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

被引：0

作者：

Zhao, Xinyue Evelyn ^{[1
]}

Hao, Wenrui ^{[2
]}

Hu, Bei ^{[3
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37212 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA

来源：

CHAOS SOLITONS & FRACTALS | 2022年 / 161卷

关键词：

Obstacleproblems; Freeboundaryproblems; Neuralnetworks; Convergencerate;

D O I：

10.1016/j.chaos.2022.112313

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 prob-lems (both 1-D and 2-D) are used to verify the convergence rate of the methods and the quality of the results.Published by Elsevier Ltd.

引用

页数：10

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