{"id":"https://openalex.org/W7167080196","doi":"https://doi.org/10.48550/arxiv.2607.00391","title":"Data-Adaptive Learning of Dynamical Systems by Matching Transfer Operators and Invariant Measures","display_name":"Data-Adaptive Learning of Dynamical Systems by Matching Transfer Operators and Invariant Measures","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7167080196","doi":"https://doi.org/10.48550/arxiv.2607.00391"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00391","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,"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.2607.00391","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126420301","display_name":"Y Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Yinong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026448528","display_name":"Jonah Botvinick-Greenhouse","orcid":"https://orcid.org/0009-0005-4690-0404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Botvinick-Greenhouse, Jonah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003942837","display_name":"Yunan Yang","orcid":"https://orcid.org/0000-0001-7238-7978"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Yunan","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/T11206","display_name":"Model Reduction and Neural Networks","score":0.6816999912261963,"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":0.6816999912261963,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.09759999811649323,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.029500000178813934,"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/pointwise","display_name":"Pointwise","score":0.7469000220298767},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6513000130653381},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5454999804496765},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4699999988079071},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4632999897003174},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.45410001277923584},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.4399999976158142},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.43209999799728394},{"id":"https://openalex.org/keywords/transfer-operator","display_name":"Transfer operator","score":0.41429999470710754}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7469000220298767},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6513000130653381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.566100001335144},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5454999804496765},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.45410001277923584},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.4399999976158142},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.41429999470710754},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.40630000829696655},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3716999888420105},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C123853557","wikidata":"https://www.wikidata.org/wiki/Q7098946","display_name":"Optimal matching","level":3,"score":0.3334999978542328},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.3328999876976013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3310000002384186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32690000534057617},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.2854999899864197},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C2777798563","wikidata":"https://www.wikidata.org/wiki/Q7603916","display_name":"State vector","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2603999972343445},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.2551000118255615},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00391","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,"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.2607.00391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00391","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,"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":"Life below water","score":0.8259165287017822,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Trajectory-based":[0],"learning":[1,172],"of":[2,11,40,55,91,109,124],"dynamical":[3,177],"systems":[4],"is":[5],"often":[6],"fragile":[7],"in":[8],"the":[9,37,60,89,106,110,115],"presence":[10],"noise,":[12],"chaos,":[13],"or":[14],"sparse":[15,159],"observations,":[16],"as":[17],"small":[18],"pointwise":[19,151],"errors":[20],"can":[21],"rapidly":[22],"amplify.":[23],"We":[24,69],"introduce":[25],"a":[26,44,64,80,92,133,164],"transition-statistics":[27,143],"approach":[28,162],"to":[29,88,119,168],"system":[30],"identification":[31],"that":[32,142],"learns":[33],"dynamics":[34,149],"by":[35],"matching":[36,102,114,144],"induced":[38],"motion":[39],"probability":[41],"mass":[42],"across":[43],"data-adaptive":[45],"mesh.":[46],"Given":[47],"trajectory":[48,152],"data,":[49],"we":[50],"build":[51],"an":[52],"unstructured":[53],"partition":[54],"state":[56,125],"space":[57],"and":[58,113,132,158,174],"approximate":[59],"Perron--Frobenius":[61],"operator":[62],"with":[63,74,86],"regularized":[65],"Ulam":[66],"transition":[67,111,117],"matrix.":[68],"replace":[70],"hard":[71],"cell":[72],"indicators":[73],"continuous,":[75],"piecewise-smooth":[76],"partition-of-unity":[77],"weights,":[78],"yielding":[79],"Markov":[81],"matrix":[82],"supporting":[83],"gradient-based":[84],"optimization":[85],"respect":[87],"parameters":[90],"learned":[93],"vector":[94],"field.":[95],"This":[96],"enables":[97],"two":[98],"related":[99],"training":[100],"objectives:":[101],"invariant":[103],"measures":[104],"through":[105],"stationary":[107],"eigenvectors":[108],"matrices,":[112],"full":[116],"matrices":[118],"capture":[120],"transport":[121],"between":[122],"regions":[123],"space.":[126],"Numerical":[127],"experiments":[128],"on":[129],"Lorenz-63,":[130],"Lorenz-96,":[131],"reduced-order":[134],"NOAA":[135],"sea":[136],"surface":[137],"temperature":[138],"forecasting":[139],"problem":[140],"show":[141],"gives":[145],"more":[146],"reliable":[147],"long-time":[148],"than":[150],"matching,":[153],"particularly":[154],"under":[155],"measurement":[156],"noise":[157],"sampling.":[160],"The":[161],"provides":[163],"robust":[165],"operator-theoretic":[166],"alternative":[167],"trajectory-level":[169],"losses":[170],"for":[171],"chaotic":[173],"partially":[175],"observed":[176],"systems.":[178]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}
