Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910571736072192 |
|---|---|
| author | Choi, Jinho Krishnan, Sivaram Park, Jihong |
| author_facet | Choi, Jinho Krishnan, Sivaram Park, Jihong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction Choi, Jinho Krishnan, Sivaram Park, Jihong Machine Learning Signal Processing 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. |
| title | Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2408.11303 |