Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers
Jason A. Platt, Stephen Gregory Penny, Timothy A. Smith, Tse‐Chun Chen, Henry D. I. Abarbanel · Chaos An Interdisciplinary Journal of Nonlinear Science · 2023
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants-such as the Lyapunov exponent spectrum and the fractal dimension-in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.