{"id":"https://openalex.org/W3190588512","doi":"https://doi.org/10.1137/20m1329597","title":"Path-Dependent Deep Galerkin Method: A Neural Network Approach to Solve Path-Dependent Partial Differential Equations","display_name":"Path-Dependent Deep Galerkin Method: A Neural Network Approach to Solve Path-Dependent Partial Differential Equations","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3190588512","doi":"https://doi.org/10.1137/20m1329597","mag":"3190588512"},"language":"en","primary_location":{"id":"doi:10.1137/20m1329597","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1329597","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082109843","display_name":"Yuri F. Saporito","orcid":"https://orcid.org/0000-0001-7265-9136"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yuri F. Saporito","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7265-9136","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039778968","display_name":"Zhaoyu Zhang","orcid":"https://orcid.org/0000-0003-0335-0535"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhaoyu Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082109843"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7065,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.84603951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"12","issue":"3","first_page":"912","last_page":"940"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.7084572315216064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.661060094833374},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.609332799911499},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5200816988945007},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5019972324371338},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47749659419059753},{"id":"https://openalex.org/keywords/mathematical-finance","display_name":"Mathematical finance","score":0.4330137372016907},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33394092321395874},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2925218939781189},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2895490229129791},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1795538365840912},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1293281614780426},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.08142849802970886}],"concepts":[{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.7084572315216064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.661060094833374},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.609332799911499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5200816988945007},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5019972324371338},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47749659419059753},{"id":"https://openalex.org/C93373587","wikidata":"https://www.wikidata.org/wiki/Q335632","display_name":"Mathematical finance","level":2,"score":0.4330137372016907},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33394092321395874},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2925218939781189},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2895490229129791},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1795538365840912},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1293281614780426},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.08142849802970886},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1329597","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1329597","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1574346102","https://openalex.org/W1646613531","https://openalex.org/W1826259864","https://openalex.org/W1971594473","https://openalex.org/W1978075626","https://openalex.org/W2018706083","https://openalex.org/W2034903716","https://openalex.org/W2064675550","https://openalex.org/W2097100146","https://openalex.org/W2107878631","https://openalex.org/W2136011614","https://openalex.org/W2158985775","https://openalex.org/W2625995436","https://openalex.org/W2749028154","https://openalex.org/W2803629276","https://openalex.org/W2899283552","https://openalex.org/W2934880396","https://openalex.org/W2962853650","https://openalex.org/W3024682624","https://openalex.org/W3099398622","https://openalex.org/W3099661895","https://openalex.org/W3101260193","https://openalex.org/W3101566353","https://openalex.org/W3102177650","https://openalex.org/W4230022934","https://openalex.org/W4297854194"],"related_works":["https://openalex.org/W1977834205","https://openalex.org/W4234445916","https://openalex.org/W4253275321","https://openalex.org/W4247818724","https://openalex.org/W4200249462","https://openalex.org/W2095450577","https://openalex.org/W4250711696","https://openalex.org/W2124287120","https://openalex.org/W1951249712","https://openalex.org/W2351235964"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,47,75],"propose":[4],"a":[5,82],"novel":[6],"numerical":[7,102],"method":[8,52,116],"for":[9],"path-dependent":[10,42,77],"partial":[11],"differential":[12],"equations":[13,16],"(PPDEs).":[14],"These":[15],"first":[17],"appeared":[18],"in":[19],"the":[20,33,49,93,96,106,112,115],"seminal":[21],"work":[22],"of":[23,54,80,84,95,114],"[B.":[24],"Dupire,":[25],"Quant.":[26],"Finance,":[27],"2019":[28],"(2009),":[29],"pp.":[30,65],"721--729],":[31],"where":[32],"functional":[34],"It\u00f4":[35],"calculus":[36],"was":[37],"developed":[38],"to":[39,67,91],"deal":[40,68],"with":[41,69],"financial":[43,107],"derivatives.":[44],"More":[45],"specifically,":[46],"generalize":[48],"deep":[50],"Galerkin":[51],"(DGM)":[53],"[J.":[55],"Sirignano":[56],"and":[57,86],"K.":[58],"Spiliopoulos,":[59],"J.":[60],"Comput.":[61],"Phys.,":[62],"375":[63],"(2018),":[64],"1339--1364]":[66],"these":[70],"equations.":[71],"The":[72],"method,":[73],"which":[74],"call":[76],"DGM,":[78],"consists":[79],"using":[81],"combination":[83],"feed-forward":[85],"long":[87],"short-term":[88],"memory":[89],"architectures":[90],"model":[92],"solution":[94],"PPDE.":[97],"We":[98],"then":[99],"analyze":[100],"several":[101],"examples,":[103],"many":[104],"from":[105],"mathematics":[108],"literature,":[109],"that":[110],"show":[111],"capabilities":[113],"under":[117],"very":[118],"different":[119],"situations.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2025-10-10T00:00:00"}
