Assimilation-Based Learning of Chaotic Dynamical Systems from Noisy and Partial Data

Despite some promising results under ideal conditions (i.e. noise-free and complete observation), learning chaotic dynamical systems from real life data is still a very challenging task. We propose a novel framework, which combines data assimilation schemes and neural network representation, namely Auto-Encoders and Ensemble Kalman Smoother, to learn the governing equations of dynamical systems. By treating the learning as a Bayesian estimation problem, our framework can deal with noisy and partial observations. Experiments on the chaotic Lorenz-63 dynamics with different noise settings demonstrate the advantages of our method over the state-of-the-art.