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This paper investigates the solution of a parabolic inverse problem basedupon the convection-diffusion-reaction equation, which can be used to estimateboth water and air pollution. We will consider both known and unknown sourcelocation: while in the first case the problem is solved using a projecteddamped Gauss-Newton, in the second one it is ill-posed and an adaptiveparametrization with time localization will be adopted to regularize it. Tosolve the optimization loop a model reduction technique (Proper OrthogonalDecomposition) is used.

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