Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs

被引：55

作者：

Cai, Zhiqiang ^{[1
]}

Chen, Jingshuang ^{[1
]}

Liu, Min ^{[2
]}

Liu, Xinyu ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

[2] Purdue Univ, Sch Mech Engn, 585 Purdue Mall, W Lafayette, IN 47907 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 420卷 / 420期

关键词：

Deep least-squares method; Neural network; Elliptic PDEs; BOUNDARY-VALUE-PROBLEMS; APPROXIMATIONS; ALGORITHM;

D O I：

10.1016/j.jcp.2020.109707

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine parameters of the deep neural network. There are various least-squares functionals for a partial differential equation. This paper focuses on the so-called first-order system least-squares (FOSLS) functional studied in [3], which is based on a first-order system of scalar second-order elliptic PDEs. Numerical results for second-order elliptic PDEs in one dimension are presented. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：13

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