{"id":"https://openalex.org/W2946056067","doi":"https://doi.org/10.1137/18m1233960","title":"Consistent Dynamic Mode Decomposition","display_name":"Consistent Dynamic Mode Decomposition","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2946056067","doi":"https://doi.org/10.1137/18m1233960","mag":"2946056067"},"language":"en","primary_location":{"id":"doi:10.1137/18m1233960","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1233960","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1905.09736","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010203098","display_name":"Omri Azencot","orcid":"https://orcid.org/0000-0001-9407-6601"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omri Azencot","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9407-6601","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085908411","display_name":"Wotao Yin","orcid":"https://orcid.org/0000-0001-6697-9731"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wotao Yin","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6697-9731","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrea Bertozzi","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":0.2777,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51858582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"3","first_page":"1565","last_page":"1585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.992900013923645,"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":0.992900013923645,"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/T10220","display_name":"Machine Fault Diagnosis Techniques","score":0.984000027179718,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/orthogonality","display_name":"Orthogonality","score":0.7256355285644531},{"id":"https://openalex.org/keywords/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.6846693754196167},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5490305423736572},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5476863980293274},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5316109657287598},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5094218850135803},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49018746614456177},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.45512694120407104},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4459717869758606},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36233922839164734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36042022705078125},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09477010369300842}],"concepts":[{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7256355285644531},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.6846693754196167},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5490305423736572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5476863980293274},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5316109657287598},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5094218850135803},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49018746614456177},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45512694120407104},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4459717869758606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36233922839164734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36042022705078125},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09477010369300842},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/18m1233960","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1233960","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.09736","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.09736","pdf_url":"https://arxiv.org/pdf/1905.09736","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":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1905.09736","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1905.09736","pdf_url":"https://arxiv.org/pdf/1905.09736","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":null,"raw_type":"text"},{"id":"mag:2946056067","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.09736.pdf","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},{"id":"pmh:oai:escholarship.org:ark:/13030/qt6fb129jq","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/6fb129jq","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, vol 18, iss 3","raw_type":"article"},{"id":"doi:10.48550/arxiv.1905.09736","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.09736","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1905.09736","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.09736","pdf_url":"https://arxiv.org/pdf/1905.09736","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":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.41999998688697815,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1704247662","display_name":"Operator Splitting Methods: Certificates and Second-Order Acceleration","funder_award_id":"1720237","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G196413677","display_name":null,"funder_award_id":"DMS-1720237","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2270235621","display_name":null,"funder_award_id":"793800","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3666116665","display_name":null,"funder_award_id":"N000141712162","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5948696453","display_name":null,"funder_award_id":"DMS-1737770","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8857385272","display_name":"Re-meshing of a given triangle mesh surface to a quad mesh using physically motivated methods based on the Ginzburg--Landau potential and solved efficiently solved via numerical splitting scheme","funder_award_id":"793800","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8998889701","display_name":"ATD: Sparsity Models for Forecasting Spatio-Temporal Human Dynamics","funder_award_id":"1737770","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1908611567","https://openalex.org/W1976481924","https://openalex.org/W1993839530","https://openalex.org/W1997054581","https://openalex.org/W2014356541","https://openalex.org/W2018089423","https://openalex.org/W2023043517","https://openalex.org/W2045079045","https://openalex.org/W2047161559","https://openalex.org/W2058775581","https://openalex.org/W2065806093","https://openalex.org/W2070685860","https://openalex.org/W2078898317","https://openalex.org/W2080914886","https://openalex.org/W2088748973","https://openalex.org/W2112823474","https://openalex.org/W2115710526","https://openalex.org/W2142058898","https://openalex.org/W2144012927","https://openalex.org/W2145962650","https://openalex.org/W2164278908","https://openalex.org/W2164954534","https://openalex.org/W2168222921","https://openalex.org/W2208344185","https://openalex.org/W2244987555","https://openalex.org/W2331372117","https://openalex.org/W2390728582","https://openalex.org/W2562388386","https://openalex.org/W2582771730","https://openalex.org/W2605532580","https://openalex.org/W2751142080","https://openalex.org/W2788613524","https://openalex.org/W2800035578","https://openalex.org/W2962782996","https://openalex.org/W2962853966","https://openalex.org/W3031689935","https://openalex.org/W3099504209","https://openalex.org/W3099803807","https://openalex.org/W3102306519","https://openalex.org/W3104556657","https://openalex.org/W3143596294","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W2339027274","https://openalex.org/W2983870448","https://openalex.org/W3202996579","https://openalex.org/W2616806001","https://openalex.org/W3171982279","https://openalex.org/W3104590783","https://openalex.org/W3039860230","https://openalex.org/W2767167368","https://openalex.org/W3042111838","https://openalex.org/W2890056239","https://openalex.org/W3176634865","https://openalex.org/W2950451513","https://openalex.org/W2886084777","https://openalex.org/W3037674050","https://openalex.org/W2746636734","https://openalex.org/W2982168727","https://openalex.org/W209789590","https://openalex.org/W1530422469","https://openalex.org/W3134690469","https://openalex.org/W2618880398"],"abstract_inverted_index":{"We":[0,153],"propose":[1],"a":[2,30,65,108,148],"new":[3],"method":[4,44,127],"for":[5,111],"computing":[6],"dynamic":[7],"mode":[8],"decomposition":[9],"evolution":[10],"matrices,":[11],"which":[12,131],"we":[13],"use":[14],"to":[15,64,84,99,106,147,157],"analyze":[16],"dynamical":[17,164],"systems.":[18,165],"Unlike":[19],"the":[20,51,54,90,112,125],"majority":[21],"of":[22,34,53,68,89,128],"existing":[23],"methods,":[24],"our":[25,80,155],"approach":[26,156],"is":[27,62,82,87,105,121,145],"based":[28],"on":[29,50,161],"variational":[31],"formulation":[32],"consisting":[33],"data":[35,55,98],"alignment":[36],"penalty":[37],"terms":[38],"and":[39,59,92,114,144],"constitutive":[40],"orthogonality":[41],"constraints.":[42],"Our":[43,102,139],"does":[45,94],"not":[46,95],"make":[47],"any":[48],"assumptions":[49],"structure":[52],"or":[56,73],"their":[57],"size,":[58],"thus":[60],"it":[61,93],"applicable":[63],"wide":[66],"range":[67],"problems":[69],"including":[70],"nonlinear":[71],"scenarios":[72],"extremely":[74],"small":[75],"observation":[76],"sets.":[77],"In":[78],"addition,":[79],"technique":[81],"robust":[83],"noise":[85],"that":[86],"independent":[88],"dynamics":[91],"require":[96],"input":[97],"be":[100],"sequential.":[101],"key":[103],"idea":[104],"introduce":[107],"regularization":[109],"term":[110],"forward":[113],"backward":[115],"dynamics.":[116],"The":[117],"obtained":[118],"minimization":[119],"problem":[120],"solved":[122],"efficiently":[123],"using":[124],"alternating":[126],"multipliers":[129],"(ADMM)":[130],"requires":[132],"two":[133],"Sylvester":[134],"equation":[135],"solves":[136],"per":[137],"iteration.":[138],"numerical":[140],"scheme":[141],"converges":[142],"empirically":[143],"similar":[146],"provably":[149],"convergent":[150],"ADMM":[151],"scheme.":[152],"compare":[154],"various":[158],"state-of-the-art":[159],"methods":[160],"several":[162],"benchmark":[163]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}