{"id":"https://openalex.org/W7163387653","doi":"https://doi.org/10.48550/arxiv.2606.03834","title":"Let the Dynamics Flow: Stable Flow Matching Dynamical Systems","display_name":"Let the Dynamics Flow: Stable Flow Matching Dynamical Systems","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163387653","doi":"https://doi.org/10.48550/arxiv.2606.03834"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.03834","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03834","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.2606.03834","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032303971","display_name":"Rodrigo P\u00e9rez\u2010Dattari","orcid":"https://orcid.org/0000-0002-9503-7783"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P\u00e9rez-Dattari, Rodrigo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137722066","display_name":"Francisco Leiva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leiva, Francisco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103096181","display_name":"Andrea Testa","orcid":"https://orcid.org/0000-0001-9364-307X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Testa, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063761733","display_name":"Leonel Rozo","orcid":"https://orcid.org/0000-0001-5970-9135"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rozo, Leonel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137760899","display_name":"Javier Ruiz del Solar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"del Solar, Javier Ruiz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136739073","display_name":"No\u00e9mie Jaquier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jaquier, No\u00e9mie","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/T10653","display_name":"Robot Manipulation and Learning","score":0.36880001425743103,"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/T10653","display_name":"Robot Manipulation and Learning","score":0.36880001425743103,"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/T12290","display_name":"Human Motion and Animation","score":0.36390000581741333,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.06780000030994415,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7578999996185303},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5550000071525574},{"id":"https://openalex.org/keywords/humanoid-robot","display_name":"Humanoid robot","score":0.5475000143051147},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5473999977111816},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.51419997215271},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.510699987411499},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.48190000653266907},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.48069998621940613},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7578999996185303},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5550000071525574},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.5475000143051147},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5473999977111816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5404000282287598},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.51419997215271},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.48190000653266907},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.48069998621940613},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.47600001096725464},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.4611999988555908},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4607999920845032},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.39239999651908875},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.35429999232292175},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.33709999918937683},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3285999894142151},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3278999924659729},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.2858000099658966},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2547000050544739},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.03834","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03834","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.2606.03834","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03834","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Flow":[0,54],"matching":[1,81],"has":[2],"recently":[3],"emerged":[4],"as":[5,24],"a":[6,36,47,59,98,103,107,138],"powerful":[7],"approach":[8],"for":[9],"imitation":[10],"learning,":[11],"enabling":[12,157],"scalable,":[13,146],"expressive,":[14],"and":[15,41,71,106,136,147,153,159,191],"multimodal":[16,148,178],"motion":[17,162],"policies.":[18],"However,":[19],"when":[20],"modeling":[21,70],"these":[22,32],"policies":[23],"dynamical":[25,77,149],"systems,":[26],"incorporating":[27],"formal":[28,72],"stability":[29,73,92],"guarantees":[30],"into":[31,113],"generative":[33,69],"models":[34],"is":[35],"prerequisite":[37],"to":[38,86,122,125,184],"ensure":[39],"safe":[40,158],"generalizable":[42],"robot":[43,140,161],"behaviors,":[44],"which":[45],"remains":[46],"significant":[48],"challenge.":[49],"This":[50],"paper":[51],"introduces":[52],"Stable":[53],"Matching":[55],"Dynamical":[56],"Systems":[57],"(SFMDS),":[58],"novel":[60],"framework":[61],"that":[62,142],"bridges":[63],"the":[64,84,114],"gap":[65],"between":[66],"highly":[67],"expressive":[68,160],"guarantees.":[74],"SFMDS":[75,143,164],"parametrizes":[76],"systems":[78,150],"via":[79],"flow":[80],"while":[82,173],"constraining":[83],"model":[85,115],"satisfy":[87],"positive":[88],"invariance":[89],"and/or":[90],"Lyapunov":[91],"conditions.":[93],"We":[94,117],"propose":[95],"two":[96],"variants:":[97],"soft":[99],"constraint":[100,110],"based":[101],"on":[102,131,137,170,177],"penalty":[104],"term,":[105],"hard":[108],"structural":[109],"embedded":[111],"directly":[112],"architecture.":[116],"further":[118],"extend":[119],"both":[120],"formulations":[121],"Lie":[123],"groups":[124],"robustly":[126],"handle":[127],"orientation":[128],"trajectories.":[129],"Experiments":[130],"benchmark":[132],"datasets,":[133,172,179],"in":[134,151],"simulation,":[135],"humanoid":[139],"show":[141],"learns":[144],"stable,":[145],"low-":[152],"high-dimensional":[154],"state":[155],"spaces,":[156],"generation.":[163],"matches":[165],"or":[166],"outperforms":[167],"state-of-the-art":[168],"methods":[169],"unimodal":[171],"substantially":[174],"improving":[175],"performance":[176],"where":[180],"competing":[181],"approaches":[182],"fail":[183],"capture":[185],"multi-modal":[186],"behaviors.":[187],"Accompanying":[188],"source":[189],"code":[190],"video":[192],"are":[193],"available":[194],"at:":[195],"https://let-the-dynamics-flow.github.io/SFMDS/.":[196]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-04T00:00:00"}