{"id":"https://openalex.org/W7220680319","doi":"https://doi.org/10.48550/arxiv.2610.04108","title":"Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics","display_name":"Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220680319","doi":"https://doi.org/10.48550/arxiv.2610.04108"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04108","pdf_url":"https://arxiv.org/pdf/2610.04108","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,"listed_in":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.04108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124768132","display_name":"Lufang Chiang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW","US"],"is_corresponding":false,"raw_author_name":"Chiang, Lufang","raw_affiliation_strings":["California Institute of Technology","National Taiwan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"National Taiwan University","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157666731","display_name":"Jiachen Yao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yao, Jiachen","raw_affiliation_strings":["California Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004578907","display_name":"Ting Lin","orcid":"https://orcid.org/0009-0000-1173-2731","observed_orcids":["https://orcid.org/0009-0000-1173-2731"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lin, Thomas Y. L.","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023215207","display_name":"Animashree Anandkumar","orcid":"https://orcid.org/0000-0002-6974-6797","observed_orcids":["https://orcid.org/0000-0002-6974-6797"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anandkumar, Anima","raw_affiliation_strings":["California Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9940999746322632,"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":0.9940999746322632,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.002099999925121665,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic-dynamics","display_name":"chaotic dynamics","score":0.753000020980835},{"id":"https://openalex.org/keywords/consistency-learning","display_name":"consistency learning","score":0.9509999752044678},{"id":"https://openalex.org/keywords/long-term-forecasting","display_name":"long-term forecasting","score":0.8080000281333923},{"id":"https://openalex.org/keywords/temporal-extrapolation","display_name":"temporal extrapolation","score":0.7300000190734863},{"id":"https://openalex.org/keywords/consistency-equations","display_name":"consistency equations","score":0.609000027179718},{"id":"https://openalex.org/keywords/physics-informed-machine-learning","display_name":"physics-informed machine learning","score":0.5139999985694885},{"id":"https://openalex.org/keywords/long-term-statistics","display_name":"long-term statistics","score":0.5090000033378601}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7426000237464905},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6686000227928162},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6392999887466431},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.5845000147819519},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4620000123977661},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3596000075340271},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.32359999418258667},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32100000977516174},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C137105694","wikidata":"https://www.wikidata.org/wiki/Q3407510","display_name":"Local consistency","level":4,"score":0.3043000102043152},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27639999985694885},{"id":"https://openalex.org/C2781402108","wikidata":"https://www.wikidata.org/wiki/Q1642961","display_name":"H\u00e9non map","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25769999623298645},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04108","pdf_url":"https://arxiv.org/pdf/2610.04108","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,"listed_in":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.04108","doi":"https://doi.org/10.48550/arxiv.2610.04108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04108","pdf_url":null,"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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.04108","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04108","pdf_url":"https://arxiv.org/pdf/2610.04108","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,"listed_in":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1013331665","display_name":null,"funder_award_id":"N00014-23-1-2654","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G2582167037","display_name":null,"funder_award_id":"N00014-23-1-2654","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220680319.pdf","grobid_xml":"https://content.openalex.org/works/W7220680319.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7125694068","https://openalex.org/W4416969237","https://openalex.org/W4414889883","https://openalex.org/W4320468821","https://openalex.org/W4296208248","https://openalex.org/W7133213573","https://openalex.org/W4281696575","https://openalex.org/W4401058140","https://openalex.org/W3170961718","https://openalex.org/W4402386287"],"abstract_inverted_index":{"Accelerating":[0],"the":[1,44,51,67,87,91],"prediction":[2],"of":[3,141],"long-term":[4,115,139],"behavior":[5],"in":[6,11,58,80,98],"chaotic":[7,103,142],"systems":[8],"is":[9],"crucial":[10],"scientific":[12],"computing.":[13],"However,":[14],"existing":[15],"methods":[16],"rely":[17],"on":[18],"numerical":[19],"solvers":[20],"or":[21],"autoregressive":[22,132],"models":[23],"that":[24,107],"advance":[25],"one":[26],"small":[27],"step":[28],"at":[29],"a":[30,54,59,70],"time,":[31],"which":[32,49],"makes":[33,110],"long":[34],"horizons":[35],"expensive.":[36],"We":[37],"instead":[38],"view":[39],"this":[40,63],"problem":[41],"as":[42,128,131],"learning":[43],"system's":[45],"time-invariant":[46,71],"evolution":[47],"operator,":[48],"jumps":[50],"state":[52],"across":[53],"large":[55],"time":[56],"span":[57],"single":[60],"evaluation.":[61],"To":[62],"end,":[64],"we":[65,105],"derive":[66],"consistency":[68,99,109],"equations":[69,84],"operator":[72,89,121],"must":[73],"satisfy,":[74],"with":[75],"differential":[76],"and":[77,114,125],"compositional":[78],"objectives":[79],"physical":[81],"time.":[82],"These":[83],"also":[85],"connect":[86],"learned":[88,120],"to":[90,138],"physics-prescribed":[92],"instant":[93],"dynamics,":[94],"enabling":[95],"physics":[96],"embedding":[97],"learning.":[100],"Across":[101],"five":[102],"systems,":[104],"find":[106],"physics-distilled":[108],"both":[111],"short-term":[112],"trajectories":[113],"statistics":[116],"more":[117],"accurate.":[118],"The":[119],"survives":[122],"temporal":[123],"extrapolation":[124],"requires":[126],"one-tenth":[127],"many":[129],"evaluations":[130],"rollout,":[133],"offering":[134],"an":[135],"efficient":[136],"route":[137],"simulation":[140],"dynamics.":[143]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-07T00:00:00"}
