{"id":"https://openalex.org/W4409441691","doi":"https://doi.org/10.1137/24m1662370","title":"Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators","display_name":"Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators","publication_year":2025,"publication_date":"2025-04-15","ids":{"openalex":"https://openalex.org/W4409441691","doi":"https://doi.org/10.1137/24m1662370"},"language":"en","primary_location":{"id":"doi:10.1137/24m1662370","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1662370","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082589336","display_name":"Matthew J. Colbrook","orcid":"https://orcid.org/0000-0003-4964-9575"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matthew J. Colbrook","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK"],"raw_orcid":"https://orcid.org/0000-0003-4964-9575","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083653191","display_name":"Catherine Drysdale","orcid":"https://orcid.org/0009-0005-0077-0309"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Catherine Drysdale","raw_affiliation_strings":["Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Birmingham, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041470871","display_name":"Andrew Horning","orcid":"https://orcid.org/0000-0003-0305-4349"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Horning","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8909,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.96511628,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"24","issue":"2","first_page":"1150","last_page":"1190"},"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":0.9959999918937683,"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.975600004196167,"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/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.9379627704620361},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.903008222579956},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6030164957046509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5981916189193726},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.5242981314659119},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.517268717288971},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4267827868461609},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36325526237487793},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32997655868530273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26602792739868164},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.264183908700943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2324305772781372},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07090526819229126}],"concepts":[{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.9379627704620361},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.903008222579956},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6030164957046509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5981916189193726},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.5242981314659119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.517268717288971},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4267827868461609},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36325526237487793},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32997655868530273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26602792739868164},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.264183908700943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2324305772781372},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07090526819229126},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/24m1662370","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1662370","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:pure.atira.dk:openaire_cris_publications/8d76f4c0-313f-4835-b635-21f3040de65c","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/8d76f4c0-313f-4835-b635-21f3040de65c","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Colbrook, M J, Drysdale, C & Horning, A 2025, 'Rigged Dynamic Mode Decomposition : Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators', SIAM Journal on Applied Dynamical Systems, vol. 24, no. 2, pp. 1150-1190. https://doi.org/10.1137/24M1662370","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3667954464","display_name":"Additional Funding for Mathematical Sciences: Isaac Newton Institute for Mathematical Sciences","funder_award_id":"EP/V521929/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320313284","display_name":"Isaac Newton Institute for Mathematical Sciences","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":89,"referenced_works":["https://openalex.org/W149522324","https://openalex.org/W196973002","https://openalex.org/W576074149","https://openalex.org/W580025611","https://openalex.org/W615000568","https://openalex.org/W1565083997","https://openalex.org/W1582592707","https://openalex.org/W1591018827","https://openalex.org/W1714751346","https://openalex.org/W1970687099","https://openalex.org/W1992685699","https://openalex.org/W1995242373","https://openalex.org/W1997054581","https://openalex.org/W1997711740","https://openalex.org/W1998527589","https://openalex.org/W2010958356","https://openalex.org/W2012352492","https://openalex.org/W2012987256","https://openalex.org/W2016844160","https://openalex.org/W2022769353","https://openalex.org/W2030380156","https://openalex.org/W2037558275","https://openalex.org/W2037769757","https://openalex.org/W2041025963","https://openalex.org/W2042231045","https://openalex.org/W2054348419","https://openalex.org/W2055124047","https://openalex.org/W2056406034","https://openalex.org/W2060806808","https://openalex.org/W2063564090","https://openalex.org/W2064361774","https://openalex.org/W2067035505","https://openalex.org/W2070959866","https://openalex.org/W2073738316","https://openalex.org/W2086615314","https://openalex.org/W2087044024","https://openalex.org/W2088907598","https://openalex.org/W2114876173","https://openalex.org/W2116317450","https://openalex.org/W2121020818","https://openalex.org/W2126479355","https://openalex.org/W2126999002","https://openalex.org/W2128089417","https://openalex.org/W2131946712","https://openalex.org/W2140130898","https://openalex.org/W2141394518","https://openalex.org/W2164954534","https://openalex.org/W2263822652","https://openalex.org/W2324610639","https://openalex.org/W2324802422","https://openalex.org/W2510030309","https://openalex.org/W2551318894","https://openalex.org/W2732181512","https://openalex.org/W2767099474","https://openalex.org/W2777417212","https://openalex.org/W2887603774","https://openalex.org/W2912475681","https://openalex.org/W2950068926","https://openalex.org/W2953392960","https://openalex.org/W2963186138","https://openalex.org/W2963611087","https://openalex.org/W2964350754","https://openalex.org/W2968477129","https://openalex.org/W2991844785","https://openalex.org/W3000187486","https://openalex.org/W3019988632","https://openalex.org/W3038118776","https://openalex.org/W3092380835","https://openalex.org/W3098172061","https://openalex.org/W3099462237","https://openalex.org/W3100610601","https://openalex.org/W3104635675","https://openalex.org/W3127953541","https://openalex.org/W3128722827","https://openalex.org/W3129637124","https://openalex.org/W3139823826","https://openalex.org/W3153337028","https://openalex.org/W3186144926","https://openalex.org/W3189651510","https://openalex.org/W3216122675","https://openalex.org/W4210577959","https://openalex.org/W4213068077","https://openalex.org/W4300293005","https://openalex.org/W4308937157","https://openalex.org/W4316690596","https://openalex.org/W4380887250","https://openalex.org/W4399045615","https://openalex.org/W4399333359","https://openalex.org/W4406599336"],"related_works":["https://openalex.org/W2245403906","https://openalex.org/W2393344178","https://openalex.org/W2597763219","https://openalex.org/W2495930062","https://openalex.org/W2014356541","https://openalex.org/W2168222921","https://openalex.org/W2992578100","https://openalex.org/W2051796801","https://openalex.org/W4396653515","https://openalex.org/W4297634015"],"abstract_inverted_index":{"We":[0,115,154],"introduce":[1],"the":[2,20,62,74,143,166,190],"Rigged":[3,51,80,181],"Dynamic":[4,95],"Mode":[5,96],"Decomposition":[6,97],"(Rigged":[7,146],"DMD)":[8],"algorithm,":[9],"which":[10],"computes":[11],"generalized":[12,68,86,122],"eigenfunction":[13],"decompositions":[14,198],"of":[15,22,197],"Koopman":[16,24,63,87],"operators.":[17],"By":[18],"considering":[19],"evolution":[21],"observables,":[23],"operators":[25],"transform":[26],"complex":[27],"nonlinear":[28],"dynamics":[29],"into":[30],"a":[31,57,105,130,160,170,176],"linear":[32],"framework":[33,132],"suitable":[34],"for":[35,85,101,121,133,192],"spectral":[36,113,125],"analysis.":[37],"While":[38],"powerful,":[39],"traditional":[40],"dynamic":[41],"mode":[42],"decomposition":[43,107],"(DMD)":[44],"techniques":[45],"often":[46],"struggle":[47],"with":[48,56,98,151,159,199],"continuous":[49,112,200],"spectra,":[50],"DMD":[52,81,147],"addresses":[53],"these":[54],"challenges":[55],"data-driven":[58],"methodology":[59],"that":[60],"approximates":[61],"operator\u2019s":[64],"resolvent":[65],"and":[66,89,111,124,169,185,195],"its":[67,78],"eigenfunctions":[69,88,123],"using":[70,138],"snapshot":[71],"data":[72],"from":[73],"system\u2019s":[75],"evolution.":[76],"At":[77],"core,":[79],"builds":[82],"wave-packet":[83],"approximations":[84],"modes":[90],"by":[91],"integrating":[92],"Measure-Preserving":[93],"Extended":[94],"high-order":[99,118],"kernels":[100],"smoothing.":[102],"This":[103,187],"provides":[104],"robust":[106],"encompassing":[108],"both":[109],"discrete":[110],"elements.":[114],"derive":[116],"explicit":[117],"convergence":[119],"theorems":[120],"measures.":[126],"Additionally,":[127],"we":[128],"propose":[129],"novel":[131],"constructing":[134],"rigged":[135],"Hilbert":[136],"spaces":[137],"time-delay":[139],"embedding,":[140],"significantly":[141],"extending":[142],"algorithm\u2019s":[144],"applicability":[145],"can":[148],"be":[149],"used":[150],"any":[152],"rigging).":[153],"provide":[155],"examples,":[156],"including":[157],"systems":[158],"Lebesgue":[161],"spectrum,":[162],"integrable":[163],"Hamiltonian":[164],"systems,":[165],"Lorenz":[167],"system,":[168],"high-Reynolds":[171],"number":[172],"lid-driven":[173],"flow":[174],"in":[175],"two-dimensional":[177],"square":[178],"cavity,":[179],"demonstrating":[180],"DMD\u2019s":[182],"convergence,":[183],"efficiency,":[184],"versatility.":[186],"work":[188],"paves":[189],"way":[191],"future":[193],"research":[194],"applications":[196],"spectra.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7}],"updated_date":"2026-08-12T07:12:00.856984","created_date":"2025-10-10T00:00:00"}