Volume 12, Issue 3
A Deep Learning Method for Elliptic Hemivariational Inequalities

Jianguo Huang, Chunmei Wang & Haoqin Wang

East Asian J. Appl. Math., 12 (2022), pp. 487-502.

Published online: 2022-04

Export citation
  • 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.

  • Keywords

Deep learning, elliptic hemivariational inequality, contact problem, mesh-free method.

  • AMS Subject Headings

65K15, 68T07, 68U99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-12-487, author = {}, title = {A Deep Learning Method for Elliptic Hemivariational Inequalities}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {3}, pages = {487--502}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.081121.161121 }, url = {http://global-sci.org/intro/article_detail/eajam/20397.html} }
TY - JOUR T1 - A Deep Learning Method for Elliptic Hemivariational Inequalities JO - East Asian Journal on Applied Mathematics VL - 3 SP - 487 EP - 502 PY - 2022 DA - 2022/04 SN - 12 DO - http://doi.org/10.4208/eajam.081121.161121 UR - https://global-sci.org/intro/article_detail/eajam/20397.html KW - Deep learning, elliptic hemivariational inequality, contact problem, mesh-free method. AB -

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.

Jianguo Huang, Chunmei Wang & Haoqin Wang. (2022). A Deep Learning Method for Elliptic Hemivariational Inequalities. East Asian Journal on Applied Mathematics. 12 (3). 487-502. doi:10.4208/eajam.081121.161121
Copy to clipboard
The citation has been copied to your clipboard