Numerical Solution of Systems of Differential Equation with Neural Networks

Abstract

We propose a physics-informed neural network (PINN) to solve boundary value system of differential equation problems. PINN is a scientific machine learning method that has been used very frequently lately to find numerical solutions of partial differential equations and offers positive results. PINNs have shown effective performance in solving a variety of differential equations, including complex derivatives and multidimensional equations. Well-trained PINNs most closely predict the numerical solutions of boundary value problems. Numerical experiments include various types of linear differential equation systems.