mlsanityData to 14 Oct 2026

When is a System Discoverable from Data? Discovery Requires Chaos

arXiv 2511.08860 ↗First posted 12 Nov 2025math.DS cs.AI cs.LGcited by 6

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Abstract (arXiv)

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.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 65 of its 177 references that are in the map. First posted on arXiv 12 Nov 2025.

Builds on

65 of 177 references.

References · 65

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38 more
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50 most cited of 65 All 65 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modelingcited by 4
  2. 2026Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approachcited by 1
  3. 2026The Dynamics of Discoverability: How Trajectories and Priors Shape Equation Recoverycited by 1
  4. 2026Symbolic recovery of PDEs from measurement datacited by 0
  5. 2026Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training errorcited by 0
  6. 2026How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limitcited by 0