On the Generalisation of Koopman Representations for Chaotic System Control

Kyriakos Hjikakou, Juan Cardenas-Cartagena, Matthia Sabatelli
Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL), PMLR 307:160-178, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v307-hjikakou26a, title = {On the Generalisation of Koopman Representations for Chaotic System Control}, author = {Hjikakou, Kyriakos and Cardenas-Cartagena, Juan and Sabatelli, Matthia}, booktitle = {Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL)}, pages = {160--178}, year = {2026}, editor = {Kim, Hyeongji and Ramírez Rivera, Adín and Ricaud, Benjamin}, volume = {307}, series = {Proceedings of Machine Learning Research}, month = {06--08 Jan}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v307/main/assets/hjikakou26a/hjikakou26a.pdf}, url = {https://proceedings.mlr.press/v307/hjikakou26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T On the Generalisation of Koopman Representations for Chaotic System Control %A Kyriakos Hjikakou %A Juan Cardenas-Cartagena %A Matthia Sabatelli %B Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL) %C Proceedings of Machine Learning Research %D 2026 %E Hyeongji Kim %E Adín Ramírez Rivera %E Benjamin Ricaud %F pmlr-v307-hjikakou26a %I PMLR %P 160--178 %U https://proceedings.mlr.press/v307/hjikakou26a.html %V 307 %X 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.
APA
Hjikakou, K., Cardenas-Cartagena, J. & Sabatelli, M.. (2026). On the Generalisation of Koopman Representations for Chaotic System Control. Proceedings of the 7th Northern Lights Deep Learning Conference (NLDL), in Proceedings of Machine Learning Research 307:160-178 Available from https://proceedings.mlr.press/v307/hjikakou26a.html.

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