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

  • Tianchen Shao*
  • , Tao Shan
  • , Maokun Li
  • , Fan Yang
  • , Shenheng Xu
  • *Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publication2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781665452366
DOIs
StatePublished - 2022
Externally publishedYes
Event2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022 - Xuzhou, China
Duration: 9 Dec 202212 Dec 2022

Publication series

Name2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022

Conference

Conference2022 International Applied Computational Electromagnetics Society Symposium, ACES-China 2022
Country/TerritoryChina
CityXuzhou
Period9/12/2212/12/22

Keywords

  • conjugate gradient method
  • deep learning
  • neural network
  • preconditioner

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