Model Selection of Dynamical Systems via Entropic Regression and Bayesian Information Criteria (Journal of Nonlinear Modeling and Analysis, 2024)
Recovering system model from noisy data is a key challenge in theanalysis of dynamical systems. Based on a data-driven identification approach,we develop a model selection algorithm called Entropy Regression BayesianInformation Criterion (ER-BIC). First, the entropy regression identificationalgorithm (ER) is used to obtain candidate models that are close to the Paretooptimum and combine as a library of candidate models. Second, BIC scorein the candidate models library is calculated using the Bayesian informationcriterion (BIC) and ranked from smallest to largest. Third, the model with thesmallest 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 andclassical ODE systems, three-dimensional Lorenz 63 and Lorenz 84 systems.The results show that the new algorithm accurately identifies the system modelunder noise and time variable $t,$ laying the foundation for nonlinear analysis.
Keywords: Data-driven; system identification; model selection; ER algorithm; BIC.