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

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  • Zhao, Xinyue Evelyn
  • Hao, Wenrui
  • Hu, Bei

Abstract

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.

Suggested Citation

  • Zhao, Xinyue Evelyn & Hao, Wenrui & Hu, Bei, 2022. "Two neural-network-based methods for solving elliptic obstacle problems," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005239
    DOI: 10.1016/j.chaos.2022.112313
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    References listed on IDEAS

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    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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    Cited by:

    1. Fujun Cao & Xiaobin Guo & Fei Gao & Dongfang Yuan, 2023. "Deep Learning Nonhomogeneous Elliptic Interface Problems by Soft Constraint Physics-Informed Neural Networks," Mathematics, MDPI, vol. 11(8), pages 1-23, April.

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