Neural network for solving differential equations

Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) are fundamental to modelling a wide range of scientific ‎and engineering phenomena, including fluid dynamics, heat conduction, and biological systems. Classical numerical methods, such as the ‎finite difference method (FDM) and finite element method (FEM), often suffer from high computational costs, difficulty in handling com-‎plex boundary conditions, and limited scalability. With the advancement of artificial intelligence, artificial neural networks (ANNs) and con-‎convolutional neural networks (CNNs) have emerged as powerful tools for solving differential equations. This paper explores the application of ‎neural networks for solving ODEs and PDEs, analyzing their effectiveness, advantages, and limitations as neural networks are predicted to ‎transform computational mathematics, offering more accurate results‎.