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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> of 0.99 for all systems, indicating successful reconstruction of the governing dynamic equations.</p>

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Reconstruction of dynamic systems using genetic algorithms with dynamic search limits

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月22日

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  • Omar Rodríguez-Abreo,
  • José L. Aragón,
  • Mario A. Quiroz-Juárez

摘要

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 \(R^2\) R 2 of 0.99 for all systems, indicating successful reconstruction of the governing dynamic equations.