Inverse Problem: a Soft Solution

After a short introduction about fundamental definitions and main issues associated with inverse problems, some examples are chosen to illustrate the application of Artificial Neural Networks (ANNs) to obtain the solution. 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 and its intensity are identified using ANNs. To illustrate the identification of special boundary conditions, an example of soft approach in the framework of self-consistent homogenization is presented. The main purpose of this work is to show that soft methods seem to be very automatic and convenient tools in solving a large family of inverse problems.