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

Xinyue Evelyn Zhao, Wenrui Hao and Bei Hu

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

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.

Keywords: Obstacle problems; Free boundary problems; Neural networks; Convergence rate (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005239

DOI: 10.1016/j.chaos.2022.112313

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