Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization
It addresses the ill-posed inverse problem of pollution source estimation, but the approach is incremental, combining existing techniques (Gauss-Newton, POD) with adaptive parametrization.
This paper solves a parabolic inverse convection-diffusion-reaction problem for pollution estimation, using an adaptive parametrization with time localization to handle ill-posedness when the source location is unknown. The method employs Proper Orthogonal Decomposition for model reduction.
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.