Parallel Computation of PINN using Iterative Domain Decomposition Method

Abstract

Physics-informed neural network (PINN) is a machine learning method for approximating the initial-boundary value problems of partial differential equations. This research focuses on parallel computation of the PINN using the iterative domain decomposition method (DDM). The DDM is known as a parallel numerical method for the finite element method (FEM) and an iterative DDM solves an interface system, which is introduced by a static condensation, using iterative methods. This research applies the iterative DDM to the PINN for the two-dimensional Poisson’s equation (differential form) and evaluates performances between FEM and PINN.