Attractor geometry limits equation discovery from data, study finds

A new research paper explores the geometric properties of attractors in dynamical systems and their impact on the ability to discover governing equations from data. The study introduces a metric, lambda_min(M), derived from the Birkhoff ergodic theorem, which quantifies how well an attractor covers function space and sets a ceiling for equation discovery. The research demonstrates that while chaos can improve this metric, it also amplifies noise, potentially leading to varied outcomes for different discovery algorithms like SINDy and PySR. The findings suggest that the inherent properties of the system's dynamics, rather than just algorithmic choices, fundamentally limit what can be learned. AI

IMPACT Provides a theoretical framework for understanding the limits of AI-driven scientific discovery by analyzing dynamical systems.

RANK_REASON Academic paper on a theoretical aspect of system discovery. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• Birkhoff ergodic theorem
• Lorenz-84
• Lorenz 96
• pysrt
• Sindy

• paper
• other

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