{"id":"https://openalex.org/W4393356445","doi":"https://doi.org/10.3390/g15020012","title":"Physics-Informed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach","display_name":"Physics-Informed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach","publication_year":2024,"publication_date":"2024-03-30","ids":{"openalex":"https://openalex.org/W4393356445","doi":"https://doi.org/10.3390/g15020012"},"language":"en","primary_location":{"id":"doi:10.3390/g15020012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g15020012","pdf_url":"https://www.mdpi.com/2073-4336/15/2/12/pdf?version=1711857110","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-4336/15/2/12/pdf?version=1711857110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043740281","display_name":"Xu Chen","orcid":"https://orcid.org/0000-0002-1006-0926"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xu Chen","raw_affiliation_strings":["Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA"],"raw_orcid":"https://orcid.org/0000-0002-1006-0926","affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102013878","display_name":"Shuo Liu","orcid":"https://orcid.org/0000-0003-0177-6102"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuo Liu","raw_affiliation_strings":["Department of Computer Science, Columbia University, New York, NY 10027, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049787333","display_name":"Xuan Di","orcid":"https://orcid.org/0000-0003-2925-7697"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xuan Di","raw_affiliation_strings":["Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA"],"raw_orcid":"https://orcid.org/0000-0003-2925-7697","affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049787333"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.4759,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68995248,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"15","issue":"2","first_page":"12","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9900000095367432,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9900000095367432,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9861999750137329,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9855999946594238,"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/scalability","display_name":"Scalability","score":0.5695286393165588},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.55321204662323},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.5025780200958252},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4282163679599762},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41718754172325134},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34702348709106445},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33166491985321045},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29768306016921997},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18193462491035461},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.09060081839561462}],"concepts":[{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5695286393165588},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.55321204662323},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.5025780200958252},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4282163679599762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41718754172325134},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34702348709106445},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33166491985321045},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29768306016921997},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18193462491035461},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.09060081839561462},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/g15020012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g15020012","pdf_url":"https://www.mdpi.com/2073-4336/15/2/12/pdf?version=1711857110","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},{"id":"pmh:oai:econstor.eu:10419/330081","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/330081","pdf_url":"https://www.econstor.eu/bitstream/10419/330081/1/games-15-00012.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:gam:jgames:v:15:y:2024:i:2:p:12-:d:1367773","is_oa":false,"landing_page_url":"https://www.mdpi.com/2073-4336/15/2/12/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:fdd2f3dcbf6a435e800fadf1acc5fe2b","is_oa":true,"landing_page_url":"https://doaj.org/article/fdd2f3dcbf6a435e800fadf1acc5fe2b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Games, Vol 15, Iss 2, p 12 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/g15020012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g15020012","pdf_url":"https://www.mdpi.com/2073-4336/15/2/12/pdf?version=1711857110","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8199999928474426}],"awards":[{"id":"https://openalex.org/G2870775145","display_name":"CAREER: Multi-scale Multi-population Mean Field Game-Theoretic Framework for the Autonomous Mobility Ecosystem","funder_award_id":"1943998","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3387330441","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320337391","funder_display_name":"Division of Civil, Mechanical and Manufacturing Innovation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393356445.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W2011000015","https://openalex.org/W2038686546","https://openalex.org/W2605995250","https://openalex.org/W2767550855","https://openalex.org/W2921843114","https://openalex.org/W2975505203","https://openalex.org/W2978236721","https://openalex.org/W3016115703","https://openalex.org/W3036157773","https://openalex.org/W3164756548","https://openalex.org/W3200003729","https://openalex.org/W3209081345","https://openalex.org/W4221161359","https://openalex.org/W4299633369","https://openalex.org/W6801370602","https://openalex.org/W6857579392"],"related_works":["https://openalex.org/W2389214306","https://openalex.org/W4235240664","https://openalex.org/W2965083567","https://openalex.org/W1838576100","https://openalex.org/W2095886385","https://openalex.org/W2889616422","https://openalex.org/W2089704382","https://openalex.org/W1983399550","https://openalex.org/W97075385","https://openalex.org/W2357523926"],"abstract_inverted_index":{"Mean-field":[0],"games":[1,24,150],"(MFGs)":[2],"are":[3,36,54],"developed":[4],"to":[5,38,49,72,112,130],"model":[6],"the":[7,63,84,123,158],"decision-making":[8],"processes":[9],"of":[10,14,30],"a":[11,108],"large":[12],"number":[13],"interacting":[15],"agents":[16],"in":[17],"multi-agent":[18],"systems.":[19],"This":[20],"paper":[21,98],"studies":[22],"mean-field":[23,33],"on":[25,59,68,135,147,151],"graphs":[26],"(G-MFGs).":[27],"The":[28,105],"equilibria":[29,34],"G-MFGs,":[31],"namely,":[32],"(MFE),":[35],"challenging":[37,79],"solve":[39],"for":[40],"their":[41,93],"high-dimensional":[42],"action":[43],"space":[44],"because":[45],"each":[46],"agent":[47],"has":[48],"make":[50],"decisions":[51],"when":[52,62,164],"they":[53],"at":[55],"junction":[56],"nodes":[57],"or":[58],"edges.":[60],"Furthermore,":[61],"initial":[64,94,117,168],"population":[65,114,118,132],"state":[66,95,133],"varies":[67],"graphs,":[69],"we":[70],"have":[71],"recompute":[73],"MFE,":[74],"which":[75],"could":[76],"be":[77],"computationally":[78],"and":[80,86,142,162],"memory-demanding.":[81],"To":[82,120],"improve":[83],"scalability":[85],"avoid":[87],"repeatedly":[88],"solving":[89],"G-MFGs":[90],"every":[91],"time":[92],"changes,":[96],"this":[97],"proposes":[99],"physics-informed":[100],"graph":[101,109],"neural":[102,110,124],"operators":[103],"(PIGNO).":[104],"PIGNO":[106,159],"utilizes":[107],"operator":[111],"generate":[113],"dynamics,":[115],"given":[116],"distributions.":[119],"better":[121],"train":[122],"operator,":[125],"it":[126],"leverages":[127],"physics":[128],"knowledge":[129],"propagate":[131],"transitions":[134],"graphs.":[136],"A":[137],"learning":[138],"algorithm":[139],"is":[140,145,160],"developed,":[141],"its":[143],"performance":[144],"evaluated":[146],"autonomous":[148],"driving":[149],"road":[152],"networks.":[153],"Our":[154],"results":[155],"demonstrate":[156],"that":[157],"scalable":[161],"generalizable":[163],"tested":[165],"under":[166],"unseen":[167],"conditions.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}