A Poisson’s Equation Solver Based on Neural Network Precondtioned CG Method

In this study, we investigate the feasibility of utilizing deep learning technique to construct preconditioners for iterative matrix solvers. A neural network (NN) is proposed to simulate the optimum-preconditioner’s mapping properties, and participates in NN-precondtioned conjugate gradient (NNPCG) method. Training and testing sets are generated by finite difference method (FDM). Numerical examples demonstrate that compared to conjugate gradient (CG) method, NN-PCG significantly improves convergence performance on solving 2-D Possion’s equation.