	integrals	integral	NOUN
ajpdis-580	10	20	.	.	PUNCT
ajpdis-580	11	1	these	these	DET
ajpdis-580	11	2	methods	method	NOUN
ajpdis-580	11	3	are	be	AUX
ajpdis-580	11	4	essential	essential	ADJ
ajpdis-580	11	5	for	for	ADP
ajpdis-580	11	6	computing	compute	VERB
ajpdis-580	11	7	areas	area	NOUN
ajpdis-580	11	8	,	,	PUNCT
ajpdis-580	11	9	volumes	volume	NOUN
ajpdis-580	11	10	,	,	PUNCT
ajpdis-580	11	11	and	and	CCONJ
ajpdis-580	11	12	probabilities	probability	NOUN
ajpdis-580	11	13	in	in	ADP
ajpdis-580	11	14	various	various	ADJ
ajpdis-580	11	15	mathematical	mathematical	ADJ
ajpdis-580	11	16	and	and	CCONJ
ajpdis-580	11	17	scientific	scientific	ADJ
ajpdis-580	11	18	contexts	contexts	NOUN
ajpdis-580	11	19	.	.	PUNCT
ajpdis-580	12	1	similarly	similarly	ADV
ajpdis-580	12	2	,	,	PUNCT
ajpdis-580	12	3	numerical	numerical	ADJ
ajpdis-580	12	4	differentiation	differentiation	NOUN
ajpdis-580	12	5	methods	method	NOUN
ajpdis-580	12	6	help	help	AUX
ajpdis-580	12	7	estimate	estimate	VERB
ajpdis-580	12	8	derivatives	derivative	NOUN
ajpdis-580	12	9	of	of	ADP
ajpdis-580	12	10	functions	function	NOUN
ajpdis-580	12	11	,	,	PUNCT
ajpdis-580	12	12	which	which	PRON
ajpdis-580	12	13	are	be	AUX
ajpdis-580	12	14	vital	vital	ADJ
ajpdis-580	12	15	in	in	ADP
ajpdis-580	12	16	fields	field	NOUN
ajpdis-580	12	17	like	like	ADP
ajpdis-580	12	18	physics	physics	NOUN
ajpdis-580	12	19	and	and	CCONJ
ajpdis-580	12	20	engineering	engineering	NOUN
ajpdis-580	12	21	.	.	PUNCT
ajpdis-580	13	1	[	[	X
ajpdis-580	13	2	1.82	1.82	NUM
ajpdis-580	13	3	]	]	PUNCT
ajpdis-580	13	4	numerical	numerical	ADJ
ajpdis-580	13	5	methods	method	NOUN
ajpdis-580	13	6	offer	offer	VERB
ajpdis-580	13	7	robust	robust	ADJ
ajpdis-580	13	8	solutions	solution	NOUN
ajpdis-580	13	9	to	to	ADP
ajpdis-580	13	10	ordinary	ordinary	ADJ
ajpdis-580	13	11	and	and	CCONJ
ajpdis-580	13	12	partial	partial	ADJ
ajpdis-580	13	13	differential	differential	ADJ
ajpdis-580	13	14	equations	equation	NOUN
ajpdis-580	13	15	.	.	PUNCT
ajpdis-580	14	1	techniques	technique	NOUN
ajpdis-580	14	2	like	like	ADP
ajpdis-580	14	3	euler	euler	PROPN
ajpdis-580	14	4	's	's	PART
ajpdis-580	14	5	method	method	NOUN
ajpdis-580	14	6	and	and	CCONJ
ajpdis-580	14	7	the	the	DET
ajpdis-580	14	8	finite	finite	ADJ
ajpdis-580	14	9	difference	difference	NOUN
ajpdis-580	14	10	method	method	NOUN
ajpdis-580	14	11	provide	provide	VERB
ajpdis-580	14	12	approximations	approximation	NOUN
ajpdis-580	14	13	to	to	PART
ajpdis-580	14	14	differential	differential	VERB
ajpdis-580	14	15	equations	equation	NOUN
ajpdis-580	14	16	that	that	PRON
ajpdis-580	14	17	describe	describe	VERB
ajpdis-580	14	18	real	real	ADJ
ajpdis-580	14	19	-	-	PUNCT
ajpdis-580	14	20	world	world	NOUN
ajpdis-580	14	21	phenomena	phenomenon	NOUN
ajpdis-580	14	22	,	,	PUNCT
ajpdis-580	14	23	from	from	ADP
ajpdis-580	14	24	fluid	fluid	ADJ
ajpdis-580	14	25	dynamics	dynamic	NOUN
ajpdis-580	14	26	to	to	ADP
ajpdis-580	14	27	population	population	NOUN
ajpdis-580	14	28	growth	growth	NOUN
ajpdis-580	14	29	.	.	PUNCT
ajpdis-580	15	1	in	in	ADP
ajpdis-580	15	2	linear	linear	PROPN
ajpdis-580	15	3	algebra	algebra	PROPN
ajpdis-580	15	4	,	,	PUNCT
ajpdis-580	15	5	numerical	numerical	ADJ
ajpdis-580	15	6	methods	method	NOUN
ajpdis-580	15	7	are	be	AUX
ajpdis-580	15	8	indispensable	indispensable	ADJ
ajpdis-580	15	9	for	for	ADP
ajpdis-580	15	10	solving	solve	VERB
ajpdis-580	15	11	large	large	ADJ
ajpdis-580	15	12	systems	system	NOUN
ajpdis-580	15	13	of	of	ADP
ajpdis-580	15	14	linear	linear	PROPN
ajpdis-580	15	15	equations	equation	NOUN
ajpdis-580	15	16	and	and	CCONJ
ajpdis-580	15	17	eigenvalue	eigenvalue	PROPN
ajpdis-580	15	18	problems	problem	NOUN
ajpdis-580	15	19	.	.	PUNCT
ajpdis-580	16	1	methods	method	NOUN
ajpdis-580	16	2	like	like	ADP
ajpdis-580	16	3	gaussian	gaussian	ADJ
ajpdis-580	16	4	elimination	elimination	NOUN
ajpdis-580	16	5	and	and	CCONJ
ajpdis-580	16	6	iterative	iterative	NOUN
ajpdis-580	16	7	techniques	technique	NOUN
ajpdis-580	16	8	such	such	ADJ
ajpdis-580	16	9	as	as	ADP
ajpdis-580	16	10	the	the	DET
ajpdis-580	16	11	jacobi	jacobi	PROPN
ajpdis-580	16	12	method	method	NOUN
ajpdis-580	16	13	and	and	CCONJ
ajpdis-580	16	14	gauss	gauss	ADJ
ajpdis-580	16	15	-	-	PUNCT
ajpdis-580	16	16	seidel	seidel	PROPN
ajpdis-580	16	17	method	method	NOUN
ajpdis-580	16	18	underpin	underpin	VERB
ajpdis-580	16	19	simulations	simulation	NOUN
ajpdis-580	16	20	and	and	CCONJ
ajpdis-580	16	21	modeling	modeling	NOUN
ajpdis-580	16	22	in	in	ADP
ajpdis-580	16	23	engineering	engineering	NOUN
ajpdis-580	16	24	and	and	CCONJ
ajpdis-580	16	25	physics	physics	PROPN
ajpdis-580	16	26	.	.	PUNCT
ajpdis-580	17	1	numerical	numerical	ADJ
ajpdis-580	17	2	methods	method	NOUN
ajpdis-580	17	3	are	be	AUX
ajpdis-580	17	4	at	at	ADP
ajpdis-580	17	5	the	the	DET
ajpdis-580	17	6	core	core	NOUN
ajpdis-580	17	7	of	of	ADP
ajpdis-580	17	8	machine	machine	NOUN
ajpdis-580	17	9	learning	learning	NOUN
ajpdis-580	17	10	algorithms	algorithm	NOUN
ajpdis-580	17	11	,	,	PUNCT
ajpdis-580	17	12	facilitating	facilitate	VERB
ajpdis-580	17	13	the	the	DET
ajpdis-580	17	14	optimization	optimization	NOUN
ajpdis-580	17	15	of	of	ADP
ajpdis-580	17	16	model	model	NOUN
ajpdis-580	17	17	parameters	parameter	NOUN
ajpdis-580	17	18	through	through	ADP
ajpdis-580	17	19	techniques	technique	NOUN
ajpdis-580	17	20	like	like	ADP
ajpdis-580	17	21	stochastic	stochastic	ADJ
ajpdis-580	17	22	127	127	NUM
ajpdis-580	17	23	american	american	ADJ
ajpdis-580	17	24	journal	journal	NOUN
ajpdis-580	17	25	of	of	ADP
ajpdis-580	17	26	public	public	ADJ
ajpdis-580	17	27	diplomacy	diplomacy	NOUN
ajpdis-580	17	28	and	and	CCONJ
ajpdis-580	17	29	international	international	ADJ
ajpdis-580	17	30	studies	study	NOUN
ajpdis-580	17	31	www	www	PROPN
ajpdis-580	17	32	.	.	PUNCT
ajpdis-580	18	1	grnjournal.us	grnjournal.us	PROPN
ajpdis-580	18	2	gradient	gradient	ADJ
ajpdis-580	18	3	descent	descent	NOUN
ajpdis-580	18	4	.	.	PUNCT
ajpdis-580	19	1	these	these	DET
ajpdis-580	19	2	methods	method	NOUN
ajpdis-580	19	3	enable	enable	VERB
ajpdis-580	19	4	the	the	DET
ajpdis-580	19	5	training	training	NOUN
ajpdis-580	19	6	of	of	ADP
ajpdis-580	19	7	complex	complex	ADJ
ajpdis-580	19	8	models	model	NOUN
ajpdis-580	19	9	that	that	PRON
ajpdis-580	19	10	underpin	underpin	VERB
ajpdis-580	19	11	modern	modern	ADJ
ajpdis-580	19	12	applications	application	NOUN
ajpdis-580	19	13	such	such	ADJ
ajpdis-580	19	14	as	as	ADP
ajpdis-580	19	15	image	image	NOUN
ajpdis-580	19	16	recognition	recognition	NOUN
ajpdis-580	19	17	and	and	CCONJ
ajpdis-580	19	18	natural	natural	ADJ
ajpdis-580	19	19	language	language	NOUN
ajpdis-580	19	20	processing	processing	NOUN
ajpdis-580	19	21	.	.	PUNCT
ajpdis-580	20	1	numerical	numerical	ADJ
ajpdis-580	20	2	simulations	simulation	NOUN
ajpdis-580	20	3	play	play	VERB
ajpdis-580	20	4	a	a	DET
ajpdis-580	20	5	critical	critical	ADJ
ajpdis-580	20	6	role	role	NOUN
ajpdis-580	20	7	in	in	ADP
ajpdis-580	20	8	informatics	informatic	NOUN
ajpdis-580	20	9	,	,	PUNCT
ajpdis-580	20	10	allowing	allow	VERB
ajpdis-580	20	11	researchers	researcher	NOUN
ajpdis-580	20	12	to	to	PART
ajpdis-580	20	13	model	model	VERB
ajpdis-580	20	14	and	and	CCONJ
ajpdis-580	20	15	study	study	VERB
ajpdis-580	20	16	complex	complex	ADJ
ajpdis-580	20	17	systems	system	NOUN
ajpdis-580	20	18	that	that	PRON
ajpdis-580	20	19	can	can	AUX
ajpdis-580	20	20	not	not	PART
ajpdis-580	20	21	be	be	AUX
ajpdis-580	20	22	easily	easily	ADV
ajpdis-580	20	23	analyzed	analyze	VERB
ajpdis-580	20	24	analytically	analytically	ADV
ajpdis-580	20	25	.	.	PUNCT
ajpdis-580	21	1	monte	monte	PROPN
ajpdis-580	21	2	carlo	carlo	PROPN
ajpdis-580	21	3	simulations	simulation	NOUN
ajpdis-580	21	4	,	,	PUNCT
ajpdis-580	21	5	finite	finite	ADJ
ajpdis-580	21	6	element	element	NOUN
ajpdis-580	21	7	analysis	analysis	NOUN
ajpdis-580	21	8	,	,	PUNCT
ajpdis-580	21	9	and	and	CCONJ
ajpdis-580	21	10	molecular	molecular	ADJ
ajpdis-580	21	11	dynamics	dynamic	NOUN
ajpdis-580	21	12	simulations	simulation	NOUN
ajpdis-580	21	13	are	be	AUX
ajpdis-580	21	14	just	just	ADV
ajpdis-580	21	15	a	a	DET
ajpdis-580	21	16	few	few	ADJ
ajpdis-580	21	17	examples	example	NOUN
ajpdis-580	21	18	of	of	ADP
ajpdis-580	21	19	how	how	SCONJ
ajpdis-580	21	20	numerical	numerical	ADJ
ajpdis-580	21	21	methods	method	NOUN
ajpdis-580	21	22	drive	drive	VERB
ajpdis-580	21	23	advancements	advancement	NOUN
ajpdis-580	21	24	in	in	ADP
ajpdis-580	21	25	informatics	informatic	NOUN
ajpdis-580	21	26	.	.	PUNCT
ajpdis-580	22	1	advancements	advancement	NOUN
ajpdis-580	22	2	in	in	ADP
ajpdis-580	22	3	high	high	ADJ
ajpdis-580	22	4	-	-	PUNCT
ajpdis-580	22	5	performance	performance	NOUN
ajpdis-580	22	6	computing	computing	NOUN
ajpdis-580	22	7	have	have	AUX
ajpdis-580	22	8	revolutionized	revolutionize	VERB
ajpdis-580	22	9	numerical	numerical	ADJ
ajpdis-580	22	10	methods	method	NOUN
ajpdis-580	22	11	,	,	PUNCT
ajpdis-580	22	12	enabling	enable	VERB
ajpdis-580	22	13	the	the	DET
ajpdis-580	22	14	solution	solution	NOUN
ajpdis-580	22	15	of	of	ADP
ajpdis-580	22	16	even	even	ADV
ajpdis-580	22	17	more	more	ADV
ajpdis-580	22	18	complex	complex	ADJ
ajpdis-580	22	19	problems	problem	NOUN
ajpdis-580	22	20	with	with	ADP
ajpdis-580	22	21	unprecedented	unprecedented	ADJ
ajpdis-580	22	22	accuracy	accuracy	NOUN
ajpdis-580	22	23	and	and	CCONJ
ajpdis-580	22	24	speed	speed	NOUN
ajpdis-580	22	25	.	.	PUNCT
ajpdis-580	23	1	parallel	parallel	ADJ
ajpdis-580	23	2	computing	computing	NOUN
ajpdis-580	23	3	,	,	PUNCT
ajpdis-580	23	4	distributed	distribute	VERB
ajpdis-580	23	5	computing	computing	NOUN
ajpdis-580	23	6	,	,	PUNCT
ajpdis-580	23	7	and	and	CCONJ
ajpdis-580	23	8	gpu	gpu	NOUN
ajpdis-580	23	9	acceleration	acceleration	NOUN
ajpdis-580	23	10	have	have	AUX
ajpdis-580	23	11	significantly	significantly	ADV
ajpdis-580	23	12	expanded	expand	VERB
ajpdis-580	23	13	the	the	DET
ajpdis-580	23	14	scope	scope	NOUN
ajpdis-580	23	15	of	of	ADP
ajpdis-580	23	16	numerical	numerical	ADJ
ajpdis-580	23	17	simulations	simulation	NOUN
ajpdis-580	23	18	and	and	CCONJ
ajpdis-580	23	19	computations	computation	NOUN
ajpdis-580	23	20	.	.	PUNCT
ajpdis-580	24	1	the	the	DET
ajpdis-580	24	2	integration	integration	NOUN
ajpdis-580	24	3	of	of	ADP
ajpdis-580	24	4	machine	machine	NOUN
ajpdis-580	24	5	learning	learn	VERB
ajpdis-580	24	6	techniques	technique	NOUN
ajpdis-580	24	7	with	with	ADP
ajpdis-580	24	8	traditional	traditional	ADJ
ajpdis-580	24	9	numerical	numerical	ADJ
ajpdis-580	24	10	methods	method	NOUN
ajpdis-580	24	11	has	have	AUX
ajpdis-580	24	12	led	lead	VERB
ajpdis-580	24	13	to	to	ADP
ajpdis-580	24	14	the	the	DET
ajpdis-580	24	15	development	development	NOUN
ajpdis-580	24	16	of	of	ADP
ajpdis-580	24	17	hybrid	hybrid	ADJ
ajpdis-580	24	18	approaches	approach	NOUN
ajpdis-580	24	19	.	.	PUNCT
ajpdis-580	25	1	neural	neural	ADJ
ajpdis-580	25	2	networks	network	NOUN
ajpdis-580	25	3	and	and	CCONJ
ajpdis-580	25	4	deep	deep	ADJ
ajpdis-580	25	5	learning	learning	NOUN
ajpdis-580	25	6	are	be	AUX
ajpdis-580	25	7	being	be	AUX
ajpdis-580	25	8	used	use	VERB
ajpdis-580	25	9	to	to	PART
ajpdis-580	25	10	enhance	enhance	VERB
ajpdis-580	25	11	the	the	DET
ajpdis-580	25	12	efficiency	efficiency	NOUN
ajpdis-580	25	13	and	and	CCONJ
ajpdis-580	25	14	accuracy	accuracy	NOUN
ajpdis-580	25	15	of	of	ADP
ajpdis-580	25	16	numerical	numerical	ADJ
ajpdis-580	25	17	methods	method	NOUN
ajpdis-580	25	18	,	,	PUNCT
ajpdis-580	25	19	particularly	particularly	ADV
ajpdis-580	25	20	in	in	ADP
ajpdis-580	25	21	solving	solve	VERB
ajpdis-580	25	22	partial	partial	ADJ
ajpdis-580	25	23	differential	differential	ADJ
ajpdis-580	25	24	equations	equation	NOUN
ajpdis-580	25	25	and	and	CCONJ
ajpdis-580	25	26	optimization	optimization	NOUN
ajpdis-580	25	27	problems	problem	NOUN
ajpdis-580	25	28	.	.	PUNCT
ajpdis-580	26	1	[	[	X
ajpdis-580	26	2	2.96	2.96	NUM
ajpdis-580	26	3	]	]	X
ajpdis-580	26	4	numerical	numerical	ADJ
ajpdis-580	26	5	methods	method	NOUN
ajpdis-580	26	6	form	form	VERB
ajpdis-580	26	7	the	the	DET
ajpdis-580	26	8	backbone	backbone	NOUN
ajpdis-580	26	9	of	of	ADP
ajpdis-580	26	10	mathematical	mathematical	ADJ
ajpdis-580	26	11	and	and	CCONJ
ajpdis-580	26	12	informatics	informatic	NOUN
ajpdis-580	26	13	research	research	NOUN
ajpdis-580	26	14	,	,	PUNCT
ajpdis-580	26	15	providing	provide	VERB
ajpdis-580	26	16	the	the	DET
ajpdis-580	26	17	means	mean	NOUN
ajpdis-580	26	18	to	to	PART
ajpdis-580	26	19	solve	solve	VERB
ajpdis-580	26	20	intricate	intricate	ADJ
ajpdis-580	26	21	problems	problem	NOUN
ajpdis-580	26	22	and	and	CCONJ
ajpdis-580	26	23	drive	drive	VERB
ajpdis-580	26	24	innovation	innovation	NOUN
ajpdis-580	26	25	across	across	ADP
ajpdis-580	26	26	various	various	ADJ
ajpdis-580	26	27	domains	domain	NOUN
ajpdis-580	26	28	.	.	PUNCT
ajpdis-580	27	1	as	as	ADP
ajpdis-580	27	2	computational	computational	ADJ
ajpdis-580	27	3	power	power	NOUN
ajpdis-580	27	4	and	and	CCONJ
ajpdis-580	27	5	techniques	technique	NOUN
ajpdis-580	27	6	continue	continue	VERB
ajpdis-580	27	7	to	to	PART
ajpdis-580	27	8	evolve	evolve	VERB
ajpdis-580	27	9	,	,	PUNCT
ajpdis-580	27	10	numerical	numerical	ADJ
ajpdis-580	27	11	methods	method	NOUN
ajpdis-580	27	12	will	will	AUX
ajpdis-580	27	13	remain	remain	VERB
ajpdis-580	27	14	an	an	DET
ajpdis-580	27	15	essential	essential	ADJ
ajpdis-580	27	16	tool	tool	NOUN
ajpdis-580	27	17	for	for	ADP
ajpdis-580	27	18	advancing	advance	VERB
ajpdis-580	27	19	both	both	CCONJ
ajpdis-580	27	20	theoretical	theoretical	ADJ
ajpdis-580	27	21	understanding	understanding	NOUN
ajpdis-580	27	22	and	and	CCONJ
ajpdis-580	27	23	practical	practical	ADJ
ajpdis-580	27	24	applications	application	NOUN
ajpdis-580	27	25	in	in	ADP
ajpdis-580	27	26	mathematics	mathematic	NOUN
ajpdis-580	27	27	and	and	CCONJ
ajpdis-580	27	28	informatics	informatic	NOUN
ajpdis-580	27	29	.	.	PUNCT
ajpdis-580	28	1	by	by	ADP
ajpdis-580	28	2	embracing	embrace	VERB
ajpdis-580	28	3	the	the	DET
ajpdis-580	28	4	synergy	synergy	NOUN
ajpdis-580	28	5	between	between	ADP
ajpdis-580	28	6	theory	theory	NOUN
ajpdis-580	28	7	and	and	CCONJ
ajpdis-580	28	8	computation	computation	NOUN
ajpdis-580	28	9	,	,	PUNCT
ajpdis-580	28	10	researchers	researcher	NOUN
ajpdis-580	28	11	and	and	CCONJ
ajpdis-580	28	12	practitioners	practitioner	NOUN
ajpdis-580	28	13	can	can	AUX
ajpdis-580	28	14	unlock	unlock	VERB
ajpdis-580	28	15	new	new	ADJ
ajpdis-580	28	16	avenues	avenue	NOUN
ajpdis-580	28	17	for	for	ADP
ajpdis-580	28	18	discovery	discovery	NOUN
ajpdis-580	28	19	and	and	CCONJ
ajpdis-580	28	20	problem	problem	NOUN
ajpdis-580	28	21	-	-	PUNCT
ajpdis-580	28	22	solving	solving	NOUN
ajpdis-580	28	23	.	.	PUNCT
ajpdis-580	29	1	while	while	SCONJ
ajpdis-580	29	2	numerical	numerical	ADJ
ajpdis-580	29	3	methods	method	NOUN
ajpdis-580	29	4	have	have	AUX
ajpdis-580	29	5	proven	prove	VERB
ajpdis-580	29	6	to	to	PART
ajpdis-580	29	7	be	be	AUX
ajpdis-580	29	8	invaluable	invaluable	ADJ
ajpdis-580	29	9	,	,	PUNCT
ajpdis-580	29	10	they	they	PRON
ajpdis-580	29	11	are	be	AUX
ajpdis-580	29	12	not	not	PART
ajpdis-580	29	13	without	without	ADP
ajpdis-580	29	14	their	their	PRON
ajpdis-580	29	15	challenges	challenge	NOUN
ajpdis-580	29	16	.	.	PUNCT
ajpdis-580	30	1	some	some	DET
ajpdis-580	30	2	numerical	numerical	ADJ
ajpdis-580	30	3	algorithms	algorithm	NOUN
ajpdis-580	30	4	may	may	AUX
ajpdis-580	30	5	exhibit	exhibit	VERB
ajpdis-580	30	6	convergence	convergence	NOUN
ajpdis-580	30	7	issues	issue	NOUN
ajpdis-580	30	8	,	,	PUNCT
ajpdis-580	30	9	numerical	numerical	ADJ
ajpdis-580	30	10	instability	instability	NOUN
ajpdis-580	30	11	,	,	PUNCT
ajpdis-580	30	12	or	or	CCONJ
ajpdis-580	30	13	sensitivity	sensitivity	NOUN
ajpdis-580	30	14	to	to	ADP
ajpdis-580	30	15	initial	initial	ADJ
ajpdis-580	30	16	conditions	condition	NOUN
ajpdis-580	30	17	.	.	PUNCT
ajpdis-580	31	1	these	these	DET
ajpdis-580	31	2	challenges	challenge	NOUN
ajpdis-580	31	3	underscore	underscore	VERB
ajpdis-580	31	4	the	the	DET
ajpdis-580	31	5	importance	importance	NOUN
ajpdis-580	31	6	of	of	ADP
ajpdis-580	31	7	careful	careful	ADJ
ajpdis-580	31	8	analysis	analysis	NOUN
ajpdis-580	31	9	,	,	PUNCT
ajpdis-580	31	10	validation	validation	NOUN
ajpdis-580	31	11	,	,	PUNCT
ajpdis-580	31	12	and	and	CCONJ
ajpdis-580	31	13	selection	selection	NOUN
ajpdis-580	31	14	of	of	ADP
ajpdis-580	31	15	appropriate	appropriate	ADJ
ajpdis-580	31	16	methods	method	NOUN
ajpdis-580	31	17	for	for	ADP
ajpdis-580	31	18	specific	specific	ADJ
ajpdis-580	31	19	problems	problem	NOUN
ajpdis-580	31	20	.	.	PUNCT
ajpdis-580	32	1	accurate	accurate	ADJ
ajpdis-580	32	2	assessment	assessment	NOUN
ajpdis-580	32	3	of	of	ADP
ajpdis-580	32	4	errors	error	NOUN
ajpdis-580	32	5	and	and	CCONJ
ajpdis-580	32	6	uncertainties	uncertainty	NOUN
ajpdis-580	32	7	associated	associate	VERB
ajpdis-580	32	8	with	with	ADP
ajpdis-580	32	9	numerical	numerical	ADJ
ajpdis-580	32	10	approximations	approximation	NOUN
ajpdis-580	32	11	is	be	AUX
ajpdis-580	32	12	crucial	crucial	ADJ
ajpdis-580	32	13	for	for	ADP
ajpdis-580	32	14	ensuring	ensure	VERB
ajpdis-580	32	15	the	the	DET
ajpdis-580	32	16	reliability	reliability	NOUN
ajpdis-580	32	17	of	of	ADP
ajpdis-580	32	18	results	result	NOUN
ajpdis-580	32	19	.	.	PUNCT
ajpdis-580	33	1	methods	method	NOUN
ajpdis-580	33	2	such	such	ADJ
ajpdis-580	33	3	as	as	ADP
ajpdis-580	33	4	error	error	NOUN
ajpdis-580	33	5	propagation	propagation	NOUN
ajpdis-580	33	6	analysis	analysis	NOUN
ajpdis-580	33	7	,	,	PUNCT
ajpdis-580	33	8	sensitivity	sensitivity	NOUN
ajpdis-580	33	9	analysis	analysis	NOUN
ajpdis-580	33	10	,	,	PUNCT
ajpdis-580	33	11	and	and	CCONJ
ajpdis-580	33	12	uncertainty	uncertainty	NOUN
ajpdis-580	33	13	quantification	quantification	NOUN
ajpdis-580	33	14	play	play	VERB
ajpdis-580	33	15	a	a	DET
ajpdis-580	33	16	pivotal	pivotal	ADJ
ajpdis-580	33	17	role	role	NOUN
ajpdis-580	33	18	in	in	ADP
ajpdis-580	33	19	understanding	understand	VERB
ajpdis-580	33	20	the	the	DET
ajpdis-580	33	21	limitations	limitation	NOUN
ajpdis-580	33	22	of	of	ADP
ajpdis-580	33	23	numerical	numerical	ADJ
ajpdis-580	33	24	solutions	solution	NOUN
ajpdis-580	33	25	and	and	CCONJ
ajpdis-580	33	26	making	make	VERB
ajpdis-580	33	27	informed	informed	ADJ
ajpdis-580	33	28	decisions	decision	NOUN
ajpdis-580	33	29	based	base	VERB
ajpdis-580	33	30	on	on	ADP
ajpdis-580	33	31	them.[3.21	them.[3.21	PROPN
ajpdis-580	33	32	]	]	PUNCT
ajpdis-580	33	33	many	many	ADJ
ajpdis-580	33	34	real	real	ADJ
ajpdis-580	33	35	-	-	PUNCT
ajpdis-580	33	36	world	world	NOUN
ajpdis-580	33	37	problems	problem	NOUN
ajpdis-580	33	38	involve	involve	VERB
ajpdis-580	33	39	multiple	multiple	ADJ
ajpdis-580	33	40	scales	scale	NOUN
ajpdis-580	33	41	and	and	CCONJ
ajpdis-580	33	42	physical	physical	ADJ
ajpdis-580	33	43	phenomena	phenomenon	NOUN
ajpdis-580	33	44	,	,	PUNCT
ajpdis-580	33	45	presenting	present	VERB
ajpdis-580	33	46	computational	computational	ADJ
ajpdis-580	33	47	challenges	challenge	NOUN
ajpdis-580	33	48	that	that	PRON
ajpdis-580	33	49	demand	demand	VERB
ajpdis-580	33	50	sophisticated	sophisticated	ADJ
ajpdis-580	33	51	numerical	numerical	ADJ
ajpdis-580	33	52	techniques	technique	NOUN
ajpdis-580	33	53	.	.	PUNCT
ajpdis-580	34	1	hybrid	hybrid	ADJ
ajpdis-580	34	2	methods	method	NOUN
ajpdis-580	34	3	that	that	PRON
ajpdis-580	34	4	combine	combine	VERB
ajpdis-580	34	5	different	different	ADJ
ajpdis-580	34	6	numerical	numerical	ADJ
ajpdis-580	34	7	approaches	approach	NOUN
ajpdis-580	34	8	,	,	PUNCT
ajpdis-580	34	9	adaptive	adaptive	ADJ
ajpdis-580	34	10	mesh	mesh	NOUN
ajpdis-580	34	11	refinement	refinement	NOUN
ajpdis-580	34	12	,	,	PUNCT
ajpdis-580	34	13	and	and	CCONJ
ajpdis-580	34	14	domain	domain	NOUN
ajpdis-580	34	15	decomposition	decomposition	NOUN
ajpdis-580	34	16	are	be	AUX
ajpdis-580	34	17	being	be	AUX
ajpdis-580	34	18	explored	explore	VERB
ajpdis-580	34	19	to	to	PART
ajpdis-580	34	20	tackle	tackle	VERB
ajpdis-580	34	21	these	these	DET
ajpdis-580	34	22	multi	multi	ADJ
ajpdis-580	34	23	-	-	ADJ
ajpdis-580	34	24	scale	scale	ADJ
ajpdis-580	34	25	and	and	CCONJ
ajpdis-580	34	26	multi	multi	ADJ
ajpdis-580	34	27	-	-	ADJ
ajpdis-580	34	28	physics	physics	ADJ
ajpdis-580	34	29	problems	problem	NOUN
ajpdis-580	34	30	effectively	effectively	ADV
ajpdis-580	34	31	.	.	PUNCT
ajpdis-580	35	1	numerical	numerical	ADJ
ajpdis-580	35	2	methods	method	NOUN
ajpdis-580	35	3	are	be	AUX
ajpdis-580	35	4	the	the	DET
ajpdis-580	35	5	unsung	unsung	ADJ
ajpdis-580	35	6	heroes	hero	NOUN
ajpdis-580	35	7	of	of	ADP
ajpdis-580	35	8	modern	modern	ADJ
ajpdis-580	35	9	mathematics	mathematic	NOUN
ajpdis-580	35	10	and	and	CCONJ
ajpdis-580	35	11	informatics	informatic	NOUN
ajpdis-580	35	12	,	,	PUNCT
ajpdis-580	35	13	enabling	enable	VERB
ajpdis-580	35	14	us	we	PRON
ajpdis-580	35	15	to	to	PART
ajpdis-580	35	16	unlock	unlock	VERB
ajpdis-580	35	17	insights	insight	NOUN
ajpdis-580	35	18	from	from	ADP
ajpdis-580	35	19	complex	complex	ADJ
ajpdis-580	35	20	mathematical	mathematical	ADJ
ajpdis-580	35	21	problems	problem	NOUN
ajpdis-580	35	22	and	and	CCONJ
ajpdis-580	35	23	harness	harness	NOUN
ajpdis-580	35	24	the	the	DET
ajpdis-580	35	25	power	power	NOUN
ajpdis-580	35	26	of	of	ADP
ajpdis-580	35	27	computation	computation	NOUN
ajpdis-580	35	28	to	to	PART
ajpdis-580	35	29	address	address	VERB
ajpdis-580	35	30	real	real	ADJ
ajpdis-580	35	31	-	-	PUNCT
ajpdis-580	35	32	world	world	NOUN
ajpdis-580	35	33	challenges	challenge	NOUN
ajpdis-580	35	34	.	.	PUNCT
ajpdis-580	36	1	from	from	ADP
ajpdis-580	36	2	simulating	simulate	VERB
ajpdis-580	36	3	the	the	DET
ajpdis-580	36	4	behavior	behavior	NOUN
ajpdis-580	36	5	of	of	ADP
ajpdis-580	36	6	subatomic	subatomic	ADJ
ajpdis-580	36	7	particles	particle	NOUN
ajpdis-580	36	8	to	to	ADP
ajpdis-580	36	9	training	train	VERB
ajpdis-580	36	10	deep	deep	ADJ
ajpdis-580	36	11	neural	neural	ADJ
ajpdis-580	36	12	networks	network	NOUN
ajpdis-580	36	13	,	,	PUNCT
ajpdis-580	36	14	numerical	numerical	ADJ
ajpdis-580	36	15	methods	method	NOUN
ajpdis-580	36	16	are	be	AUX
ajpdis-580	36	17	the	the	DET
ajpdis-580	36	18	driving	drive	VERB
ajpdis-580	36	19	force	force	NOUN
ajpdis-580	36	20	behind	behind	ADP
ajpdis-580	36	21	countless	countless	ADJ
ajpdis-580	36	22	scientific	scientific	ADJ
ajpdis-580	36	23	and	and	CCONJ
ajpdis-580	36	24	technological	technological	ADJ
ajpdis-580	36	25	advancements	advancement	NOUN
ajpdis-580	36	26	.	.	PUNCT
ajpdis-580	37	1	as	as	SCONJ
ajpdis-580	37	2	we	we	PRON
ajpdis-580	37	3	continue	continue	VERB
ajpdis-580	37	4	to	to	PART
ajpdis-580	37	5	push	push	VERB
ajpdis-580	37	6	the	the	DET
ajpdis-580	37	7	boundaries	boundary	NOUN
ajpdis-580	37	8	of	of	ADP
ajpdis-580	37	9	what	what	PRON
ajpdis-580	37	10	is	be	AUX
ajpdis-580	37	11	possible	possible	ADJ
ajpdis-580	37	12	in	in	ADP
ajpdis-580	37	13	both	both	CCONJ
ajpdis-580	37	14	theoretical	theoretical	ADJ
ajpdis-580	37	15	research	research	NOUN
ajpdis-580	37	16	and	and	CCONJ
ajpdis-580	37	17	practical	practical	ADJ
ajpdis-580	37	18	applications	application	NOUN
ajpdis-580	37	19	,	,	PUNCT
ajpdis-580	37	20	the	the	DET
ajpdis-580	37	21	role	role	NOUN
ajpdis-580	37	22	of	of	ADP
ajpdis-580	37	23	numerical	numerical	ADJ
ajpdis-580	37	24	methods	method	NOUN
ajpdis-580	37	25	will	will	AUX
ajpdis-580	37	26	only	only	ADV
ajpdis-580	37	27	become	become	VERB
ajpdis-580	37	28	more	more	ADV
ajpdis-580	37	29	pronounced	pronounced	ADJ
ajpdis-580	37	30	.	.	PUNCT
ajpdis-580	38	1	by	by	ADP
ajpdis-580	38	2	embracing	embrace	VERB
ajpdis-580	38	3	these	these	DET
ajpdis-580	38	4	methods	method	NOUN
ajpdis-580	38	5	,	,	PUNCT
ajpdis-580	38	6	we	we	PRON
ajpdis-580	38	7	embark	embark	VERB
ajpdis-580	38	8	on	on	ADP
ajpdis-580	38	9	a	a	DET
ajpdis-580	38	10	journey	journey	NOUN
ajpdis-580	38	11	of	of	ADP
ajpdis-580	38	12	discovery	discovery	NOUN
ajpdis-580	38	13	,	,	PUNCT
ajpdis-580	38	14	innovation	innovation	NOUN
ajpdis-580	38	15	,	,	PUNCT
ajpdis-580	38	16	and	and	CCONJ
ajpdis-580	38	17	progress	progress	NOUN
ajpdis-580	38	18	that	that	PRON
ajpdis-580	38	19	has	have	VERB
ajpdis-580	38	20	the	the	DET
ajpdis-580	38	21	potential	potential	NOUN
ajpdis-580	38	22	to	to	PART
ajpdis-580	38	23	reshape	reshape	VERB
ajpdis-580	38	24	the	the	DET
ajpdis-580	38	25	future	future	NOUN
ajpdis-580	38	26	of	of	ADP
ajpdis-580	38	27	mathematics	mathematic	NOUN
ajpdis-580	38	28	,	,	PUNCT
ajpdis-580	38	29	informatics	informatic	NOUN
ajpdis-580	38	30	,	,	PUNCT
ajpdis-580	38	31	and	and	CCONJ
ajpdis-580	38	32	beyond	beyond	ADP
ajpdis-580	38	33	.	.	PUNCT
ajpdis-580	39	1	references	reference	NOUN
ajpdis-580	39	2	:	:	PUNCT
ajpdis-580	39	3	1	1	X
ajpdis-580	39	4	.	.	X
ajpdis-580	39	5	press	press	NOUN
ajpdis-580	39	6	,	,	PUNCT
ajpdis-580	39	7	w.	w.	PROPN
ajpdis-580	39	8	h.	h.	PROPN
ajpdis-580	39	9	,	,	PUNCT
ajpdis-580	39	10	teukolsky	teukolsky	PROPN
ajpdis-580	39	11	,	,	PUNCT
ajpdis-580	39	12	s.	s.	PROPN
ajpdis-580	39	13	a.	a.	PROPN
ajpdis-580	39	14	,	,	PUNCT
ajpdis-580	39	15	vetterling	vetterle	VERB
ajpdis-580	39	16	,	,	PUNCT
ajpdis-580	39	17	w.	w.	PROPN
ajpdis-580	39	18	t.	t.	PROPN
ajpdis-580	39	19	,	,	PUNCT
ajpdis-580	39	20	&	&	CCONJ
ajpdis-580	39	21	flannery	flannery	PROPN
ajpdis-580	39	22	,	,	PUNCT
ajpdis-580	39	23	b.	b.	PROPN
ajpdis-580	39	24	p.	p.	PROPN
ajpdis-580	39	25	(	(	PUNCT
ajpdis-580	39	26	2007	2007	NUM
ajpdis-580	39	27	)	)	PUNCT
ajpdis-580	39	28	.	.	PUNCT
ajpdis-580	40	1	numerical	numerical	ADJ
ajpdis-580	40	2	recipes	recipe	NOUN
ajpdis-580	40	3	:	:	PUNCT
ajpdis-580	40	4	the	the	DET
ajpdis-580	40	5	art	art	NOUN
ajpdis-580	40	6	of	of	ADP
ajpdis-580	40	7	scientific	scientific	ADJ
ajpdis-580	40	8	computing	computing	NOUN
ajpdis-580	40	9	(	(	PUNCT
ajpdis-580	40	10	3rd	3rd	ADJ
ajpdis-580	40	11	ed	ed	NOUN
ajpdis-580	40	12	.	.	PUNCT
ajpdis-580	40	13	)	)	PUNCT
ajpdis-580	40	14	.	.	PUNCT
ajpdis-580	41	1	cambridge	cambridge	PROPN
ajpdis-580	41	2	university	university	PROPN
ajpdis-580	41	3	press	press	NOUN
ajpdis-580	41	4	.	.	PUNCT
ajpdis-580	42	1	2	2	X
ajpdis-580	42	2	.	.	X
ajpdis-580	42	3	burden	burden	NOUN
ajpdis-580	42	4	,	,	PUNCT
ajpdis-580	42	5	r.	r.	PROPN
ajpdis-580	42	6	l.	l.	PROPN
ajpdis-580	42	7	,	,	PUNCT
ajpdis-580	42	8	&	&	CCONJ
ajpdis-580	42	9	faires	faire	NOUN
ajpdis-580	42	10	,	,	PUNCT
ajpdis-580	42	11	j.	j.	PROPN
ajpdis-580	42	12	d.	d.	PROPN
ajpdis-580	42	13	(	(	PUNCT
ajpdis-580	42	14	2016	2016	NUM
ajpdis-580	42	15	)	)	PUNCT
ajpdis-580	42	16	.	.	PUNCT
ajpdis-580	43	1	numerical	numerical	ADJ
ajpdis-580	43	2	analysis	analysis	NOUN
ajpdis-580	43	3	(	(	PUNCT
ajpdis-580	43	4	10th	10th	ADJ
ajpdis-580	43	5	ed	ed	NOUN
ajpdis-580	43	6	.	.	PUNCT
ajpdis-580	43	7	)	)	PUNCT
ajpdis-580	43	8	.	.	PUNCT
ajpdis-580	44	1	cengage	cengage	PROPN
ajpdis-580	44	2	learning	learning	PROPN
ajpdis-580	44	3	.	.	PUNCT
ajpdis-580	45	1	3	3	X
ajpdis-580	45	2	.	.	X
ajpdis-580	45	3	quarteroni	quarteroni	NOUN
ajpdis-580	45	4	,	,	PUNCT
ajpdis-580	45	5	a.	a.	PROPN
ajpdis-580	45	6	,	,	PUNCT
ajpdis-580	45	7	sacco	sacco	PROPN
ajpdis-580	45	8	,	,	PUNCT
ajpdis-580	45	9	r.	r.	PROPN
ajpdis-580	45	10	,	,	PUNCT
ajpdis-580	45	11	&	&	CCONJ
ajpdis-580	45	12	saleri	saleri	PROPN
ajpdis-580	45	13	,	,	PUNCT
ajpdis-580	45	14	f.	f.	PROPN
ajpdis-580	45	15	(	(	PUNCT
ajpdis-580	45	16	2007	2007	NUM
ajpdis-580	45	17	)	)	PUNCT
ajpdis-580	45	18	.	.	PUNCT
ajpdis-580	46	1	numerical	numerical	PROPN
ajpdis-580	46	2	mathematics	mathematics	PROPN
ajpdis-580	46	3	(	(	PUNCT
ajpdis-580	46	4	2nd	2nd	ADJ
ajpdis-580	46	5	ed	ed	NOUN
ajpdis-580	46	6	.	.	PUNCT
ajpdis-580	46	7	)	)	PUNCT
ajpdis-580	46	8	.	.	PUNCT
ajpdis-580	47	1	springer	springer	NOUN
ajpdis-580	47	2	.	.	PUNCT