On the Generalisation of Koopman Representations for Chaotic System Control

• URL: http://arxiv.org/abs/2508.18954v1
• Date: Tue, 26 Aug 2025 11:49:50 GMT
• Title: On the Generalisation of Koopman Representations for Chaotic System Control
• Authors: Kyriakos Hjikakou, Juan Diego Cardenas Cartagena, Matthia Sabatelli,
• Abstract summary: This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems.<n>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.
• Score: 1.338174941551702
• License: http://creativecommons.org/licenses/by/4.0/
• 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. A project page is available at https://kikisprdx.github.io/.

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