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arXiv · 2412.02894

Reconstruction of dynamic systems using genetic algorithms with dynamic search limits

Omar Rodríguez-Abreo·José Luis Aragón·Mario Alan Quiroz-Juárez
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Abstract

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.

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Omar Rodríguez-Abreo, José Luis Aragón, Mario Alan Quiroz-Juárez. 2024-12-03. Reconstruction of dynamic systems using genetic algorithms with dynamic search limits. https://arxiv.org/abs/2412.02894

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