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Statistical Mechanics of Dynamical System Identification
March 5, 2024, 2:43 p.m. | Andrei A. Klishin, Joseph Bakarji, J. Nathan Kutz, Krithika Manohar
cs.LG updates on arXiv.org arxiv.org
Abstract: Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanical approach to analyze sparse equation discovery algorithms, which typically balance data fit and parsimony through a trial-and-error selection of hyperparameters. In this framework, statistical mechanics offers tools to analyze the interplay between complexity and fitness, in analogy to that done between entropy and energy. To establish this analogy, we define the optimization procedure as a two-level …
abstract algorithms analyze arxiv balance challenge cond-mat.stat-mech cs.lg data discovery equation error framework identification math.oc physics.comp-ph statistical through tools type
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