DEVELOPMENT AND OPTIMIZATION OF PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

Abstract

This study investigates the application of physics-informed neural networks (PINNs) for solving Poisson equations in both 1D and 2D domains and compares them with finite difference method. Additionally, the study explores the capability of multi-task learning with PINNs, where the network not only predicts the solution but also estimates unknown parameters. In the case of a second-order differential equation with a varying coefficient, PINNs successfully approximated both the source term and the varying coefficient while achieving low training loss. The model demonstrated excellent generalization capabilities and accurate reconstruction of the underlying system parameters, showing the potential of PINNs in complex physical simulations.