Two neural-network-based methods for solving elliptic obstacle problems

Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks, and the cost functions are taken as the energy minimization of the obstacle problems. We rigorously prove the convergence of the two schemes and derive the convergence rates with the number of neurons N. In the simulations, two example problems (both 1-D and 2-D) are used to verify the convergence rate of the methods and the quality of the results.

Original languageEnglish (US)
Article number112313
JournalChaos, Solitons and Fractals
StatePublished - Aug 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Mathematics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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