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Previous work has shown that transfer learning can be used effectively with ESNs for a single-orbit prediction. The novelty of our paper lies in our use of this pairing to predict the long-term statistical properties of spatiotemporally chaotic PDEs. Nevertheless, we also show that transfer learning nontrivially improves the length of time that predictions of individual gKS trajectories remain accurate.<\/jats:p>","DOI":"10.1063\/5.0283121","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T13:59:41Z","timestamp":1770040781000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7975-7492","authenticated-orcid":false,"given":"Mohammad Shah","family":"Alam","sequence":"first","affiliation":[{"name":"Department of Natural and Behavioral Sciences, Sul Ross State University 1 , Eagle Pass, Texas 78852,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7119-491X","authenticated-orcid":false,"given":"William","family":"Ott","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Houston 2 , Houston, Texas 77204,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3978-4047","authenticated-orcid":false,"given":"Ilya","family":"Timofeyev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Houston 2 , Houston, Texas 77204,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,2,2]]},"reference":[{"key":"2026020208593716600_c1","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1126\/science.1091277","article-title":"Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication","volume":"304","year":"2004","journal-title":"Science"},{"key":"2026020208593716600_c2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2012.07.005","article-title":"Re-visiting the echo state property","volume":"35","year":"2012","journal-title":"Neural Netw."},{"key":"2026020208593716600_c3","doi-asserted-by":"publisher","first-page":"81033","DOI":"10.1109\/ACCESS.2023.3299296","article-title":"A survey on reservoir computing and its interdisciplinary applications beyond traditional machine learning","volume":"11","year":"2023","journal-title":"IEEE Access"},{"key":"2026020208593716600_c4"},{"key":"2026020208593716600_c5"},{"key":"2026020208593716600_c6","doi-asserted-by":"publisher","first-page":"2531","DOI":"10.1162\/089976602760407955","article-title":"Real-time computing without stable states: A new framework for neural computation based on perturbations","volume":"14","year":"2002","journal-title":"Neural Comput."},{"key":"2026020208593716600_c7","doi-asserted-by":"publisher","first-page":"820","DOI":"10.1109\/TNN.2006.872357","article-title":"A tighter bound for the echo state property","volume":"17","year":"2006","journal-title":"IEEE Trans. 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