{"id":"https://openalex.org/W2971452749","doi":"https://doi.org/10.1109/cdc40024.2019.9029955","title":"Efficient Identification of Linear Evolutions in Nonlinear Vector Fields: Koopman Invariant Subspaces","display_name":"Efficient Identification of Linear Evolutions in Nonlinear Vector Fields: Koopman Invariant Subspaces","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2971452749","doi":"https://doi.org/10.1109/cdc40024.2019.9029955","mag":"2971452749"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9029955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9029955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1909.01419v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045305893","display_name":"Masih Haseli","orcid":"https://orcid.org/0000-0002-2133-8516"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Masih Haseli","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA","University of California,Department of Mechanical & Aerospace Engineering,San Diego,CA,USA,92093"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California,Department of Mechanical & Aerospace Engineering,San Diego,CA,USA,92093","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027913099","display_name":"Jorge Cort\u00e9s","orcid":"https://orcid.org/0000-0001-9582-5184"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jorge Cortes","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA","University of California,Department of Mechanical & Aerospace Engineering,San Diego,CA,USA,92093"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California,Department of Mechanical & Aerospace Engineering,San Diego,CA,USA,92093","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045305893"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.2896,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54524735,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"1","issue":null,"first_page":"1746","last_page":"1751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11008","display_name":"Aerodynamics and Acoustics in Jet Flows","score":0.977400004863739,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8758999109268188},{"id":"https://openalex.org/keywords/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.8129356503486633},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6113717555999756},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.5905511379241943},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.555147647857666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5473390817642212},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.5162487030029297},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4382725954055786},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.434165358543396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42429038882255554},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4159723222255707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3206104338169098},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30407196283340454},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1876143515110016}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8758999109268188},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.8129356503486633},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6113717555999756},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.5905511379241943},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.555147647857666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5473390817642212},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.5162487030029297},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4382725954055786},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.434165358543396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42429038882255554},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4159723222255707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3206104338169098},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30407196283340454},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1876143515110016},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc40024.2019.9029955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9029955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"mag:2971452749","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1909.01419v1","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2971452749","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1909.01419v1","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1591018827","https://openalex.org/W1908611567","https://openalex.org/W1997054581","https://openalex.org/W2014356541","https://openalex.org/W2060806808","https://openalex.org/W2067035505","https://openalex.org/W2078898317","https://openalex.org/W2164954534","https://openalex.org/W2172945660","https://openalex.org/W2208344185","https://openalex.org/W2395962256","https://openalex.org/W2405158121","https://openalex.org/W2561027863","https://openalex.org/W2594932112","https://openalex.org/W2730644873","https://openalex.org/W2735197468","https://openalex.org/W2766388929","https://openalex.org/W2892564416","https://openalex.org/W2972990939","https://openalex.org/W3038118776","https://openalex.org/W6740316558","https://openalex.org/W6743945476","https://openalex.org/W6749583154"],"related_works":["https://openalex.org/W2405158121","https://openalex.org/W3192648755","https://openalex.org/W2551533301","https://openalex.org/W3007673416","https://openalex.org/W3186107553","https://openalex.org/W2969440291","https://openalex.org/W2972990939","https://openalex.org/W3207464297","https://openalex.org/W2184825356","https://openalex.org/W2323091168","https://openalex.org/W781784501","https://openalex.org/W2159498192","https://openalex.org/W2727126511","https://openalex.org/W140552201","https://openalex.org/W2782745581","https://openalex.org/W2972127637","https://openalex.org/W2795167762","https://openalex.org/W2616426907","https://openalex.org/W3212231661","https://openalex.org/W2285590168"],"abstract_inverted_index":{"This":[0,151],"paper":[1],"presents":[2],"a":[3,19,24,54,96],"data-driven":[4],"approach":[5],"to":[6,43,66,73,108,123,154,161],"identify":[7,162],"finite-dimensional":[8],"Koopman":[9,16,46,142],"invariant":[10,143],"subspaces":[11],"and":[12,23,98,118],"eigenfunctions":[13],"of":[14,21,26,29,76,104,115,126,139,148],"the":[15,30,36,45,57,61,67,77,102,109,113,124,137,140,146,149,156],"operator.":[17,47],"Given":[18],"dictionary":[20,62],"functions":[22],"collection":[25],"data":[27],"snapshots":[28],"dynamical":[31],"system,":[32],"we":[33,130],"rely":[34],"on":[35,112,136],"Extended":[37],"Dynamic":[38],"Mode":[39],"Decomposition":[40,159],"(EDMD)":[41],"method":[42],"approximate":[44],"We":[48,93],"start":[49],"by":[50,60,80],"establishing":[51],"that,":[52],"if":[53],"function":[55],"in":[56,120,145],"space":[58],"generated":[59],"evolves":[63],"linearly":[64],"according":[65,107],"dynamics,":[68],"then":[69,94],"it":[70],"must":[71],"correspond":[72],"an":[74,132],"eigenvector":[75],"matrix":[78],"obtained":[79],"EDMD.":[81],"A":[82],"counterexample":[83],"shows":[84],"that":[85],"this":[86,128],"necessary":[87,97],"condition":[88,100],"is":[89],"however":[90],"not":[91],"sufficient.":[92],"propose":[95,131],"sufficient":[99],"for":[101],"identification":[103,138],"linear":[105,163,167],"evolutions":[106,164],"dynamics":[110],"based":[111,135],"application":[114],"EDMD":[116],"forward":[117],"backward":[119],"time.":[121],"Due":[122],"complexity":[125],"checking":[127],"condition,":[129],"alternative":[133],"characterization":[134],"largest":[141],"subspace":[144],"span":[147],"dictionary.":[150],"leads":[152],"us":[153],"introduce":[155],"Symmetric":[157],"Subspace":[158],"strategy":[160],"using":[165],"efficient":[166],"algebraic":[168],"methods.":[169],"Various":[170],"simulations":[171],"illustrate":[172],"our":[173],"results.":[174]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
