Solving Ordinary Differential Equations Using Artificial Neural Networks: A Comprehensive Approach

Abstract

Ordinary Differential Equations (ODEs) are fundamental to modelling a wide range of phenomena across various scientific and engineering disciplines. Traditional numerical methods for solving ODEs, while effective, can be computationally intensive and may struggle with complex or high-dimensional problems. Recently, Artificial Neural Networks (ANNs) have emerged as a promising alternative for solving ODEs, leveraging their ability to approximate complex functions and patterns. This paper explores the application of ANNs in solving ODEs, presenting a detailed overview of various neural network architectures and training techniques used to address this problem. We discuss the advantages and limitations of ANNs compared to classical methods, present case studies demonstrating their effectiveness, and propose a framework for integrating ANNs into existing ODE-solving strategies. Our findings suggest that ANNs offer a flexible and efficient approach for certain classes of ODEs, paving the way for further research and practical applications.