研究：混沌是动力系统可从数据中发现的前提，保守系统本质上不可发现

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Abstract:The deep learning revolution has enabled major AI advances in physical sciences, particularly in discovering dynamical systems from observational data. Yet the reliability of learned surrogates and symbolically discovered models is often undermined by non-uniqueness: models may fit observed trajectories perfectly, but lack genuine predictive power. We show that chaos, despite its association with unpredictability, is often what makes governing equations discoverable. We prove that the classical Lorenz system is analytically discoverable and verify experimentally that for many systems out-of-domain generalization emerges precisely at chaos onset. Conservative systems, by contrast, are inherently non-discoverable from data alone. The prevalence of chaotic systems in benchmarks may have inadvertently obscured this limitation. These findings help explain why AI excels at weather forecasting, yet struggles in many engineering applications: the systems most amenable to discovery (chaotic ones) are often least amenable to control.

Comments:	Newest version contains complete discoverability classification
Subjects:	Dynamical Systems (math.DS); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Numerical Analysis (math.NA); Chaotic Dynamics (nlin.CD)
Cite as:	arXiv:2511.08860 [math.DS]
	(or arXiv:2511.08860v3 [math.DS] for this version)
	https://doi.org/10.48550/arXiv.2511.08860 arXiv-issued DOI via DataCite

Submission history

From: Zakhar Shumaylov [view email]
[v1] Wed, 12 Nov 2025 00:35:54 UTC (10,023 KB)
[v2] Fri, 3 Jul 2026 10:13:28 UTC (10,260 KB)
[v3] Wed, 14 Oct 2026 15:30:32 UTC (8,553 KB)