Identification of Contamination Flux in a Domain of Porous Media as an Inverse Problem Solved with Artificial Neural Networks

For a steady state convection problem, assuming given concentration field values in a few measurement points and hydraulic head values in the same piezometers, the source of the concentration, its intensity and diffusivity vector are deduced using Artificial Neural Networks (ANNs). ANNs are trained with data extracted from Finite Difference (FD) solution of a classical convection problem, called below direct problem. We suppose that the velocity field is derivable from a hydraulic head field, the values of which are also given in few points of measurements. The numerical analysis is exemplified for homogeneous and non-homogeneous field of velocity. A corresponding inverse problem can be easily identified: the identification of source position of the suspension that propagates in the domain of porous medium. Analogously another inverse problem can be proposed for the diffusivity vector D. To solve the inverse problems, we focus our attention on the widely used ANN with nodes organized in layers. The values obtained at the nodes of the output layer (result of the network activity) as well as those given by the user to the input nodes, are interpreted in terms of the modeled problem