Prediction-Consistent Koopman Autoencoders

Indranil Nayak, Debdipta Goswami, Mrinal Kumar, Fernando L. Teixeira

Keywords: Scientific machine learning, nonlinear dynamics, time-series forecasting, long-term predictions, Koopman operator, Koopman autoencoders, prediction consistency, consistency regularization, limited training data, noisy training data

TL;DR: We propose the prediction-consistent Koopman autoencoder (pcKAE) for accurate long-term forecasting of nonlinear dynamical systems from limited and noisy training data.

Abstract: Data-driven modeling of high-dimensional spatio-temporal dynamical systems, which are often governed by nonlinear partial differential equations (PDEs), poses a serious challenge in the absence of sufficient or high-quality training data. Recently developed Koopman autoencoders (KAEs) leverage the expressivity of deep neural networks (DNNs) and the spectral structure of Koopman operator to learn a reduced-order feature space exhibiting simpler linear dynamics. However, limited and noisy training datasets present a significant roadblock and results in a lack of generalizability due to inconsistency in training data. In this paper we propose the prediction-consistent Koopman autoencoder (pcKAE) which is capable of generating accurate long-term predictions even with limited and noisy training data. We introduce a consistency regularization term that enforces consistency among predictions at different time-steps, making pcKAE more robust and generalizable compared to its counterparts. An analytical justification is presented for such consistency regularization using the Koopman spectral theory. Experimentally, we demonstrate that with limited training data, pcKAE outperforms existing state-of-the-art KAE models for several test-cases, ranging from simple pendulum to kinetic plasmas, fluid flows and sea surface temperature data.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 4553