Reconstruction of dynamic systems using genetic algorithms with dynamic search limits
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913596544385024 |
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| author | Rodríguez-Abreo, Omar Aragón, José Luis Quiroz-Juárez, Mario Alan |
| author_facet | Rodríguez-Abreo, Omar Aragón, José Luis Quiroz-Juárez, Mario Alan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction of dynamic systems using genetic algorithms with dynamic search limits Rodríguez-Abreo, Omar Aragón, José Luis Quiroz-Juárez, Mario Alan Neural and Evolutionary Computing Dynamical Systems Chaotic Dynamics 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. |
| title | Reconstruction of dynamic systems using genetic algorithms with dynamic search limits |
| topic | Neural and Evolutionary Computing Dynamical Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2412.02894 |