Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
arXiv:1911.02109 · doi:10.1016/j.jcp.2020.109707
Abstract
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.
15 pages, 6 figures, 5 tables, accepted by Journal of Computational Physics