{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T04:37:05Z","timestamp":1782016625858,"version":"3.54.5"},"reference-count":63,"publisher":"World Scientific Pub Co Pte Ltd","issue":"16","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12272230"],"award-info":[{"award-number":["12272230"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,12,30]]},"abstract":"<jats:p> Machine Learning (ML) is highly data dependent. But all data contain noise. Especially for chaotic systems, due to the famous \u201cbutterfly-effect\u201d, small disturbances can grow exponentially to the same order of magnitude as the physical solution so that numerical simulations of chaos become badly polluted. A fundamental and open problem is how data noise in chaotic systems influences short and long-term predictions of ML based on such badly polluted data. Ultra-chaos, whose statistics are sensitive to small disturbances, is a new concept in chaos theory. In this paper, the influence of data noise on ML of chaos is investigated in detail by comparing predictions with three ML models based on a \u201cclean\u201d dataset given by Clean Numerical Simulation (CNS), and a \u201cbadly polluted\u201d dataset given by the traditional Runge\u2013Kutta method. It is found that neither data noise nor ML prediction deviation influence the long-term statistics of ML predictions for normal-chaos. However, data noise has a significant influence on the statistics of ML predictions for ultra-chaos: this might pose a great challenge for ML that is a part of AI. <\/jats:p>","DOI":"10.1142\/s021812742450202x","type":"journal-article","created":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T10:23:38Z","timestamp":1732875818000},"source":"Crossref","is-referenced-by-count":5,"title":["Ultra-Chaos: A Great Challenge for Machine Learning and AI"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5582-2090","authenticated-orcid":false,"given":"Yu","family":"Yang","sequence":"first","affiliation":[{"name":"School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. 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