Machine-Precision Prediction of Low-Dimensional Chaotic Systems

Data-driven emulation of chaotic dynamics in the Earth system is a central challenge in modern climate science. Low-dimensional systems such as the Lorenz-63 model, derived in the context of atmospheric convection, 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 system-agnostic method matches the accuracy of standard numerical ODE solvers using the systems' governing equations. For the Lorenz-63 system, we obtain valid prediction times of 36 Lyapunov times, and even up to 105 Lyapunov times with favorable precision configurations, dramatically outperforming prior work, which 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 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.