On the Generalisation of Koopman Representations for Chaotic System Control
This work addresses the challenge of multi-task learning in physics-informed machine learning for chaotic systems, offering incremental improvements in representation transferability.
This paper tackles the problem of generalizing Koopman-based representations for chaotic dynamical systems across prediction and control tasks, using the Lorenz system as a testbed, and shows that Koopman embeddings outperform baselines with accurate and data-efficient performance, including no degradation when fine-tuning pre-trained transformers.
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/.