Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction

TL;DR

This paper introduces a novel Koopman autoencoder method that uses singular value decomposition to control eigenvalues, significantly improving long-term prediction accuracy in nonlinear dynamic systems.

Contribution

It proposes leveraging SVD of the Koopman matrix to effectively control eigenvalues, enhancing long-term forecasting performance in data-driven models.

Findings

The SVD-based approach effectively stabilizes eigenvalues near the unit circle.

Experimental results show improved long-term prediction over baseline methods.

The method reduces training complexity for eigenvalue control.

Abstract

The Koopman autoencoder, a data-driven technique, has gained traction for modeling nonlinear dynamics using deep learning methods in recent years. Given the linear characteristics inherent to the Koopman operator, controlling its eigenvalues offers an opportunity to enhance long-term prediction performance, a critical task for forecasting future trends in time-series datasets with long-term behaviors. However, controlling eigenvalues is challenging due to high computational complexity and difficulties in managing them during the training process. To tackle this issue, we propose leveraging the singular value decomposition (SVD) of the Koopman matrix to adjust the singular values for better long-term prediction. Experimental results demonstrate that, during training, the loss term for singular values effectively brings the eigenvalues close to the unit circle, and the proposed approach outperforms existing baseline methods for long-term prediction tasks.