{"id":"https://openalex.org/W7224797262","doi":"https://doi.org/10.48550/arxiv.2610.39897","title":"Data-driven Random-feature Approximation of Koopman Generators of Nonlinear Continuous-time Systems","display_name":"Data-driven Random-feature Approximation of Koopman Generators of Nonlinear Continuous-time Systems","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224797262","doi":"https://doi.org/10.48550/arxiv.2610.39897"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39897","pdf_url":"https://arxiv.org/pdf/2610.39897","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39897","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092785353","display_name":"Ana Cukarska","orcid":"https://orcid.org/0009-0007-2920-9026","observed_orcids":["https://orcid.org/0009-0007-2920-9026"]},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"\u010cukarska, Ana","raw_affiliation_strings":["Munich Data Science Institute","School of Computation, Information and Technology , Technical University of Munich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munich Data Science Institute","institution_ids":[]},{"raw_affiliation_string":"School of Computation, Information and Technology , Technical University of Munich , Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5119841258","display_name":"Maximilian Gollwitzer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gollwitzer, Maximilian","raw_affiliation_strings":["Munich Data Science Institute","School of Computation, Information and Technology , Technical University of Munich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munich Data Science Institute","institution_ids":[]},{"raw_affiliation_string":"School of Computation, Information and Technology , Technical University of Munich , Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137310221","display_name":"Viola Muning Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Li, Viola Muning","raw_affiliation_strings":["Munich Data Science Institute","School of Computation, Information and Technology , Technical University of Munich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munich Data Science Institute","institution_ids":[]},{"raw_affiliation_string":"School of Computation, Information and Technology , Technical University of Munich , Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028269840","display_name":"Vladyslav Fediukov","orcid":"https://orcid.org/0009-0009-9257-3909","observed_orcids":["https://orcid.org/0009-0009-9257-3909"]},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fediukov, Vladyslav","raw_affiliation_strings":["Munich Data Science Institute","School of Computation, Information and Technology , Technical University of Munich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munich Data Science Institute","institution_ids":[]},{"raw_affiliation_string":"School of Computation, Information and Technology , Technical University of Munich , Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075158815","display_name":"Zahra Monfared","orcid":"https://orcid.org/0009-0004-7054-9231","observed_orcids":["https://orcid.org/0009-0004-7054-9231"]},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Monfared, Zahra","raw_affiliation_strings":["Department of Mathematics and Computer Science , Heidelberg University , Germany","Interdisciplinary Center for Scientific Computing (IWR)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , Heidelberg University , Germany","institution_ids":["https://openalex.org/I223822909"]},{"raw_affiliation_string":"Interdisciplinary Center for Scientific Computing (IWR)","institution_ids":["https://openalex.org/I223822909"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065128348","display_name":"Felix Dietrich","orcid":"https://orcid.org/0000-0002-2906-1769","observed_orcids":["https://orcid.org/0000-0002-2906-1769"]},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dietrich, Felix","raw_affiliation_strings":["Munich Data Science Institute","School of Computation, Information and Technology , Technical University of Munich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Munich Data Science Institute","institution_ids":[]},{"raw_affiliation_string":"School of Computation, Information and Technology , Technical University of Munich , Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9990000128746033,"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":0.9990000128746033,"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/T11236","display_name":"Control Systems and Identification","score":0.00019999999494757503,"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/T11416","display_name":"Numerical methods for differential equations","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/koopman-operator","display_name":"Koopman operator","score":0.9409999847412109},{"id":"https://openalex.org/keywords/random-features","display_name":"random features","score":0.7699999809265137},{"id":"https://openalex.org/keywords/continuous-time-dynamical-systems","display_name":"continuous-time dynamical systems","score":0.843999981880188},{"id":"https://openalex.org/keywords/extended-dynamic-mode-decomposition","display_name":"extended dynamic mode decomposition","score":0.7480000257492065},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.8399999737739563},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7009999752044678},{"id":"https://openalex.org/keywords/exponential-boundedness","display_name":"exponential boundedness","score":0.9049999713897705},{"id":"https://openalex.org/keywords/trajectory-prediction","display_name":"trajectory prediction","score":0.5130000114440918},{"id":"https://openalex.org/keywords/nonlinear-systems","display_name":"nonlinear systems","score":0.44699999690055847}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6414999961853027},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5620999932289124},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5275999903678894},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4957999885082245},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47209998965263367},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3937999904155731},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3865000009536743},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39897","pdf_url":"https://arxiv.org/pdf/2610.39897","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.39897","doi":"https://doi.org/10.48550/arxiv.2610.39897","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39897","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:2610.39897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39897","pdf_url":"https://arxiv.org/pdf/2610.39897","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224797262.pdf","grobid_xml":"https://content.openalex.org/works/W7224797262.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3006550916","https://openalex.org/W7160451611","https://openalex.org/W4402386985","https://openalex.org/W7129352686","https://openalex.org/W1591018827","https://openalex.org/W4287086219","https://openalex.org/W4312045216","https://openalex.org/W4409173662","https://openalex.org/W4412084989","https://openalex.org/W3200221942"],"abstract_inverted_index":{"Learning":[0],"continuous-time":[1,225],"dynamical":[2,36,80],"systems":[3,37,81],"from":[4,227],"data":[5],"is":[6,15,21,26,58,102,126,157],"an":[7,65],"active":[8],"area":[9],"of":[10,55,61,69,90,95,141,168,171,222],"research.":[11],"The":[12,33,122,150],"Koopman":[13,56,92,97,238],"formalism":[14,34],"often":[16],"used":[17],"here,":[18],"because":[19],"it":[20],"a":[22,43,62,103,109,191,204],"flexible":[23],"approach":[24,156],"that":[25,154,207],"informative":[27],"about":[28],"the":[29,52,59,70,91,96,139,172,176,182,196,200,220,237],"system's":[30],"fundamental":[31],"properties.":[32],"represents":[35],"through":[38],"linear":[39],"operators":[40,57],"acting":[41],"on":[42,78,236],"suitable":[44],"function":[45,71,113],"space.":[46,72],"A":[47],"practical":[48],"difficulty":[49],"arising":[50],"in":[51,82],"numerical":[53,88,151,183],"approximation":[54,117,170,202],"choice":[60],"``dictionary'',":[63],"meaning":[64],"effective":[66,112],"finite-dimensional":[67],"representation":[68,114,123],"In":[73,179],"this":[74],"paper,":[75],"we":[76,86,124,165,185,218],"focus":[77],"learning":[79,224],"continuous-time,":[83],"and":[84,111,147,159,175,203,231],"so":[85],"consider":[87],"approximations":[89],"generator":[93],"instead":[94],"operator.":[98],"Our":[99],"main":[100],"contribution":[101],"data-driven":[104],"random-feature":[105],"method":[106,143],"to":[107,131,181],"obtain":[108],"parsimonious":[110],"for":[115,144,195],"Galerkin":[116],"methods":[118],"such":[119],"as":[120],"gEDMD.":[121],"construct":[125],"data-informed,":[127],"which":[128],"allows":[129],"us":[130],"improve":[132],"upon":[133],"data-agnostic":[134],"methods.":[135],"We":[136],"empirically":[137],"demonstrate":[138],"suitability":[140],"our":[142,155,169,216],"forecasting":[145],"tasks":[146],"system":[148],"analysis.":[149],"experiments":[152],"show":[153],"accurate,":[158],"faster":[160],"than":[161],"iterative":[162],"optimization.":[163],"Further,":[164],"prove":[166],"convergence":[167,193],"vector":[173],"field":[174],"resulting":[177],"trajectories.":[178],"addition":[180],"results,":[184],"also":[186],"make":[187],"theoretical":[188],"contributions,":[189],"including":[190],"general":[192],"criterion":[194],"semigroup":[197],"generated":[198],"by":[199],"gEDMD":[201,208],"counterexample":[205],"showing":[206],"does":[209],"not":[210],"generally":[211],"preserve":[212],"exponential":[213],"boundedness.":[214],"With":[215],"contribution,":[217],"advance":[219],"frontier":[221],"efficiently":[223],"dynamics":[226],"data,":[228],"towards":[229],"interpretable":[230],"mathematically":[232],"robust":[233],"modelling":[234],"based":[235],"framework.":[239]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}