Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization

TL;DR

This paper addresses solving a parabolic inverse convection-diffusion-reaction problem for pollution estimation, introducing adaptive parametrization and model reduction techniques to handle ill-posedness and unknown source locations.

Contribution

It presents a novel adaptive parametrization method combined with Proper Orthogonal Decomposition for regularizing and solving inverse problems with unknown source locations.

Findings

Effective regularization of ill-posed inverse problems

Successful estimation of pollution sources

Improved computational efficiency through model reduction

Abstract

This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location: while in the first case the problem is solved using a projected damped Gauss-Newton, in the second one it is ill-posed and an adaptive parametrization with time localization will be adopted to regularize it. To solve the optimization loop a model reduction technique (Proper Orthogonal Decomposition) is used.