A Deep Learning Method for Elliptic Hemivariational Inequalities

Jianguo Huang, Chunmei Wang, Haoqin Wang

Research output: Contribution to journalArticlepeer-review

Abstract

Deep learning method for solving elliptic hemivariational inequalities is constructed. Using a variational formulation of the corresponding inequality, we reduce it to an unconstrained expectation minimization problem and solve the last one by a stochastic optimization algorithm. The method is applied to a frictional bilateral contact problem and to a frictionless normal compliance contact problem. Numerical experiments show that for fine meshes, the method approximates the solution with accuracy similar to the virtual element method. Besides, the use of local adaptive activation functions improves accuracy and has almost the same computational cost.

Original languageEnglish
Pages (from-to)487-502
Number of pages16
JournalEast Asian Journal on Applied Mathematics
Volume12
Issue number3
DOIs
StatePublished - 2022

Keywords

  • Deep learning
  • contact problem
  • elliptic hemivariational inequality
  • mesh-free method

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