{"id":"https://openalex.org/W4392874187","doi":"https://doi.org/10.1137/23m1561397","title":"Leveraging Multitime Hamilton\u2013Jacobi PDEs for Certain Scientific Machine Learning Problems","display_name":"Leveraging Multitime Hamilton\u2013Jacobi PDEs for Certain Scientific Machine Learning Problems","publication_year":2024,"publication_date":"2024-03-15","ids":{"openalex":"https://openalex.org/W4392874187","doi":"https://doi.org/10.1137/23m1561397"},"language":"en","primary_location":{"id":"doi:10.1137/23m1561397","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1561397","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/2441157","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101844000","display_name":"Paula Chen","orcid":"https://orcid.org/0000-0003-0439-9330"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paula Chen","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912 USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031706939","display_name":"Tingwei Meng","orcid":"https://orcid.org/0000-0001-7467-601X"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]},{"id":"https://openalex.org/I2799798094","display_name":"UCLA Health","ror":"https://ror.org/01d88se56","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2799798094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tingwei Meng","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90025 USA"],"raw_orcid":"https://orcid.org/0000-0001-7467-601X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90025 USA","institution_ids":["https://openalex.org/I161318765","https://openalex.org/I2799798094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021341531","display_name":"Zongren Zou","orcid":"https://orcid.org/0009-0000-0095-3539"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zongren Zou","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912 USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076546851","display_name":"J\u00e9r\u00f4me Darbon","orcid":"https://orcid.org/0000-0003-0483-7919"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Darbon","raw_affiliation_strings":["Corresponding author. Division of Applied Mathematics, Brown University, Providence, RI 02912 USA"],"raw_orcid":"https://orcid.org/0000-0003-0483-7919","affiliations":[{"raw_affiliation_string":"Corresponding author. Division of Applied Mathematics, Brown University, Providence, RI 02912 USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009658255","display_name":"George Em Karniadakis","orcid":"https://orcid.org/0000-0002-9713-7120"},"institutions":[{"id":"https://openalex.org/I142606810","display_name":"Pacific Northwest National Laboratory","ror":"https://ror.org/05h992307","country_code":"US","type":"facility","lineage":["https://openalex.org/I1325736334","https://openalex.org/I1330989302","https://openalex.org/I142606810","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I2801280572","display_name":"Environmental Molecular Sciences Laboratory","ror":"https://ror.org/04rc0xn13","country_code":"US","type":"facility","lineage":["https://openalex.org/I1325736334","https://openalex.org/I1330989302","https://openalex.org/I142606810","https://openalex.org/I2801280572","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Em Karniadakis","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912 USA, and Pacific Northwest National Laboratory, Richland, WA 99354 USA"],"raw_orcid":"https://orcid.org/0000-0002-9713-7120","affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912 USA, and Pacific Northwest National Laboratory, Richland, WA 99354 USA","institution_ids":["https://openalex.org/I142606810","https://openalex.org/I2801280572"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101844000"],"corresponding_institution_ids":["https://openalex.org/I27804330"],"apc_list":null,"apc_paid":null,"fwci":2.6957,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89797398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"46","issue":"2","first_page":"C216","last_page":"C248"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9833999872207642,"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":0.9771999716758728,"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/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.593444287776947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5725913643836975},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5450482964515686},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.5450289249420166},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5289245843887329},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4903910160064697},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.46972501277923584},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4501759707927704},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4095671474933624},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.351929634809494},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09980577230453491}],"concepts":[{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.593444287776947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5725913643836975},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5450482964515686},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.5450289249420166},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5289245843887329},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4903910160064697},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.46972501277923584},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4501759707927704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4095671474933624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.351929634809494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09980577230453491},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1561397","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1561397","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"},{"id":"pmh:oai:osti.gov:2441157","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/2441157","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:2441157","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/2441157","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2711541269","display_name":null,"funder_award_id":"FA9550-20-1-0358","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6893006968","display_name":null,"funder_award_id":"DOE-MMICS SEA-CROGS DE-SC0023191","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8834641238","display_name":null,"funder_award_id":"FA9550-20-1-0358","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320333578","display_name":"Office of the Under Secretary of Defense","ror":null},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W177930832","https://openalex.org/W644523282","https://openalex.org/W1543750907","https://openalex.org/W1978744409","https://openalex.org/W1983627164","https://openalex.org/W1990244934","https://openalex.org/W1993885150","https://openalex.org/W2050188930","https://openalex.org/W2092663520","https://openalex.org/W2108761738","https://openalex.org/W2112299196","https://openalex.org/W2122410182","https://openalex.org/W2149811200","https://openalex.org/W2239043582","https://openalex.org/W2239232218","https://openalex.org/W2492294785","https://openalex.org/W2560647685","https://openalex.org/W2749028154","https://openalex.org/W2767915842","https://openalex.org/W2788388592","https://openalex.org/W2803629276","https://openalex.org/W2899283552","https://openalex.org/W2919115771","https://openalex.org/W2952169641","https://openalex.org/W2963395620","https://openalex.org/W2995022099","https://openalex.org/W2995576031","https://openalex.org/W3007809852","https://openalex.org/W3035965352","https://openalex.org/W3038272362","https://openalex.org/W3086293388","https://openalex.org/W3099188500","https://openalex.org/W3099878876","https://openalex.org/W3112673444","https://openalex.org/W3159649695","https://openalex.org/W3160577147","https://openalex.org/W3164854098","https://openalex.org/W4244726376","https://openalex.org/W4309748696","https://openalex.org/W4310497802","https://openalex.org/W4315628777","https://openalex.org/W4389067443","https://openalex.org/W4391652323"],"related_works":["https://openalex.org/W4200506717","https://openalex.org/W587735977","https://openalex.org/W2029860844","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W2720912673","https://openalex.org/W2203843426","https://openalex.org/W2963459055","https://openalex.org/W2116748936","https://openalex.org/W2049369111"],"abstract_inverted_index":{"Hamilton-Jacobi":[0],"partial":[1],"differential":[2,18,159],"equations":[3],"(HJ":[4],"PDEs)":[5],"have":[6],"deep":[7],"connections":[8],"with":[9],"a":[10,30,48,68,106,119],"wide":[11],"range":[12],"of":[13,70,85,89,122,183,190],"fields,":[14],"including":[15],"optimal":[16,115],"control,":[17],"games,":[19],"and":[20,60,135,179,197],"imaging":[21],"sciences.":[22],"By":[23],"considering":[24],"the":[25,40,61,71,83,86,127,130,136,156,177,188],"time":[26],"variable":[27],"to":[28,39,67,73,147,161],"be":[29,37],"higher":[31],"dimensional":[32],"quantity,":[33],"HJ":[34,76,108],"PDEs":[35],"can":[36],"extended":[38],"multi-time":[41,62,75,107],"case.":[42],"In":[43],"this":[44,79,123],"paper,":[45],"we":[46,81,98,103,125,170],"establish":[47],"novel":[49],"theoretical":[50,145],"connection":[51,146],"between":[52,129],"specific":[53],"optimization":[54],"problems":[55],"arising":[56],"in":[57,187],"machine":[58,91,167],"learning":[59,92,101],"Hopf":[63],"formula,":[64],"which":[65],"corresponds":[66],"representation":[69],"solution":[72],"certain":[74,90],"PDEs.":[77],"Through":[78],"connection,":[80,124],"increase":[82],"interpretability":[84],"training":[87,164],"process":[88],"applications":[93],"by":[94,111],"showing":[95],"that":[96,175],"when":[97],"solve":[99,105],"these":[100],"problems,":[102],"also":[104],"PDE":[109],"and,":[110],"extension,":[112],"its":[113],"corresponding":[114],"control":[116],"problem.":[117],"As":[118],"first":[120],"exploration":[121],"develop":[126],"relation":[128],"regularized":[131],"linear":[132],"regression":[133],"problem":[134],"Linear":[137],"Quadratic":[138],"Regulator":[139],"(LQR).":[140],"We":[141],"then":[142],"leverage":[143],"our":[144,184],"adapt":[148],"standard":[149],"LQR":[150],"solvers":[151],"(namely,":[152],"those":[153],"based":[154],"on":[155],"Riccati":[157],"ordinary":[158],"equations)":[160],"design":[162],"new":[163],"approaches":[165],"for":[166],"learning.":[168],"Lastly,":[169],"provide":[171],"some":[172],"numerical":[173],"examples":[174],"demonstrate":[176],"versatility":[178],"possible":[180],"computational":[181],"advantages":[182],"Riccati-based":[185],"approach":[186],"context":[189],"continual":[191],"learning,":[192,196],"post-training":[193],"calibration,":[194],"transfer":[195],"sparse":[198],"dynamics":[199],"identification.":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
