{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T16:51:03Z","timestamp":1772988663989,"version":"3.50.1"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643686318","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:p>Forecasting chaotic dynamics beyond a few Lyapunov times is difficult because infinitesimal errors grow exponentially. Existing Echo State Networks (ESNs) mitigate this growth but employ reservoirs whose Euclidean geometry is mismatched to the stretch\u2013and\u2013fold structure of chaos. We introduce the Hyperbolic Embedding Reservoir (HypER), an ESN whose neurons are sampled in the Poincar\u00e9 ball and whose connections decay exponentially with hyperbolic distance. This negative-curvature construction embeds an exponential metric directly into the latent space, aligning the reservoir\u2019s local expansion\u2013contraction spectrum with the system\u2019s Lyapunov directions while preserving standard ESN features such as sparsity, leaky integration and spectral-radius control. Training is limited to a Tikhonov-regularised read-out. On the chaotic Lorenz-63 and R\u00f6ssler systems, and the hyperchaotic Chen\u2013Ueta attractor, HypER consistently lengthens the mean valid-prediction horizon beyond Euclidean and graph-structured ESN baselines, with statistically significant gains confirmed over 30 independent runs; parallel results on real-world benchmarks\u2014including heart-rate variability from the Santa Fe and MIT-BIH datasets, and international sunspot numbers\u2014corroborate its advantage. We further establish a lower bound on the rate of state divergence for HypER, mirroring Lyapunov growth. In the interest of reproducibility, we release our implementation at https:\/\/github.com\/deepdyn\/HypER and provide a full technical appendix (proofs, ablations, hyperparameters) in the arXiv preprint at DOI: 10.48550\/arXiv.2508.18196.<\/jats:p>","DOI":"10.3233\/faia251184","type":"book-chapter","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:53:54Z","timestamp":1761126834000},"source":"Crossref","is-referenced-by-count":1,"title":["HypER: Hyperbolic Echo State Networks for Capturing Stretch-and-Fold Dynamics in Chaotic Flows"],"prefix":"10.3233","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5372-3355","authenticated-orcid":false,"given":"Pradeep","family":"Singh","sequence":"first","affiliation":[{"name":"Machine Intelligence Lab, Department of Computer Science and Engineering, IIT Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sutirtha","family":"Ghosh","sequence":"additional","affiliation":[{"name":"Machine Intelligence Lab, Department of Computer Science and Engineering, IIT Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashutosh","family":"Kumar","sequence":"additional","affiliation":[{"name":"Machine Intelligence Lab, Department of Computer Science and Engineering, IIT Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Hrishit B P","sequence":"additional","affiliation":[{"name":"Machine Intelligence Lab, Department of Computer Science and Engineering, IIT Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Balasubramanian","family":"Raman","sequence":"additional","affiliation":[{"name":"Machine Intelligence Lab, Department of Computer Science and Engineering, IIT Roorkee, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2025"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA251184","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:53:55Z","timestamp":1761126835000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA251184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"ISBN":["9781643686318"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia251184","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,21]]}}}