{"ID":2895241,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09652","arxiv_id":"2507.09652","title":"Machine-Precision Prediction of Low-Dimensional Chaotic Systems","abstract":"Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up to machine precision: using ordinary least squares regression on high-degree polynomial features with 512-bit arithmetic, our method exceeds the accuracy of standard 64-bit numerical ODE solvers of the true underlying dynamical systems. Depending on the configuration, we obtain valid prediction times of 32 to 105 Lyapunov times for the Lorenz-63 system, dramatically outperforming prior work that reaches 13 Lyapunov times at most. We further validate our results on Thomas' Cyclically Symmetric Attractor, a non-polynomial chaotic system that is considerably more complex than the Lorenz-63 model, and show that similar results extend also to higher dimensions using the spatiotemporally chaotic Lorenz-96 model. Our findings suggest that learning low-dimensional chaotic systems from noise-free data is a solved problem.","short_abstract":"Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up to machine precision: using ordinary least squares regression on high-degree poly...","url_abs":"https://arxiv.org/abs/2507.09652","url_pdf":"https://arxiv.org/pdf/2507.09652v1","authors":"[\"Christof Schötz\",\"Niklas Boers\"]","published":"2025-07-13T14:36:47Z","proceeding":"nlin.CD","tasks":"[\"nlin.CD\",\"cs.LG\",\"math.DS\"]","methods":"[]","has_code":false}