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Express"],"published-print":{"date-parts":[[2026,7,27]]},"abstract":"<jats:p>Time-delay embedding is a prominent method in neural networks to improve the performance of predictions of the dynamics of nonlinear systems. Applied to reservoir computing, a recurrent machine learning model in which the output weights are trained only, an improved prediction performance for a broader range of hyperparameters can be realized. Here, we present an optical implementation of reservoir computing on the basis of a spatial light modulator. In addition to the high parallelism of the optical setup and the fast processing capabilities with scalable numbers of neurons, a recursive cascading effect is generated for successful optical delay embedding. Our laboratory experiment is evaluated for the one-dimensional Kuramoto-Sivashinsky equation and is found to perform better than a classical implementation of reservoir computing.<\/jats:p>","DOI":"10.1364\/oe.595960","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T15:00:09Z","timestamp":1781708409000},"page":"28496","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Delay-embedding for recurrence in optical reservoir computing"],"prefix":"10.1364","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6201-0122","authenticated-orcid":true,"given":"Anja","family":"Bartelmei","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01weqhp73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7811-2870","authenticated-orcid":true,"given":"Maximilian","family":"Zier","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01weqhp73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f6rg","family":"Schumacher","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01weqhp73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8031-4787","authenticated-orcid":true,"given":"Stefan","family":"Sinzinger","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01weqhp73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,23]]},"reference":[{"key":"oe-34-15-28496-R1","author":"Davidson","year":"2015"},{"key":"oe-34-15-28496-R2","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","type":"journal-article","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. 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