Robust Prediction of High-Dimensional Dynamical Systems using Koopman Deep Networks

Abstract: We present a new deep learning approach for the analysis and processing of time series data. At the core of our work is the Koopman operator which fully encodes a nonlinear dynamical system. Unlike the majority of Koopman-based models, we consider dynamics for which the Koopman operator is invertible. We exploit the structure of these systems to design a novel Physically-Constrained Learning (PCL) model that takes into account the inverse dynamics while penalizing for inverse prediction. Our architecture is composed of an autoencoder component and two Koopman layers for the dynamics and their inverse. To motivate our network design, we investigate the connection between invertible Koopman operators and pointwise maps, and our analysis yields a loss term which we employ in practice. To evaluate our work, we consider several challenging nonlinear systems including the pendulum, fluid flows on curved domains and real climate data. We compare our approach to several baseline methods, and we demonstrate that it yields the best results for long time predictions and in noisy settings.

machine learningdynamical systemsapplied physics

Audience: researchers in the topic

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Workshop on Scientific-Driven Deep Learning (SciDL)

Series comments: When: 8:00-14:30pm (PST) on Wednesday July 1, 2020 Where: berkeley.zoom.us/j/95609096856 Details: scidl.netlify.app/