Solving initial value problems using multilayer perceptron artificial neural networks

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.