Machine-Precision Prediction of Low-Dimensional Chaotic Systems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918090733780992 |
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| author | Schötz, Christof Boers, Niklas |
| author_facet | Schötz, Christof Boers, Niklas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine-Precision Prediction of Low-Dimensional Chaotic Systems Schötz, Christof Boers, Niklas Chaotic Dynamics Machine Learning Dynamical Systems 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. |
| title | Machine-Precision Prediction of Low-Dimensional Chaotic Systems |
| topic | Chaotic Dynamics Machine Learning Dynamical Systems |
| url | https://arxiv.org/abs/2507.09652 |