{"id":"https://openalex.org/W7153047644","doi":"https://doi.org/10.48550/arxiv.2604.07762","title":"Generative optimal transport via forward-backward HJB matching","display_name":"Generative optimal transport via forward-backward HJB matching","publication_year":2026,"publication_date":"2026-04-09","ids":{"openalex":"https://openalex.org/W7153047644","doi":"https://doi.org/10.48550/arxiv.2604.07762"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07762","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07762","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.07762","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133337752","display_name":"Haiqian Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Haiqian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027233020","display_name":"Vishaal Krishnan","orcid":"https://orcid.org/0000-0002-2279-8848"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krishnan, Vishaal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063811075","display_name":"Sumit Sinha","orcid":"https://orcid.org/0000-0002-8364-5175"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sinha, Sumit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133334997","display_name":"L. Mahadevan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mahadevan, L.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.5989999771118164,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11804","display_name":"Quantum many-body systems","score":0.5989999771118164,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.08860000222921371,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.05939999967813492,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5131999850273132},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.4961000084877014},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4932999908924103},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4878000020980835},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46619999408721924},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4560999870300293},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.43050000071525574},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.3919999897480011}],"concepts":[{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5131999850273132},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.4961000084877014},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4932999908924103},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4878000020980835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47920000553131104},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46619999408721924},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.43050000071525574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41130000352859497},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3873000144958496},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3702999949455261},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.35269999504089355},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.31119999289512634},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2865000069141388},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07762","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07762","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.07762","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07762","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4611275792121887}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Controlling":[0],"the":[1,45,49,59,89,94,109,113,131,137,161,178,207,214,219],"evolution":[2],"of":[3,34,84,177,190,195],"a":[4,9,14,36,68,106,151,186,241],"many-body":[5],"stochastic":[6,29,61,191,245],"system":[7,37],"from":[8,44,130],"disordered":[10,50],"reference":[11],"state":[12],"to":[13,99,168,232],"structured":[15,46],"target":[16,47,90,179],"ensemble,":[17],"characterized":[18],"empirically":[19],"through":[20],"samples,":[21],"arises":[22],"naturally":[23],"in":[24,193,235],"non-equilibrium":[25,252],"statistical":[26,253],"mechanics":[27],"and":[28,75,140,201,218,251],"control.":[30],"The":[31,52,182],"natural":[32,53],"relaxation":[33,134,163],"such":[35],"-":[38,42,92,160,170],"driven":[39],"by":[40,104],"diffusion":[41],"runs":[43],"toward":[48],"reference.":[51],"question":[54],"is":[55,58,97,148],"then:":[56],"what":[57],"minimum-work":[60],"process":[62,81],"that":[63,86,165,212],"reverses":[64],"this":[65,79,103,145],"relaxation,":[66],"given":[67],"pathwise":[69],"cost":[70,203,226],"functional":[71],"combining":[72],"spatial":[73,202,225],"penalties":[74],"control":[76],"effort?":[77],"Computing":[78],"optimal":[80,246],"requires":[82],"knowledge":[83,176],"trajectories":[85,159],"already":[87],"sample":[88],"ensemble":[91],"precisely":[93],"object":[95],"one":[96],"trying":[98],"construct.":[100],"We":[101,205],"resolve":[102],"establishing":[105],"time-reversal":[107],"duality:":[108],"value":[110,216],"function":[111,217],"governing":[112],"hard":[114],"backward":[115,173],"dynamics":[116],"satisfies":[117],"an":[118],"equivalent":[119],"forward-in-time":[120],"HJB":[121],"equation,":[122],"whose":[123],"solution":[124],"can":[125],"be":[126],"read":[127],"off":[128],"directly":[129],"tractable":[132],"forward":[133,146,158],"trajectories.":[135],"Via":[136],"Cole-Hopf":[138],"transformation":[139],"its":[141],"associated":[142],"Feynman-Kac":[143],"representation,":[144],"potential":[147],"computed":[149],"as":[150],"path-space":[152,196],"free":[153,197],"energy":[154],"averaged":[155],"over":[156],"these":[157],"same":[162],"paths":[164],"are":[166],"easy":[167],"simulate":[169],"without":[171],"any":[172],"simulation":[174],"or":[175],"beyond":[180],"samples.":[181],"resulting":[183],"framework":[184],"provides":[185],"physically":[187],"interpretable":[188],"description":[189],"transport":[192,229],"terms":[194],"energy,":[198],"risk-sensitive":[199],"control,":[200,247],"geometry.":[204],"illustrate":[206],"theory":[208],"with":[209],"numerical":[210],"examples":[211],"visualize":[213],"learned":[215],"induced":[220],"controlled":[221],"diffusions,":[222],"demonstrating":[223],"how":[224],"fields":[227],"shape":[228],"geometry":[230],"analogously":[231],"Fermat's":[233],"Principle":[234],"inhomogeneous":[236],"media.":[237],"Our":[238],"results":[239],"establish":[240],"unifying":[242],"connection":[243],"between":[244],"Schr\u00f6dinger":[248],"bridge":[249],"theory,":[250],"mechanics.":[254]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-11T00:00:00"}
