{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T13:41:21Z","timestamp":1791380481933,"version":"4.3.3"},"reference-count":31,"publisher":"AIP Publishing","issue":"1","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP22K11919"],"award-info":[{"award-number":["JP22K11919"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP22H00516"],"award-info":[{"award-number":["JP22H00516"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP22K14274"],"award-info":[{"award-number":["JP22K14274"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003382","name":"Core Research for Evolutional Science and Technology","doi-asserted-by":"publisher","award":["JP-MJCR1913"],"award-info":[{"award-number":["JP-MJCR1913"]}],"id":[{"id":"10.13039\/501100003382","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,1,1]]},"abstract":"<jats:p>We apply dynamic mode decomposition (DMD) to elementary cellular automata (ECA). Three types of DMD methods are considered, and the reproducibility of the system dynamics and Koopman eigenvalues from observed time series is investigated. While standard DMD fails to reproduce the system dynamics and Koopman eigenvalues associated with a given periodic orbit in some cases, Hankel DMD with delay-embedded time series improves reproducibility. However, Hankel DMD can still fail to reproduce all the Koopman eigenvalues in specific cases. We propose an extended DMD method for ECA that uses nonlinearly transformed time series with discretized Walsh functions and show that it can completely reproduce the dynamics and Koopman eigenvalues. Linear-algebraic backgrounds for the reproducibility of the system dynamics and Koopman eigenvalues are also discussed.<\/jats:p>","DOI":"10.1063\/5.0159069","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T18:14:09Z","timestamp":1705947249000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4657-5227","authenticated-orcid":false,"given":"Keisuke","family":"Taga","sequence":"first","affiliation":[{"name":"Department of Physics, School of Advanced Science and Engineering, Waseda University 1 , Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8508-4677","authenticated-orcid":false,"given":"Yuzuru","family":"Kato","sequence":"additional","affiliation":[{"name":"Department of Complex and Intelligent Systems, School of Systems Information Science, Future University Hakodate 2 , Hakodate, Hokkaido 041-8655, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4551-0859","authenticated-orcid":false,"given":"Yoshihiro","family":"Yamazaki","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Advanced Science and Engineering, Waseda University 1 , Tokyo 169-8555, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7789-4709","authenticated-orcid":false,"given":"Yoshinobu","family":"Kawahara","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology, Osaka University 3 , Osaka 565-0871, Japan and , Tokyo 103-0027, Japan"},{"name":"Center for Advanced Intelligence Project, RIKEN 3 , Osaka 565-0871, Japan and , Tokyo 103-0027, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3394-0392","authenticated-orcid":false,"given":"Hiroya","family":"Nakao","sequence":"additional","affiliation":[{"name":"Department of Systems and Control Engineering, School of Engineering, Tokyo Institute of Technology 4 , Tokyo 152-8552, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,1,22]]},"reference":[{"key":"2024012218140299000_c1","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1073\/pnas.17.5.315","volume":"17","year":"1931","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2024012218140299000_c2","doi-asserted-by":"publisher","first-page":"587","DOI":"10.2307\/1968537","volume":"33","year":"1932","journal-title":"Ann. Math."},{"key":"2024012218140299000_c3","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s11071-005-2824-x","volume":"41","year":"2005","journal-title":"Nonlinear Dyn."},{"key":"2024012218140299000_c4","doi-asserted-by":"publisher","first-page":"047510","DOI":"10.1063\/1.4772195","volume":"22","year":"2012","journal-title":"Chaos"},{"key":"2024012218140299000_c5","doi-asserted-by":"publisher","first-page":"1925","DOI":"10.1137\/17M116207X","volume":"17","year":"2018","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"2024012218140299000_c6","volume-title":"The Koopman Operator in Systems and Control","year":"2020"},{"key":"2024012218140299000_c7","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1137\/21M1401243","volume":"64","year":"2022","journal-title":"SIAM Rev."},{"key":"2024012218140299000_c8","doi-asserted-by":"publisher","first-page":"6010634","DOI":"10.1155\/2018\/6010634","volume":"2018","journal-title":"Complexity"},{"key":"2024012218140299000_c9","doi-asserted-by":"publisher","first-page":"071901","DOI":"10.1103\/PhysRevFluids.3.071901","volume":"3","year":"2018","journal-title":"Phys. Rev. Fluids"},{"key":"2024012218140299000_c10","doi-asserted-by":"publisher","first-page":"113131","DOI":"10.1063\/5.0011470","volume":"30","year":"2020","journal-title":"Chaos"},{"key":"2024012218140299000_c11","doi-asserted-by":"publisher","first-page":"2803","DOI":"10.1137\/19M1305033","volume":"19","year":"2020","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"2024012218140299000_c12","doi-asserted-by":"publisher","first-page":"043102","DOI":"10.1063\/5.0137088","volume":"33","year":"2023","journal-title":"Chaos"},{"key":"2024012218140299000_c13","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1017\/S0022112010001217","volume":"656","year":"2010","journal-title":"J. Fluid Mech."},{"key":"2024012218140299000_c14","doi-asserted-by":"publisher","first-page":"391","DOI":"10.3934\/jcd.2014.1.391","volume":"1","year":"2014","journal-title":"J. Comput. Dyn."},{"key":"2024012218140299000_c15","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1016\/j.ifacol.2016.10.248","volume":"49","year":"2016","journal-title":"IFAC-PapersOnLine"},{"key":"2024012218140299000_c16","volume-title":"Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems","year":"2016"},{"key":"2024012218140299000_c17","first-page":"911","volume":"29","year":"2016","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"2024012218140299000_c18","doi-asserted-by":"publisher","first-page":"2096","DOI":"10.1137\/17M1125236","volume":"16","year":"2017","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"2024012218140299000_c19","doi-asserted-by":"publisher","first-page":"103111","DOI":"10.1063\/1.4993854","volume":"27","year":"2017","journal-title":"Chaos"},{"key":"2024012218140299000_c20","doi-asserted-by":"publisher","first-page":"103121","DOI":"10.1063\/5.0059202","volume":"31","year":"2021","journal-title":"Chaos"},{"key":"2024012218140299000_c21","volume-title":"A New Kind of Science","year":"2002"},{"key":"2024012218140299000_c22","volume-title":"The Geometry and Pigmentation of Seashells"},{"key":"2024012218140299000_c23","doi-asserted-by":"publisher","first-page":"5439","DOI":"10.1088\/0305-4470\/31\/24\/006","volume":"31","year":"1998","journal-title":"J. Phys. A: Math. Gen."},{"key":"2024012218140299000_c24","doi-asserted-by":"publisher","first-page":"105001","DOI":"10.7566\/JPSJ.88.105001","volume":"88","year":"2019","journal-title":"J. Phys. Soc. Jpn."},{"key":"2024012218140299000_c25","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1103\/RevModPhys.55.601","volume":"55","year":"1983","journal-title":"Rev. Mod. Phys."},{"key":"2024012218140299000_c26","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1038\/s41467-017-00030-8","volume":"8","year":"2017","journal-title":"Nat. Commun."},{"key":"2024012218140299000_c27","doi-asserted-by":"publisher","first-page":"5789","DOI":"10.1088\/0305-4470\/37\/22\/006","volume":"37","year":"2004","journal-title":"J. Phys. A: Math. Gen."},{"key":"2024012218140299000_c28","doi-asserted-by":"publisher","first-page":"241\u2013264","DOI":"10.1112\/plms\/s2-34.1.241","volume":"s2\u201334","year":"1932","journal-title":"Proc. London Math. Soc."},{"key":"2024012218140299000_c29","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/s13538-011-0052-z","volume":"42","year":"2012","journal-title":"Braz. J. Phys."},{"key":"2024012218140299000_c30","doi-asserted-by":"publisher","first-page":"9610826","DOI":"10.1155\/2019\/9610826","volume":"2019","year":"2019","journal-title":"Complexity"},{"key":"2024012218140299000_c31"}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0159069\/18701937\/013125_1_5.0159069.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0159069\/18701937\/013125_1_5.0159069.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T18:14:15Z","timestamp":1705947255000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/34\/1\/013125\/3061409\/Dynamic-mode-decomposition-for-Koopman-spectral"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,1]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0159069","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,1]]},"published":{"date-parts":[[2024,1,1]]},"article-number":"013125"}}