Forecasting Sequential Data using Consistent Koopman Autoencoders

TL;DR

This paper introduces a novel Consistent Koopman Autoencoder that leverages forward and backward dynamics to improve forecasting of nonlinear dynamical systems, demonstrating accuracy and robustness on complex time series.

Contribution

The work presents a new autoencoder model based on Koopman theory that explicitly incorporates bidirectional dynamics, offering improved predictions over existing methods.

Findings

Achieves accurate long-term forecasts on high-dimensional data

Demonstrates robustness to noise in time series predictions

Computationally comparable to existing models

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.