Search

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. [ABSTRACT FROM AUTHOR]

Reservoir computers (RCs) are a class of recurrent neural networks (RNNs) that can be used for forecasting the future of observed time series data. As with all RNNs, selecting the hyperparameters in the network to yield excellent forecasting presents a challenge when training on new inputs. We analyze a method based on predictive generalized synchronization (PGS) that gives direction in designing and evaluating the architecture and hyperparameters of an RC. To determine the occurrences of PGS, we rely on the auxiliary method to provide a computationally efficient pre-training test that guides hyperparameter selection. We provide a metric for evaluating the RC using the reproduction of the input system's Lyapunov exponents that demonstrates robustness in prediction. [ABSTRACT FROM AUTHOR]