{"id":"https://openalex.org/W7160521138","doi":"https://doi.org/10.48550/arxiv.2605.04917","title":"Koopman Identification of Nonlinear Systems via Reservoir Liftings","display_name":"Koopman Identification of Nonlinear Systems via Reservoir Liftings","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160521138","doi":"https://doi.org/10.48550/arxiv.2605.04917"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04917","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04917","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.2605.04917","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074701231","display_name":"Weibin Gu","orcid":"https://orcid.org/0000-0002-5083-9408"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gu, Weibin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135604125","display_name":"Chen Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019720113","display_name":"Lu Shi","orcid":"https://orcid.org/0000-0001-8352-2813"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Lu","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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.6590999960899353,"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"}},"topics":[{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.6590999960899353,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.326200008392334,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.7594000101089478},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7046999931335449},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.6638000011444092},{"id":"https://openalex.org/keywords/reservoir-computing","display_name":"Reservoir computing","score":0.6276000142097473},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.5715000033378601},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5622000098228455},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47110000252723694},{"id":"https://openalex.org/keywords/nonlinear-system-identification","display_name":"Nonlinear system identification","score":0.46889999508857727},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4523000121116638},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.44339999556541443}],"concepts":[{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.7594000101089478},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7046999931335449},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.6638000011444092},{"id":"https://openalex.org/C135796866","wikidata":"https://www.wikidata.org/wiki/Q7315328","display_name":"Reservoir computing","level":4,"score":0.6276000142097473},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5622000098228455},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47110000252723694},{"id":"https://openalex.org/C22157029","wikidata":"https://www.wikidata.org/wiki/Q17080460","display_name":"Nonlinear system identification","level":4,"score":0.46889999508857727},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43950000405311584},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43689998984336853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41530001163482666},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41040000319480896},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.40549999475479126},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4009000062942505},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.375900000333786},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.3472999930381775},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31290000677108765},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04917","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04917","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.2605.04917","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04917","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":{"Learning":[0],"tractable":[1],"linear":[2],"representations":[3],"of":[4,69,93,120],"nonlinear":[5,123],"dynamical":[6,126],"systems":[7],"via":[8],"Koopman":[9,43,72,98],"operator":[10],"theory":[11],"is":[12,48],"often":[13],"hindered":[14],"by":[15,25,51],"dictionary":[16,44],"selection,":[17],"temporal":[18,46],"memory":[19,82,92],"encoding,":[20],"and":[21,65,125,135],"numerical":[22,67],"ill-conditioning.":[23],"Inspired":[24],"Reservoir":[26],"Computing":[27],"(RC)":[28],"paradigm,":[29],"this":[30],"paper":[31],"introduces":[32],"the":[33,58,70,90,94,103,121],"RC-Koopman":[34,112],"framework,":[35],"which":[36,97],"interprets":[37],"reservoir":[38,81,95],"as":[39],"a":[40,114],"stateful,":[41],"finite-dimensional":[42],"whose":[45],"depth":[47],"explicitly":[49],"controlled":[50],"its":[52],"spectral":[53,76],"radius.":[54],"We":[55],"show":[56],"that":[57,111],"Echo":[59],"State":[60],"Property":[61],"(ESP)":[62],"guarantees":[63],"well-posedness":[64],"favorable":[66,115],"conditioning":[68],"lifted":[71,104],"approximation.":[73],"A":[74],"correlation-based":[75],"radius":[77],"selection":[78],"algorithm":[79],"aligns":[80],"with":[83],"dominant":[84],"system":[85],"timescales.":[86],"Analysis":[87],"reveals":[88],"how":[89],"finite":[91],"determines":[96],"eigenfunctions":[99],"remain":[100],"observable":[101],"from":[102],"features.":[105],"Evaluation":[106],"on":[107],"synthetic":[108],"benchmarks":[109],"demonstrates":[110],"achieves":[113],"balance":[116],"between":[117],"reconstruction":[118],"accuracy":[119],"underlying":[122],"dynamics":[124],"stability,":[127],"compared":[128],"to":[129],"Extended":[130],"Dynamic":[131],"Mode":[132],"Decomposition":[133],"(EDMD)":[134],"Hankel-based":[136],"lifting":[137],"approaches.":[138],"Code":[139],"available":[140],"at:":[141],"https://github.com/NEAR-the-future/RC-Koopman.git":[142]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-08T00:00:00"}