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.
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Assimilation-Based Learning of Chaotic Dynamical Systems from Noisy and Partial Data
Semantic Scholar · Physics · 2020
Abstract
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.