In this paper we show how to augment classical methods for inverse problems with artificial
neural networks. The neural network acts as a prior for the coefficient to be estimated from …

In this work we analyze the inverse problem of recovering a space-dependent potential
coefficient in an elliptic/parabolic problem from distributed observation. We establish novel …

In this paper we study the inverse problem of identifying the diffusion matrix in an elliptic
PDE from measurements. The convex energy functional method with Tikhonov …

In this paper we discuss the potential of using artificial neural networks as smooth priors in
classical methods for inverse problems for PDEs. Exploring that neural networks are global …

Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data
of the gradient of the solution is an important nonlinear and ill-posed inverse problem …

This work is devoted to the nonlinear inverse problem of identifying the reaction coefficient in
an elliptic boundary value problem from single Cauchy data on a part of the boundary. We …

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-
connected domains, that is the reconstruction of a harmonic function from knowledge of the …

Two different approaches for solving a nonlinear coefficient inverse problem are
investigated in this paper. As a classical approach, we use the finite element method to …