Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction
This work addresses a specific bottleneck in data-driven forecasting for time-series datasets, offering an incremental improvement in eigenvalue management.
The paper tackled the challenge of controlling eigenvalues in Koopman autoencoders for long-term prediction by using singular value decomposition to adjust singular values, resulting in improved performance over baseline methods in experiments.
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.