{"id":"https://openalex.org/W3207768523","doi":"https://doi.org/10.23919/acc53348.2022.9867829","title":"Learning the Koopman Eigendecomposition: A Diffeomorphic Approach","display_name":"Learning the Koopman Eigendecomposition: A Diffeomorphic Approach","publication_year":2022,"publication_date":"2022-06-08","ids":{"openalex":"https://openalex.org/W3207768523","doi":"https://doi.org/10.23919/acc53348.2022.9867829","mag":"3207768523"},"language":"en","primary_location":{"id":"doi:10.23919/acc53348.2022.9867829","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc53348.2022.9867829","pdf_url":null,"source":{"id":"https://openalex.org/S4363607732","display_name":"2022 American Control Conference (ACC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ieeexplore.ieee.org/document/9867829","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050172743","display_name":"Petar Bevanda","orcid":"https://orcid.org/0000-0001-8205-3322"},"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":"Petar Bevanda","raw_affiliation_strings":["Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059089555","display_name":"Johannes Kirmayr","orcid":null},"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":"Johannes Kirmayr","raw_affiliation_strings":["Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052275481","display_name":"Stefan Sosnowski","orcid":"https://orcid.org/0000-0001-5308-3733"},"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":"Stefan Sosnowski","raw_affiliation_strings":["Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024376647","display_name":"Sandra Hirche","orcid":"https://orcid.org/0000-0001-7819-5926"},"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":"Sandra Hirche","raw_affiliation_strings":["Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Munich,Chair of Information-Oriented Control,Department of Electrical and Computer Engineering,Munich,Germany,D-80333","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":4.0272,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.94032922,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2736","last_page":"2741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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":1.0,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9398000240325928,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10857","display_name":"Advanced Electron Microscopy Techniques and Applications","score":0.9334999918937683,"subfield":{"id":"https://openalex.org/subfields/1315","display_name":"Structural Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6860640645027161},{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.684506893157959},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6123476624488831},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5915191173553467},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.5599761009216309},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5324880480766296},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5291351079940796},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4685666859149933},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4381115436553955},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3000877797603607},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07257029414176941}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6860640645027161},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.684506893157959},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6123476624488831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5915191173553467},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.5599761009216309},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5324880480766296},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5291351079940796},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4685666859149933},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4381115436553955},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3000877797603607},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07257029414176941},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.23919/acc53348.2022.9867829","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc53348.2022.9867829","pdf_url":null,"source":{"id":"https://openalex.org/S4363607732","display_name":"2022 American Control Conference (ACC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1732550","is_oa":true,"landing_page_url":"https://ieeexplore.ieee.org/document/9867829","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"","raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1732550","is_oa":true,"landing_page_url":"https://ieeexplore.ieee.org/document/9867829","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"","raw_type":"ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1591018827","https://openalex.org/W1972945640","https://openalex.org/W1997054581","https://openalex.org/W2008881650","https://openalex.org/W2014356541","https://openalex.org/W2069159682","https://openalex.org/W2126877537","https://openalex.org/W2298163601","https://openalex.org/W2482944896","https://openalex.org/W2490771025","https://openalex.org/W2492599031","https://openalex.org/W2525674169","https://openalex.org/W2730644873","https://openalex.org/W2761385663","https://openalex.org/W2963090522","https://openalex.org/W2963490775","https://openalex.org/W2963611087","https://openalex.org/W2963765797","https://openalex.org/W2989766687","https://openalex.org/W2991491427","https://openalex.org/W3006550916","https://openalex.org/W3009152446","https://openalex.org/W3012086497","https://openalex.org/W3036415528","https://openalex.org/W3045720215","https://openalex.org/W3098713169","https://openalex.org/W3099674394","https://openalex.org/W3101392902","https://openalex.org/W3127347971","https://openalex.org/W3141321221","https://openalex.org/W3153125130","https://openalex.org/W3217481449","https://openalex.org/W4226043100","https://openalex.org/W4226080023","https://openalex.org/W6727856608","https://openalex.org/W6779565673"],"related_works":["https://openalex.org/W2553624996","https://openalex.org/W1818205321","https://openalex.org/W4294596679","https://openalex.org/W2963700530","https://openalex.org/W2773692590","https://openalex.org/W2133777788","https://openalex.org/W4302193581","https://openalex.org/W2019334392","https://openalex.org/W2479626317","https://openalex.org/W2551583418"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,11,48,58,66],"novel":[3],"data-driven":[4],"approach":[5,113],"for":[6,65,102],"learning":[7,69],"linear":[8,39],"representations":[9],"of":[10,13,24,41,86,92,111],"class":[12],"stable":[14,84],"nonlinear":[15,35,42,49],"systems":[16],"using":[17],"Koopman":[18,30,103],"eigenfunctions.":[19],"Utilizing":[20],"the":[21,34,73,87,93,98],"spectral":[22],"equivalence":[23],"topologically":[25],"conjugate":[26],"systems,":[27],"we":[28],"construct":[29],"eigenfunctions":[31,104],"corresponding":[32],"to":[33,37,97],"system":[36,50],"form":[38],"predictors":[40],"systems.":[43],"The":[44,62,90,109],"conjugacy":[45],"map":[46],"between":[47],"and":[51],"its":[52],"Jacobian":[53],"linearization":[54],"is":[55,75,82,114],"learned":[56,80],"via":[57],"diffeomorphic":[59,76,94],"neural":[60],"network.":[61],"latter":[63],"allows":[64],"well-defined,":[67],"supervised":[68],"problem":[70],"formulation.":[71],"Given":[72],"learner":[74,95],"per":[77],"construction,":[78],"our":[79,112],"model":[81],"asymptotically":[83],"regardless":[85],"representation":[88],"accuracy.":[89],"universality":[91],"leads":[96],"universal":[99],"approximation":[100],"ability":[101],"-":[105],"admitting":[106],"suitable":[107],"expressivity.":[108],"efficacy":[110],"demonstrated":[115],"in":[116],"simulations.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2021-10-25T00:00:00"}