Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems
This addresses the problem of solving PDE-based problems without labeled data for researchers in computational physics and engineering, though it appears incremental as it builds on existing neural network methods for PDEs.
The paper tackles solving forward and inverse problems for partial differential equations (PDEs) using an unsupervised deep learning algorithm, achieving a mesh-free approach applicable to arbitrary regular domains, with specific application to Electrical Impedance Tomography in 2D second-order elliptical systems with non-constant coefficients.
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.