{"id":"https://openalex.org/W7165735597","doi":"https://doi.org/10.48550/arxiv.2606.24824","title":"Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching","display_name":"Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165735597","doi":"https://doi.org/10.48550/arxiv.2606.24824"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.24824","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24824","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2606.24824","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035383693","display_name":"P Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Peiyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139227938","display_name":"Jian Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059946961","display_name":"Jiashu Pan","orcid":"https://orcid.org/0000-0002-8619-4015"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pan, Jiashu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139254605","display_name":"Ruiqi Feng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Ruiqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139286416","display_name":"Tao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078600050","display_name":"Zhi-Ming Ma","orcid":"https://orcid.org/0000-0001-6453-4368"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Zhi-Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139269818","display_name":"Yuan-Sen Ting","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ting, Yuan-Sen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079778707","display_name":"G. Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Gongjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139281183","display_name":"Tailin Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Tailin","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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.4458000063896179,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.4458000063896179,"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 methods for differential equations","score":0.1151999980211258,"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/T10244","display_name":"Chaos control and synchronization","score":0.09130000323057175,"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/chaotic","display_name":"Chaotic","score":0.703000009059906},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5098000168800354},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5097000002861023},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.48249998688697815},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.47440001368522644},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4611999988555908},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.3961000144481659}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.703000009059906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5152000188827515},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5098000168800354},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5097000002861023},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.47440001368522644},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4611999988555908},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4352000057697296},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4066999852657318},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39169999957084656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37770000100135803},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C197247276","wikidata":"https://www.wikidata.org/wiki/Q5072843","display_name":"Chaotic scattering","level":3,"score":0.29019999504089355},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27250000834465027},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.24824","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24824","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.24824","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24824","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6030018329620361}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Modeling":[0],"chaotic":[1,10,29,59,170],"systems":[2,70,142],"is":[3],"crucial":[4],"yet":[5],"challenging.":[6],"Inverse":[7],"problems":[8,166],"in":[9,115,157],"dynamics,":[11,117],"namely":[12],"inferring":[13],"initial":[14,50],"conditions":[15],"from":[16],"final":[17,52],"states,":[18],"remain":[19],"largely":[20],"unsolved":[21],"because":[22],"of":[23,49,58,102,107,129,137,150,167],"ill-posedness,":[24],"non-uniqueness,":[25],"instability,":[26],"and":[27,51,61,86],"potentially":[28],"time-reverse":[30],"dynamics.":[31,171],"We":[32],"address":[33],"this":[34],"open":[35],"problem":[36,114],"with":[37,71,123],"Bidirectional":[38],"Conditional":[39],"Flow":[40],"Matching":[41],"(Bi-CFM),":[42],"which":[43],"learns":[44],"bidirectional":[45],"mappings":[46],"between":[47],"distributions":[48],"states":[53],"to":[54,77,127,163],"capture":[55],"the":[56,82,110,130],"stochasticity":[57],"evolution":[60],"mitigate":[62],"exponential":[63],"error":[64],"accumulation":[65],"over":[66,96],"time.":[67],"Furthermore,":[68],"for":[69],"conservation":[72,121,124],"laws,":[73,122],"we":[74],"extend":[75],"it":[76],"Conservation-constrained":[78],"Bi-CFM":[79,91],"(CBi-CFM).":[80],"Across":[81],"classic":[83],"Lorenz,":[84],"Circuit,":[85],"high-dimensional":[87],"Lorenz":[88],"96":[89],"systems,":[90],"improves":[92],"five":[93],"distribution-level":[94],"metrics":[95],"baselines":[97],"while":[98],"achieving":[99],"a":[100,160],"speedup":[101],"more":[103],"than":[104],"two":[105],"orders":[106],"magnitude.":[108],"In":[109],"three-body":[111],"planet-planet":[112],"scattering":[113],"planetary":[116],"CBi-CFM":[118],"better":[119],"respects":[120],"errors":[125],"comparable":[126],"those":[128],"ground":[131],"truth.":[132],"Finally,":[133],"on":[134],"real":[135],"observations":[136],"globular":[138],"clusters,":[139],"collisional":[140],"million-body":[141],"shaped":[143],"by":[144],"$\\sim":[145],"10^{10}$":[146],"years":[147],"(10":[148],"Gyr)":[149],"evolution,":[151],"our":[152],"method":[153],"represents":[154],"an":[155],"advance":[156],"accuracy,":[158],"establishing":[159],"scalable":[161],"route":[162],"solving":[164],"inverse":[165],"long-timescale":[168],"real-world":[169]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-25T00:00:00"}
