On the Generalisation of Koopman Representations for Chaotic System Control
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914006339420160 |
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| author | Hjikakou, Kyriakos Cartagena, Juan Diego Cardenas Sabatelli, Matthia |
| author_facet | Hjikakou, Kyriakos Cartagena, Juan Diego Cardenas Sabatelli, Matthia |
| contents | This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a three-stage methodology: learning Koopman embeddings through autoencoding, pre-training a transformer on next-state prediction, and fine-tuning for safety-critical control. Our results show that Koopman embeddings outperform both standard and physics-informed PCA baselines, achieving accurate and data-efficient performance. Notably, fixing the pre-trained transformer weights during fine-tuning leads to no performance degradation, indicating that the learned representations capture reusable dynamical structure rather than task-specific patterns. These findings support the use of Koopman embeddings as a foundation for multi-task learning in physics-informed machine learning. A project page is available at https://kikisprdx.github.io/. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Generalisation of Koopman Representations for Chaotic System Control Hjikakou, Kyriakos Cartagena, Juan Diego Cardenas Sabatelli, Matthia Machine Learning This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a three-stage methodology: learning Koopman embeddings through autoencoding, pre-training a transformer on next-state prediction, and fine-tuning for safety-critical control. Our results show that Koopman embeddings outperform both standard and physics-informed PCA baselines, achieving accurate and data-efficient performance. Notably, fixing the pre-trained transformer weights during fine-tuning leads to no performance degradation, indicating that the learned representations capture reusable dynamical structure rather than task-specific patterns. These findings support the use of Koopman embeddings as a foundation for multi-task learning in physics-informed machine learning. A project page is available at https://kikisprdx.github.io/. |
| title | On the Generalisation of Koopman Representations for Chaotic System Control |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.18954 |