Reconstruction of dynamic systems using genetic algorithms with dynamic search limits

TL;DR

This paper presents a genetic algorithm-based method for reconstructing the governing equations of dynamic systems from time-series data, effectively handling local optima and simplifying models.

Contribution

It introduces modifications to genetic algorithms for better term selection and escaping local optima in the context of system identification.

Findings

Achieved high accuracy with R-squared of 0.99

Reconstructed equations with an integral square error below 0.22

Successfully applied to linear, nonlinear, and Lorenz systems

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.