Statistical Mechanics of Dynamical System Identification

Understand

Recovering dynamical equations from observed noisy data is the central challenge of system identification.

• We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and parsimony via hyperparameter tuning.
• In this framework, statistical mechanics offers tools to analyze the interplay between complexity and fitness similarly to that of entropy and energy in physical systems.
• To establish this analogy, we define the hyperparameter optimization procedure as a two-level Bayesian inference problem that separates variable selection from coefficient inference and enables the computation of the posterior parameter distribution in closed form.