LAUSR

Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system’s dynamics from experimental data remains a significant challenge without a definitive solution. In this study, evolutionary computing techniques are presented to estimate the governing equations of a dynamical system using time-series data. The main approach is to propose a candidate functions with unknown coefficients, and subsequently perform a parametric estimation using genetic algorithms. Some of the main contributions of the present study are an adequate modification of the genetic algorithm to remove terms with minimal contributions, and a mechanism to escape local optima during the search. To evaluate the proposed method, we applied it to three dynamical systems: a linear model, a nonlinear model, and the Lorenz system. Our results demonstrate a reconstruction with an integral square error below 0.22 and a coefficient of determination R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document} of 0.99 for all systems, indicating successful reconstruction of the governing dynamic equations.