Forecasting Sequential Data using Consistent Koopman Autoencoders

Abstract

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.

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Cited by in corpus (7)

• Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
• Continuous-in-Depth Neural Networks
• Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting
• Kernel-based parameter estimation of dynamical systems with unknown observation functions
• Modes of Homogeneous Gradient Flows
• Cross-Node Federated Graph Neural Network for Spatio-Temporal Data Modeling
• Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder