2024/12/03 by Omar Rodríguez-Abreo, J. L. Aragón, Rodríguez-Abreo, Omar +3
Engineering · #Advanced Control Systems Optimization #Algorithm #Computer science #Genetic algorithm #Machine learning
paper · pdf · doi:10.48550/arxiv.2412.02894
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/12/03 · openalex created_date 2024/12/06 · openalex updated_date 2026/07/28
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 polynomial equations 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 R-squared of 0.99 for all systems, indicating successful reconstruction of the governing dynamic equations.