{"id":"https://openalex.org/W3129637124","doi":"https://doi.org/10.1137/21m1401243","title":"Modern Koopman Theory for Dynamical Systems","display_name":"Modern Koopman Theory for Dynamical Systems","publication_year":2022,"publication_date":"2022-05-01","ids":{"openalex":"https://openalex.org/W3129637124","doi":"https://doi.org/10.1137/21m1401243","mag":"3129637124"},"language":"en","primary_location":{"id":"doi:10.1137/21m1401243","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1401243","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5062653961","display_name":"Steven L. Brunton","orcid":"https://orcid.org/0000-0002-6565-5118"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven L. Brunton","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6565-5118","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004426104","display_name":"Marko Budi\u0161i\u0107","orcid":"https://orcid.org/0000-0002-4992-0284"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marko Budi\u0161i\u0107","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4992-0284","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085393443","display_name":"Eurika Kaiser","orcid":"https://orcid.org/0000-0001-6049-0812"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eurika Kaiser","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6049-0812","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083450863","display_name":"J. Nathan Kutz","orcid":"https://orcid.org/0000-0002-6004-2275"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Nathan Kutz","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":50.3338,"has_fulltext":false,"cited_by_count":501,"citation_normalized_percentile":{"value":0.99957242,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"64","issue":"2","first_page":"229","last_page":"340"},"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9843999743461609,"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9732000231742859,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.7139037847518921},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6867788434028625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5912107229232788},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5673648118972778},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5430244207382202},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4969017803668976},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.48159119486808777},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.48107171058654785},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.43825241923332214},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4239228367805481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3270045518875122},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.16268417239189148}],"concepts":[{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.7139037847518921},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6867788434028625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5912107229232788},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5673648118972778},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5430244207382202},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4969017803668976},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.48159119486808777},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.48107171058654785},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.43825241923332214},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4239228367805481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3270045518875122},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.16268417239189148},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1401243","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1401243","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1123836689","display_name":null,"funder_award_id":"W911NF-19-1-0045","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G4891811929","display_name":null,"funder_award_id":"W911NF-17-1-0045","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6052167412","display_name":"HDR: I-DIRSE-FW: Accelerating the Engineering Design and Manufacturing Life-Cycle with Data Science","funder_award_id":"1934292","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G615320561","display_name":null,"funder_award_id":"HR011-16-C-0016","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":493,"referenced_works":["https://openalex.org/W86907751","https://openalex.org/W91588129","https://openalex.org/W135863185","https://openalex.org/W169034099","https://openalex.org/W189321991","https://openalex.org/W210359992","https://openalex.org/W588139629","https://openalex.org/W614362261","https://openalex.org/W1057021034","https://openalex.org/W1497399181","https://openalex.org/W1506169651","https://openalex.org/W1512798540","https://openalex.org/W1520128606","https://openalex.org/W1520892678","https://openalex.org/W1522319528","https://openalex.org/W1535144613","https://openalex.org/W1549386224","https://openalex.org/W1572164227","https://openalex.org/W1575974143","https://openalex.org/W1591018827","https://openalex.org/W1592958377","https://openalex.org/W1597840575","https://openalex.org/W1631607997","https://openalex.org/W1635210704","https://openalex.org/W1723433682","https://openalex.org/W1763926976","https://openalex.org/W1802196594","https://openalex.org/W1860903952","https://openalex.org/W1867384304","https://openalex.org/W1908611567","https://openalex.org/W1927681941","https://openalex.org/W1964418103","https://openalex.org/W1965324089","https://openalex.org/W1967994787","https://openalex.org/W1969563507","https://openalex.org/W1970687099","https://openalex.org/W1972949070","https://openalex.org/W1975452069","https://openalex.org/W1975534246","https://openalex.org/W1975739906","https://openalex.org/W1976481924","https://openalex.org/W1979769287","https://openalex.org/W1980844039","https://openalex.org/W1981193003","https://openalex.org/W1981214426","https://openalex.org/W1981353078","https://openalex.org/W1985868255","https://openalex.org/W1986218785","https://openalex.org/W1986893967","https://openalex.org/W1987236926","https://openalex.org/W1989544083","https://openalex.org/W1990318523","https://openalex.org/W1992685699","https://openalex.org/W1992728683","https://openalex.org/W1993438131","https://openalex.org/W1993839530","https://openalex.org/W1994368767","https://openalex.org/W1994953169","https://openalex.org/W1997054581","https://openalex.org/W1997126009","https://openalex.org/W1997815317","https://openalex.org/W1998727969","https://openalex.org/W1998765060","https://openalex.org/W1998902509","https://openalex.org/W2000778604","https://openalex.org/W2001097642","https://openalex.org/W2001659478","https://openalex.org/W2002902303","https://openalex.org/W2006554089","https://openalex.org/W2008881650","https://openalex.org/W2008995486","https://openalex.org/W2011296693","https://openalex.org/W2012302931","https://openalex.org/W2013610941","https://openalex.org/W2014356541","https://openalex.org/W2016211524","https://openalex.org/W2016315007","https://openalex.org/W2016319810","https://openalex.org/W2020934201","https://openalex.org/W2021972235","https://openalex.org/W2023043517","https://openalex.org/W2027607804","https://openalex.org/W2027701333","https://openalex.org/W2027889814","https://openalex.org/W2030380156","https://openalex.org/W2035419682","https://openalex.org/W2036490427","https://openalex.org/W2037558275","https://openalex.org/W2038516800","https://openalex.org/W2040690030","https://openalex.org/W2041025963","https://openalex.org/W2044069082","https://openalex.org/W2045384647","https://openalex.org/W2050048613","https://openalex.org/W2050651297","https://openalex.org/W2053040607","https://openalex.org/W2053095324","https://openalex.org/W2054201152","https://openalex.org/W2054686405","https://openalex.org/W2054714794","https://openalex.org/W2055316018","https://openalex.org/W2056436142","https://openalex.org/W2058975882","https://openalex.org/W2060806808","https://openalex.org/W2061383882","https://openalex.org/W2061723278","https://openalex.org/W2063018656","https://openalex.org/W2063564090","https://openalex.org/W2063819580","https://openalex.org/W2064361774","https://openalex.org/W2064793353","https://openalex.org/W2065806093","https://openalex.org/W2067035505","https://openalex.org/W2067765015","https://openalex.org/W2069159682","https://openalex.org/W2070685860","https://openalex.org/W2071665095","https://openalex.org/W2072020500","https://openalex.org/W2073738316","https://openalex.org/W2073787051","https://openalex.org/W2074388175","https://openalex.org/W2077157707","https://openalex.org/W2077342808","https://openalex.org/W2078206849","https://openalex.org/W2078898317","https://openalex.org/W2079533476","https://openalex.org/W2080914886","https://openalex.org/W2084341220","https://openalex.org/W2084430802","https://openalex.org/W2084755618","https://openalex.org/W2087044024","https://openalex.org/W2089996117","https://openalex.org/W2090131196","https://openalex.org/W2092928868","https://openalex.org/W2094361202","https://openalex.org/W2094686470","https://openalex.org/W2097098299","https://openalex.org/W2097388431","https://openalex.org/W2097581696","https://openalex.org/W2098382127","https://openalex.org/W2098514243","https://openalex.org/W2100238376","https://openalex.org/W2100881658","https://openalex.org/W2101080583","https://openalex.org/W2105338713","https://openalex.org/W2114876173","https://openalex.org/W2115710526","https://openalex.org/W2117684310","https://openalex.org/W2117756735","https://openalex.org/W2118253161","https://openalex.org/W2118575947","https://openalex.org/W2118830060","https://openalex.org/W2120101088","https://openalex.org/W2120953452","https://openalex.org/W2122175380","https://openalex.org/W2122424119","https://openalex.org/W2125116327","https://openalex.org/W2126887346","https://openalex.org/W2126999002","https://openalex.org/W2128536454","https://openalex.org/W2129812935","https://openalex.org/W2130212796","https://openalex.org/W2130682193","https://openalex.org/W2135046866","https://openalex.org/W2135466564","https://openalex.org/W2137595289","https://openalex.org/W2140998418","https://openalex.org/W2145096794","https://openalex.org/W2148087508","https://openalex.org/W2149650283","https://openalex.org/W2149929409","https://openalex.org/W2152742892","https://openalex.org/W2152896489","https://openalex.org/W2154338503","https://openalex.org/W2155846280","https://openalex.org/W2157300063","https://openalex.org/W2159786849","https://openalex.org/W2164954534","https://openalex.org/W2168090960","https://openalex.org/W2168222921","https://openalex.org/W2169967276","https://openalex.org/W2170054433","https://openalex.org/W2170714674","https://openalex.org/W2172945660","https://openalex.org/W2173835935","https://openalex.org/W2185048068","https://openalex.org/W2208344185","https://openalex.org/W2215349127","https://openalex.org/W2239232218","https://openalex.org/W2249650787","https://openalex.org/W2254437089","https://openalex.org/W2266932692","https://openalex.org/W2277245261","https://openalex.org/W2291876840","https://openalex.org/W2296616510","https://openalex.org/W2297483870","https://openalex.org/W2311231005","https://openalex.org/W2313551992","https://openalex.org/W2313953460","https://openalex.org/W2319450871","https://openalex.org/W2321240973","https://openalex.org/W2324802422","https://openalex.org/W2328819313","https://openalex.org/W2332297685","https://openalex.org/W2334374518","https://openalex.org/W2341174028","https://openalex.org/W2395962256","https://openalex.org/W2399643973","https://openalex.org/W2405892775","https://openalex.org/W2467067030","https://openalex.org/W2473533240","https://openalex.org/W2484228318","https://openalex.org/W2487770199","https://openalex.org/W2488424576","https://openalex.org/W2492870335","https://openalex.org/W2509969228","https://openalex.org/W2510030309","https://openalex.org/W2516285675","https://openalex.org/W2534240011","https://openalex.org/W2549774780","https://openalex.org/W2550111547","https://openalex.org/W2550753746","https://openalex.org/W2551318894","https://openalex.org/W2551533301","https://openalex.org/W2552979726","https://openalex.org/W2557007068","https://openalex.org/W2559655401","https://openalex.org/W2561027863","https://openalex.org/W2561819197","https://openalex.org/W2564386551","https://openalex.org/W2565432921","https://openalex.org/W2566199617","https://openalex.org/W2568560373","https://openalex.org/W2582771730","https://openalex.org/W2584339899","https://openalex.org/W2585298970","https://openalex.org/W2591704465","https://openalex.org/W2594932112","https://openalex.org/W2597042608","https://openalex.org/W2605255410","https://openalex.org/W2605295971","https://openalex.org/W2605532580","https://openalex.org/W2608227839","https://openalex.org/W2611154832","https://openalex.org/W2612690371","https://openalex.org/W2615252773","https://openalex.org/W2615735362","https://openalex.org/W2620889299","https://openalex.org/W2621497448","https://openalex.org/W2635039932","https://openalex.org/W2730644873","https://openalex.org/W2732181512","https://openalex.org/W2739844829","https://openalex.org/W2740586183","https://openalex.org/W2746980346","https://openalex.org/W2748760860","https://openalex.org/W2751142080","https://openalex.org/W2765372792","https://openalex.org/W2765842354","https://openalex.org/W2765861397","https://openalex.org/W2766388929","https://openalex.org/W2767376248","https://openalex.org/W2767487833","https://openalex.org/W2773571561","https://openalex.org/W2775659970","https://openalex.org/W2777417212","https://openalex.org/W2782591075","https://openalex.org/W2783869220","https://openalex.org/W2784412233","https://openalex.org/W2785195724","https://openalex.org/W2785514482","https://openalex.org/W2795067111","https://openalex.org/W2795688958","https://openalex.org/W2795982117","https://openalex.org/W2796188682","https://openalex.org/W2796933812","https://openalex.org/W2800035578","https://openalex.org/W2803477776","https://openalex.org/W2803512261","https://openalex.org/W2808506538","https://openalex.org/W2810719353","https://openalex.org/W2810798408","https://openalex.org/W2883377409","https://openalex.org/W2887053799","https://openalex.org/W2887432454","https://openalex.org/W2887603774","https://openalex.org/W2889716319","https://openalex.org/W2891039272","https://openalex.org/W2892564416","https://openalex.org/W2898623516","https://openalex.org/W2899283552","https://openalex.org/W2901625726","https://openalex.org/W2902105539","https://openalex.org/W2902132588","https://openalex.org/W2904677466","https://openalex.org/W2904764104","https://openalex.org/W2907600550","https://openalex.org/W2911792890","https://openalex.org/W2912279961","https://openalex.org/W2916469819","https://openalex.org/W2937374275","https://openalex.org/W2941517668","https://openalex.org/W2946329399","https://openalex.org/W2947655929","https://openalex.org/W2951061033","https://openalex.org/W2962749092","https://openalex.org/W2962782996","https://openalex.org/W2963006871","https://openalex.org/W2963013180","https://openalex.org/W2963065344","https://openalex.org/W2963116251","https://openalex.org/W2963186138","https://openalex.org/W2963198642","https://openalex.org/W2963218230","https://openalex.org/W2963269142","https://openalex.org/W2963294772","https://openalex.org/W2963401716","https://openalex.org/W2963448313","https://openalex.org/W2963490775","https://openalex.org/W2963535512","https://openalex.org/W2963609158","https://openalex.org/W2963611087","https://openalex.org/W2963638622","https://openalex.org/W2963764551","https://openalex.org/W2963765797","https://openalex.org/W2963823985","https://openalex.org/W2963874965","https://openalex.org/W2963895143","https://openalex.org/W2963942037","https://openalex.org/W2963982496","https://openalex.org/W2964119648","https://openalex.org/W2964129632","https://openalex.org/W2964350754","https://openalex.org/W2964917500","https://openalex.org/W2966398373","https://openalex.org/W2968169371","https://openalex.org/W2968477129","https://openalex.org/W2968800745","https://openalex.org/W2971179937","https://openalex.org/W2972246420","https://openalex.org/W2972469579","https://openalex.org/W2972510165","https://openalex.org/W2973004389","https://openalex.org/W2973022759","https://openalex.org/W2973119841","https://openalex.org/W2973226598","https://openalex.org/W2979786244","https://openalex.org/W2980309004","https://openalex.org/W2980428466","https://openalex.org/W2981080108","https://openalex.org/W2981246174","https://openalex.org/W2981825520","https://openalex.org/W2983023174","https://openalex.org/W2986332384","https://openalex.org/W2986795381","https://openalex.org/W2986903508","https://openalex.org/W2991844785","https://openalex.org/W2993471559","https://openalex.org/W2996064936","https://openalex.org/W2997318655","https://openalex.org/W2999026783","https://openalex.org/W3000187486","https://openalex.org/W3000352593","https://openalex.org/W3003383168","https://openalex.org/W3003922491","https://openalex.org/W3004311099","https://openalex.org/W3006550916","https://openalex.org/W3007433014","https://openalex.org/W3008005432","https://openalex.org/W3008321886","https://openalex.org/W3008586589","https://openalex.org/W3009152446","https://openalex.org/W3009887398","https://openalex.org/W3010501116","https://openalex.org/W3011877437","https://openalex.org/W3012046555","https://openalex.org/W3012294986","https://openalex.org/W3012894137","https://openalex.org/W3013279290","https://openalex.org/W3013803313","https://openalex.org/W3014853108","https://openalex.org/W3019988632","https://openalex.org/W3020690188","https://openalex.org/W3021107381","https://openalex.org/W3029571026","https://openalex.org/W3033602550","https://openalex.org/W3033823039","https://openalex.org/W3034565332","https://openalex.org/W3034655405","https://openalex.org/W3036818215","https://openalex.org/W3038118776","https://openalex.org/W3040536995","https://openalex.org/W3043552674","https://openalex.org/W3046212064","https://openalex.org/W3046676639","https://openalex.org/W3081317218","https://openalex.org/W3084942782","https://openalex.org/W3088290697","https://openalex.org/W3090325895","https://openalex.org/W3092216445","https://openalex.org/W3092923133","https://openalex.org/W3093080684","https://openalex.org/W3093397140","https://openalex.org/W3094624870","https://openalex.org/W3098172061","https://openalex.org/W3098196555","https://openalex.org/W3098232754","https://openalex.org/W3098287931","https://openalex.org/W3098607878","https://openalex.org/W3098732481","https://openalex.org/W3098734061","https://openalex.org/W3098781239","https://openalex.org/W3098898877","https://openalex.org/W3098951945","https://openalex.org/W3099211663","https://openalex.org/W3099423575","https://openalex.org/W3099462237","https://openalex.org/W3099504209","https://openalex.org/W3099674394","https://openalex.org/W3099803807","https://openalex.org/W3100015594","https://openalex.org/W3100184721","https://openalex.org/W3100426126","https://openalex.org/W3100769368","https://openalex.org/W3100771563","https://openalex.org/W3101190453","https://openalex.org/W3101211657","https://openalex.org/W3101219234","https://openalex.org/W3101360817","https://openalex.org/W3101378293","https://openalex.org/W3101392902","https://openalex.org/W3101468015","https://openalex.org/W3101607551","https://openalex.org/W3101700534","https://openalex.org/W3102013942","https://openalex.org/W3102091866","https://openalex.org/W3102140816","https://openalex.org/W3102306519","https://openalex.org/W3102448572","https://openalex.org/W3102548437","https://openalex.org/W3102923851","https://openalex.org/W3103045662","https://openalex.org/W3103987666","https://openalex.org/W3104009841","https://openalex.org/W3104037750","https://openalex.org/W3104165299","https://openalex.org/W3104208014","https://openalex.org/W3104343133","https://openalex.org/W3104556657","https://openalex.org/W3105245152","https://openalex.org/W3105414711","https://openalex.org/W3105778049","https://openalex.org/W3106034762","https://openalex.org/W3106111631","https://openalex.org/W3109381375","https://openalex.org/W3111722701","https://openalex.org/W3114529347","https://openalex.org/W3117366218","https://openalex.org/W3118080324","https://openalex.org/W3118286305","https://openalex.org/W3123603494","https://openalex.org/W3124944419","https://openalex.org/W3126228179","https://openalex.org/W3126331428","https://openalex.org/W3126673178","https://openalex.org/W3133720149","https://openalex.org/W3133989388","https://openalex.org/W3136945292","https://openalex.org/W3137474564","https://openalex.org/W3137898953","https://openalex.org/W3140564639","https://openalex.org/W3141034409","https://openalex.org/W3150782421","https://openalex.org/W3153137857","https://openalex.org/W3157934565","https://openalex.org/W3158061203","https://openalex.org/W3159554723","https://openalex.org/W3161200675","https://openalex.org/W3163453057","https://openalex.org/W3167461778","https://openalex.org/W3169372165","https://openalex.org/W3175664076","https://openalex.org/W3176259658","https://openalex.org/W3179372756","https://openalex.org/W3180197665","https://openalex.org/W3186605155","https://openalex.org/W3198465839","https://openalex.org/W3201106141","https://openalex.org/W3209120121","https://openalex.org/W4213367101","https://openalex.org/W4220834549","https://openalex.org/W4230003953","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W3085009157","https://openalex.org/W1541871911","https://openalex.org/W2119813522","https://openalex.org/W2050811761","https://openalex.org/W2230606337","https://openalex.org/W2573078457","https://openalex.org/W2505854718","https://openalex.org/W2044696633","https://openalex.org/W2735833300","https://openalex.org/W4238935091"],"abstract_inverted_index":{"The":[0,124],"field":[1,237],"of":[2,61,70,75,81,94,126,157,205,224,238,254],"dynamical":[3,148,255],"systems":[4,96,109],"is":[5,129,153],"being":[6],"transformed":[7],"by":[8],"the":[9,50,68,76,89,114,151,179,234,251],"mathematical":[10],"tools":[11],"and":[12,18,23,92,110,166,170,187,213,216,231,248],"algorithms":[13],"emerging":[14],"from":[15],"modern":[16,206],"computing":[17],"data":[19,165],"science.":[20],"First-principles":[21],"derivations":[22],"asymptotic":[24],"reductions":[25],"are":[26,57,242],"giving":[27],"way":[28],"to":[29,87,132,143,189,193,244],"data-driven":[30],"approaches":[31,146],"that":[32,241],"formulate":[33],"models":[34],"in":[35,53,59,112,155,195,233],"operator-theoretic":[36],"or":[37],"probabilistic":[38],"frameworks.":[39],"Koopman":[40,127,191,207],"spectral":[41],"theory":[42,140,192],"has":[43,84],"emerged":[44],"as":[45,178],"a":[46,120,221],"dominant":[47],"perspective":[48],"over":[49],"past":[51],"decade,":[52],"which":[54,113],"nonlinear":[55,82,95],"dynamics":[56,83,115],"represented":[58],"terms":[60,156],"an":[62,203],"infinite-dimensional":[63],"linear":[64,79,103,118],"operator":[65,208],"acting":[66],"on":[67],"space":[69],"all":[71],"possible":[72],"measurement":[73],"functions":[74],"system.":[77],"This":[78],"representation":[80],"tremendous":[85],"potential":[86],"enable":[88],"prediction,":[90],"estimation,":[91],"control":[93],"with":[97,220],"standard":[98],"textbook":[99],"methods":[100,219],"developed":[101,186],"for":[102,147,162],"systems.":[104,256],"However,":[105],"obtaining":[106],"finite-dimensional":[107],"coordinate":[108],"embeddings":[111],"appear":[116],"approximately":[117],"remains":[119],"central":[121],"open":[122],"challenge.":[123],"success":[125],"analysis":[128],"due":[130],"primarily":[131],"three":[133],"key":[134,229],"factors:":[135],"(1)":[136],"there":[137],"exists":[138],"rigorous":[139],"connecting":[141],"it":[142,160],"classical":[144],"geometric":[145],"systems;":[149],"(2)":[150],"approach":[152],"formulated":[154],"measurements,":[158],"making":[159],"ideal":[161],"leveraging":[163],"big":[164],"machine":[167,239],"learning":[168,240],"techniques;":[169],"(3)":[171],"simple,":[172],"yet":[173],"powerful":[174],"numerical":[175],"algorithms,":[176],"such":[177],"dynamic":[180],"mode":[181],"decomposition":[182],"(DMD),":[183],"have":[184],"been":[185],"extended":[188],"reduce":[190],"practice":[194],"real-world":[196],"applications.":[197,225],"In":[198],"this":[199],"review,":[200],"we":[201],"provide":[202],"overview":[204],"theory,":[209],"describing":[210],"recent":[211],"theoretical":[212,252],"algorithmic":[214],"developments":[215,247],"highlighting":[217],"these":[218],"diverse":[222],"range":[223],"We":[226],"also":[227],"discuss":[228],"advances":[230],"challenges":[232],"rapidly":[235],"growing":[236],"likely":[243],"drive":[245],"future":[246],"significantly":[249],"transform":[250],"landscape":[253]},"counts_by_year":[{"year":2026,"cited_by_count":68},{"year":2025,"cited_by_count":168},{"year":2024,"cited_by_count":113},{"year":2023,"cited_by_count":97},{"year":2022,"cited_by_count":35},{"year":2021,"cited_by_count":20}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}