Model Selection of Dnamical Systems via Entropic Regression and Bayesian Information Criteria

Recovering system model from noisy data is a key challenge in the analysis of dynamical systems. Based on a data-driven identification approach, we develop a model selection algorithm called Entropy Regression Bayesian Information Criterion (ER-BIC). First, the entropy regression identification algorithm (ER) is used to obtain candidate models that are close to the Pareto optimum and combine as a library of candidate models. Second, BIC score in the candidate models library is calculated using the Bayesian information criterion (BIC) and ranked from smallest to largest. Third, the model with the smallest BIC score is selected as the one we need to optimize. Finally, the ER-BIC algorithm is applied to several classical dynamical systems, including one-dimensional polynomial and RC circuit systems, two-dimensional Duffing and classical ODE systems, three-dimensional Lorenz 63 and Lorenz 84 systems. The results show that the new algorithm accurately identifies the system model under noise and time variable $t$, laying the foundation for nonlinear analysis.