Machine-Precision Prediction of Low-Dimensional Chaotic Systems

• URL: http://arxiv.org/abs/2507.09652v1
• Date: Sun, 13 Jul 2025 14:36:47 GMT
• Title: Machine-Precision Prediction of Low-Dimensional Chaotic Systems
• Abstract summary: We show that learning from low-dimensional chaotic systems can be achieved up to machine precision.<n>We obtain valid prediction times of 32 to 105 Lyapunov times for the Lorenz-63 system.<n>Our findings suggest that learning low-temporal chaotic systems from noisefree data is a problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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