  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.
