Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks

Understand

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 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 the recurrent neural network architecture of reservoir computing.
• Results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model, both typical test cases for numerical weather prediction.