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When is a System Discoverable from Data? Discovery Requires Chaos

arXiv — cs.LG•Thursday, November 13, 2025 at 5:00:00 AM
NeutralArtificial Intelligence
Recent research highlights the importance of chaos in the discovery of dynamical systems from observational data within the physical sciences. While the deep learning revolution has advanced AI applications, the reliability of models often suffers from non-uniqueness, leading to questions about the conditions under which governing equations can be uniquely identified. The study reveals that chaos, typically seen as unpredictable, is essential for ensuring that systems can be discovered in continuous function spaces. Notably, it shows that systems chaotic across their entire domain can be identified from a single trajectory, while those chaotic on strange attractors can be analytically discovered under specific geometric conditions. This understanding is crucial as it addresses limitations in current modeling approaches.
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