{"id":"https://openalex.org/W3168972368","doi":"https://doi.org/10.1109/tits.2021.3106259","title":"A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation","display_name":"A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation","publication_year":2021,"publication_date":"2021-09-08","ids":{"openalex":"https://openalex.org/W3168972368","doi":"https://doi.org/10.1109/tits.2021.3106259","mag":"3168972368"},"language":"en","primary_location":{"id":"doi:10.1109/tits.2021.3106259","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2021.3106259","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Intelligent Transportation Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.03142","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rongye Shi","orcid":"https://orcid.org/0000-0003-4298-9358"},"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":"Rongye Shi","raw_affiliation_strings":["Department of Civil Engineering and Engineering Mechanics, Columbia University, New York City, NY, USA"],"raw_orcid":"https://orcid.org/0000-0003-4298-9358","affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Engineering Mechanics, Columbia University, New York City, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhaobin Mo","orcid":null},"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":"Zhaobin Mo","raw_affiliation_strings":["Department of Civil Engineering and Engineering Mechanics, Columbia University, New York City, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Engineering Mechanics, Columbia University, New York City, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Kuang Huang","orcid":null},"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":"Kuang Huang","raw_affiliation_strings":["Department of Applied Physics and Applied Mathematics, Columbia University, New York City, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics and Applied Mathematics, Columbia University, New York City, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":null,"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":false,"raw_author_name":"Xuan Di","raw_affiliation_strings":["Department of Civil Engineering and Engineering Mechanics, Columbia University, New York City, NY, 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 City, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":null,"display_name":"Qiang Du","orcid":null},"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":"Qiang Du","raw_affiliation_strings":["Department of Applied Physics and Applied Mathematics, Columbia University, New York City, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics and Applied Mathematics, Columbia University, New York City, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":6.1903,"has_fulltext":false,"cited_by_count":114,"citation_normalized_percentile":{"value":0.97347823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"23","issue":"8","first_page":"11688","last_page":"11698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.5016000270843506,"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"}},"topics":[{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.5016000270843506,"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"}},{"id":"https://openalex.org/T11344","display_name":"Traffic Prediction and Management Techniques","score":0.3264999985694885,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.04390000179409981,"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/traffic-flow","display_name":"Traffic flow (computer networking)","score":0.6165000200271606},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.6079999804496765},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5680999755859375},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5669000148773193},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5497999787330627},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5171999931335449},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.44209998846054077},{"id":"https://openalex.org/keywords/data-modeling","display_name":"Data modeling","score":0.3837999999523163}],"concepts":[{"id":"https://openalex.org/C207512268","wikidata":"https://www.wikidata.org/wiki/Q3074551","display_name":"Traffic flow (computer networking)","level":2,"score":0.6165000200271606},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.6079999804496765},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5680999755859375},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5669000148773193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5651999711990356},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5562999844551086},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5497999787330627},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5171999931335449},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.44209998846054077},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.367900013923645},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3601999878883362},{"id":"https://openalex.org/C489000","wikidata":"https://www.wikidata.org/wiki/Q747385","display_name":"Data flow diagram","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.28859999775886536},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.2768999934196472},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2632000148296356},{"id":"https://openalex.org/C16671368","wikidata":"https://www.wikidata.org/wiki/Q230885","display_name":"State diagram","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.2603999972343445},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tits.2021.3106259","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tits.2021.3106259","pdf_url":null,"source":{"id":"https://openalex.org/S144771191","display_name":"IEEE Transactions on Intelligent Transportation Systems","issn_l":"1524-9050","issn":["1524-9050","1558-0016"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Intelligent Transportation Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2106.03142","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.03142","pdf_url":"https://arxiv.org/pdf/2106.03142","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2106.03142","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.03142","pdf_url":"https://arxiv.org/pdf/2106.03142","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3959939786","display_name":"Mathematical and Numerical Analysis of Asymptotically Compatible Discretization of Nonlocal Models","funder_award_id":"2012562","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5514588798","display_name":"RTG: Research Training in Applied Mathematics at Columbia University","funder_award_id":"1937254","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8398478472","display_name":"GOALI: Collaborative Research: Model-Predictive Safety Systems for Predictive Detection of Operation Hazards","funder_award_id":"1704833","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1522301498","https://openalex.org/W1555627060","https://openalex.org/W1986800845","https://openalex.org/W2004891103","https://openalex.org/W2012149957","https://openalex.org/W2020224078","https://openalex.org/W2020641160","https://openalex.org/W2029465969","https://openalex.org/W2036680980","https://openalex.org/W2039417141","https://openalex.org/W2056833816","https://openalex.org/W2090035883","https://openalex.org/W2093921901","https://openalex.org/W2095797625","https://openalex.org/W2105200734","https://openalex.org/W2116666705","https://openalex.org/W2130448123","https://openalex.org/W2165992156","https://openalex.org/W2272200996","https://openalex.org/W2334686861","https://openalex.org/W2593182953","https://openalex.org/W2605264395","https://openalex.org/W2745110207","https://openalex.org/W2940640769","https://openalex.org/W2963624982","https://openalex.org/W3000553448","https://openalex.org/W3117049966","https://openalex.org/W3117223116","https://openalex.org/W3135178273","https://openalex.org/W3138181334","https://openalex.org/W3139257611","https://openalex.org/W3177261102","https://openalex.org/W3191167287","https://openalex.org/W4244133811","https://openalex.org/W6600645789","https://openalex.org/W6631943919","https://openalex.org/W6638908295","https://openalex.org/W6779707486","https://openalex.org/W6786042757","https://openalex.org/W6790517252","https://openalex.org/W6795845102"],"related_works":["https://openalex.org/W2180469977","https://openalex.org/W2063184644","https://openalex.org/W613134948","https://openalex.org/W576447651","https://openalex.org/W619280466","https://openalex.org/W607682641","https://openalex.org/W2157162617","https://openalex.org/W43780660","https://openalex.org/W170165282","https://openalex.org/W2040387224"],"abstract_inverted_index":{"Traffic":[0],"state":[1],"estimation":[2,113,198],"(TSE)":[3],"bifurcates":[4],"into":[5,71],"two":[6],"main":[7],"categories,":[8],"model-driven":[9,45,73],"and":[10,46,111,147,152,200,208],"data-driven":[11,47],"(e.g.,":[12],"machine":[13],"learning,":[14,107],"ML)":[15],"approaches,":[16],"while":[17],"each":[18],"suffers":[19],"from":[20,88,124],"either":[21],"deficient":[22],"physics":[23],"or":[24,93,130],"small":[25],"data.":[26],"To":[27],"mitigate":[28],"these":[29],"limitations,":[30],"recent":[31],"studies":[32],"introduced":[33],"hybrid":[34],"methods,":[35,207],"such":[36],"as":[37,132,157,159],"physics-informed":[38,56],"deep":[39,57],"learning":[40,58],"(PIDL),":[41],"which":[42,67],"contains":[43],"both":[44],"components.":[48],"This":[49,115],"paper":[50,116],"contributes":[51],"an":[52],"improved":[53,197],"paradigm,":[54],"called":[55],"with":[59,121],"a":[60,77,81,86],"fundamental":[61,82],"diagram":[62,83],"learner":[63],"(PIDL":[64],"+":[65,98,141,173,192],"FDL),":[66],"integrates":[68],"ML":[69],"terms":[70,195],"the":[72,101,105,137,154,165,171,177,187,190,210,215],"component":[74],"to":[75,91,143,212],"learn":[76,214],"functional":[78],"form":[79],"of":[80,103,139,189,196],"(FD),":[84],"i.e.,":[85],"mapping":[87],"traffic":[89,128,133,149],"density":[90,129],"flow":[92,150],"velocity.":[94],"The":[95,183],"proposed":[96],"PIDL":[97,140,172,191],"FDL":[99,142,193],"has":[100],"advantages":[102],"performing":[104],"TSE":[106,120,175,206],"model":[108,160],"parameter":[109],"identification,":[110],"FD":[112,155,166,218],"simultaneously.":[114],"focuses":[117],"on":[118],"highway":[119],"observed":[122],"data":[123,201],"loop":[125],"detectors,":[126],"using":[127,176],"velocity":[131],"variables.":[134],"We":[135,168],"demonstrate":[136],"use":[138],"solve":[144],"popular":[145],"first-order":[146],"second-order":[148],"models":[151],"reconstruct":[153],"relation":[156],"well":[158],"parameters":[161],"that":[162],"are":[163],"outside":[164],"term.":[167],"then":[169],"evaluate":[170],"FDL-based":[174],"Next":[178],"Generation":[179],"SIMulation":[180],"(NGSIM)":[181],"dataset.":[182],"experimental":[184],"results":[185],"show":[186],"superiority":[188],"in":[194],"accuracy":[199],"efficiency":[202],"over":[203],"advanced":[204],"baseline":[205],"additionally,":[209],"capacity":[211],"properly":[213],"unknown":[216],"underlying":[217],"relation.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":19},{"year":2025,"cited_by_count":38},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2021-06-22T00:00:00"}