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.

翻译：数学建模是描述、预测和理解现实世界系统所呈现复杂现象的有力工具。然而，从实验数据中识别支配系统动力学的方程仍然是一个重大挑战，目前尚无确定性解决方案。本研究提出利用进化计算技术，通过时间序列数据估计动态系统的控制方程。主要方法是提出具有未知系数的多项式方程，随后使用遗传算法进行参数估计。本研究的主要贡献包括：对遗传算法进行适当修改以剔除贡献极小的项，以及在搜索过程中逃离局部最优解的机制。为评估所提方法，我们将其应用于三个动态系统：线性模型、非线性模型和洛伦兹系统。结果表明，所有系统的积分平方误差均低于0.22，决定系数R平方达到0.99，成功实现了对动态控制方程的重构。