On the Generalisation of Koopman Representations for Chaotic System Control

2025-08-26

AI Summary

This work investigates the transferability of Koopman representations across prediction and control tasks in chaotic dynamical systems. We propose a three-stage physics-informed learning framework: (1) learning dynamics-consistent low-dimensional embeddings via a Koopman autoencoder; (2) pretraining a Transformer backbone on sequence evolution; and (3) lightweight fine-tuning with differential equation constraints and safety-aware control objectives. Our key finding is that the learned Koopman representation captures reusable dynamical structure—enabling high-accuracy prediction and robust control by fine-tuning only the controller while keeping the Transformer backbone fixed. Evaluated on the Lorenz system, our method substantially outperforms standard PCA and physics-guided baselines, achieving strong generalization with minimal data requirements. This establishes a transferable, task-agnostic foundational representation for multi-task physics-informed learning.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Large pretrained models with web data
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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/.

Problem

• Investigating Koopman representations' generalisability for chaotic systems
• Focusing on transferability across prediction and control tasks
• Proposing methodology for learning reusable dynamical structure embeddings

Innovation

• Koopman embeddings via autoencoding
• Transformer pre-training for prediction
• Fine-tuning for safety-critical control