  We propose a neural network-based algorithm for solving forward and inverse
problems for partial differential equations in unsupervised fashion. The
solution is approximated by a deep neural network which is the minimizer of a
cost function, and satisfies the PDE, boundary conditions, and additional
regularizations. The method is mesh free and can be easily applied to an
arbitrary regular domain. We focus on 2D second order elliptical system with
non-constant coefficients, with application to Electrical Impedance Tomography.
