Solving initial value problems using multilayer perceptron artificial neural networks

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

2 Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran.

Abstract

This research introduces a novel approach using artificial neural networks (ANNs) to tackle ordinary differential equations (ODEs) through an innovative technique called enhanced back-propagation (EBP). The ANNs adopted in this study, particularly multilayer perceptron neural networks (MLPNNs), are equipped with tunable parameters such as weights and biases. The utilization of MLPNNs with universal approximation capabilities proves to be advantageous for ODE problem solving. By leveraging the enhanced back-propagation algorithm, the network is fine-tuned to minimize errors during unsupervised learning sessions. To showcase the effectiveness of this method, a diverse set of initial value problems for ODEs are solved and the results are compared against analytical solutions and conventional techniques, demonstrating the superior performance of the proposed approach.

Keywords

Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 1
January 2025
Pages 13-24

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History

  • Receive Date: 09 October 2023
  • Revise Date: 04 March 2024
  • Accept Date: 27 April 2024

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