In this work we investigate the numerical identification of the diffusion coefficient in elliptic
and parabolic problems using neural networks (NNs). The numerical scheme is based on …

We shall study in this paper the convergence rates of the Tikhonov regularized solutions for
the recovery of the radiativities in elliptic and parabolic systems in general dimensional …

We investigate the problem of learning a water quality model (BOD-DO model) from given
data. Assuming that all parameters in the model are constants, we reformulate the problem …

This paper provides a theoretical study of reconstructing absorption and scattering
coefficients based on the radiative transport equation (RTE) by using the total variation …

Descent gradient methods are the most frequently used algorithms for computing
regularizers of inverse problems. They are either directly applied to the discrepancy term …

We investigate the convergence rates for total variation regularization of the problem of
identifying (i) the coefficient q in the Neumann problem for the elliptic equation− div (q∇ u) …

In this paper, the inverse problem of finding a coefficient in a second order elliptic equation
is investigated. The conditions for the existence and uniqueness of the classical solution of …

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 …

We shall study the convergence rates of the Tikhonov regularizations for the identification of
the diffusivity q (x) in a parabolic–elliptic system. The H 1 regularization and a mixed L p–H 1 …

In this paper we investigate the problem of recovering the source f in the elliptic system from
an observation z of the state u on a part of the boundary, where the functions and j are given …