Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks
This addresses the challenge of improving numerical weather prediction accuracy for meteorologists and climate scientists, though it appears incremental as it builds on existing recurrent neural network architectures like reservoir computing.
The paper tackles the problem of forecasting chaotic dynamical systems with limited data by introducing a training method that enforces dynamical invariants like Lyapunov exponents and fractal dimension, resulting in longer and more stable forecasts as demonstrated on the Lorenz 1996 system and a spectral quasi-geostrophic model.
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.