Identification of parameters in ordinary differential equation systems using artificial neural networks

Francisco Javier  Duque Aldaz; Fernando Raúl  Rodríguez-Flores; José  Carmona Tapia

doi:10.36097/rsan.v1iEspecial_2.2826

Authors

Francisco Javier Duque Aldaz Universidad de Guayaquil https://orcid.org/0000-0001-9533-1635
Fernando Raúl Rodríguez-Flores Universidad de la Habana https://orcid.org/0009-0002-8275-7631
José Carmona Tapia Universidad de Almería https://orcid.org/0000-0001-9319-4382

DOI:

https://doi.org/10.36097/rsan.v1iEspecial_2.2826

Keywords:

Numerical methods, parameter tuning, artificial neural networks, Backpropagation algorithm, Levenberg-Marquardt method

Abstract

The identification of parameters in systems of differential equations has been a complex scientific challenge, with limited traditional methods for modeling nonlinear physical phenomena and inconsistent experimental data. The objective was to compare an artificial neural network trained with Backpropagation and optimized by Levenberg-Marquardt against classical numerical methods to identify parameters in ordinary differential equations. A multilayer neural network was designed with one input, a hidden layer of 10 neurons and two outputs. The model was trained with experimental data divided into training, validation and test sets, using the Levenberg-Marquardt algorithm to fit its parameters. Accuracy was evaluated by comparing with the Runge-Kutta-based numerical method ODE45. The neural network demonstrated superior performance, achieving an accurate and less computationally complex approximation. While the ODE45 method presented good overall fits, it showed limitations at specific intervals due to spikes and discontinuities in the simulated functions. The neural network exhibited robustness in handling nonlinear dynamics, predicting with high accuracy the behavior of the system without requiring an explicit mathematical model. Its ability to recognize complex patterns with tolerable error margins consolidated it as an effective tool for dynamic systems. In conclusion, artificial neural networks were confirmed as a robust methodological alternative, allowing the modeling of dynamic nonlinear systems with simplicity, flexibility and scalability potential.

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