{"id":"https://openalex.org/W4412146560","doi":"https://doi.org/10.1137/24m1681033","title":"SOC-MartNet: A Martingale Neural Network for the Hamilton\u2013Jacobi\u2013Bellman Equation Without Explicit \\(\\boldsymbol{\\inf\\nolimits_{u \\in}}\\)\\(\\boldsymbol{{}_{U}H}\\) in Stochastic Optimal Controls","display_name":"SOC-MartNet: A Martingale Neural Network for the Hamilton\u2013Jacobi\u2013Bellman Equation Without Explicit \\(\\boldsymbol{\\inf\\nolimits_{u \\in}}\\)\\(\\boldsymbol{{}_{U}H}\\) in Stochastic Optimal Controls","publication_year":2025,"publication_date":"2025-07-10","ids":{"openalex":"https://openalex.org/W4412146560","doi":"https://doi.org/10.1137/24m1681033"},"language":"en","primary_location":{"id":"doi:10.1137/24m1681033","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1681033","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5044102523","display_name":"Wei Cai","orcid":"https://orcid.org/0000-0002-7622-4532"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wei Cai","raw_affiliation_strings":["Corresponding author. Department of Mathematics, Southern Methodist University, Dallas, TX 75275 USA"],"raw_orcid":"https://orcid.org/0000-0002-7622-4532","affiliations":[{"raw_affiliation_string":"Corresponding author. Department of Mathematics, Southern Methodist University, Dallas, TX 75275 USA","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025007315","display_name":"Shuixin Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuixin Fang","raw_affiliation_strings":["Joint first author. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0009-0002-0646-6365","affiliations":[{"raw_affiliation_string":"Joint first author. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210120485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004294250","display_name":"Tao Zhou","orcid":"https://orcid.org/0000-0001-5040-8571"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Zhou","raw_affiliation_strings":["Corresponding author. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Corresponding author. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044102523"],"corresponding_institution_ids":["https://openalex.org/I178169726"],"apc_list":null,"apc_paid":null,"fwci":7.0828,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.97124256,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"47","issue":"4","first_page":"C795","last_page":"C819"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11236","display_name":"Control Systems and Identification","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.7742927074432373},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.7474863529205322},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.5366496443748474},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5186247229576111},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4340517520904541},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37969911098480225},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3727276921272278},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.352003812789917},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.290679931640625},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.168157160282135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09552118182182312}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742927074432373},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.7474863529205322},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.5366496443748474},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5186247229576111},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4340517520904541},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37969911098480225},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3727276921272278},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.352003812789917},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.290679931640625},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.168157160282135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09552118182182312},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1681033","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1681033","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8533620077","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322847","display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","ror":"https://ror.org/031141b54"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W1507126399","https://openalex.org/W1647881072","https://openalex.org/W1966419611","https://openalex.org/W1977176662","https://openalex.org/W2032316144","https://openalex.org/W2077040879","https://openalex.org/W2098745223","https://openalex.org/W2149636389","https://openalex.org/W2149747548","https://openalex.org/W2159510648","https://openalex.org/W2588542536","https://openalex.org/W2618654391","https://openalex.org/W2625995436","https://openalex.org/W2770316314","https://openalex.org/W2803629276","https://openalex.org/W2899283552","https://openalex.org/W2899507754","https://openalex.org/W2903857590","https://openalex.org/W2959078751","https://openalex.org/W2963692341","https://openalex.org/W2964110066","https://openalex.org/W2964179106","https://openalex.org/W2990138404","https://openalex.org/W2993551995","https://openalex.org/W3007470329","https://openalex.org/W3011669027","https://openalex.org/W3016378723","https://openalex.org/W3043050416","https://openalex.org/W3099661895","https://openalex.org/W3104441224","https://openalex.org/W3110941460","https://openalex.org/W3132715927","https://openalex.org/W3162644644","https://openalex.org/W3200565419","https://openalex.org/W4212780424","https://openalex.org/W4231021340","https://openalex.org/W4235679898","https://openalex.org/W4246042613","https://openalex.org/W4296060623","https://openalex.org/W4297087551","https://openalex.org/W4309748696","https://openalex.org/W4385356755","https://openalex.org/W4396690897","https://openalex.org/W4402200522"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2358967034","https://openalex.org/W2155717523","https://openalex.org/W2024495128","https://openalex.org/W4319881067","https://openalex.org/W3130577778","https://openalex.org/W1974398766","https://openalex.org/W2087292112","https://openalex.org/W2025391447","https://openalex.org/W2542390217"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}