A neural network based parametrization method for distributed parameter identification

We consider distributed parameter systems governed by elliptic or parabolic partial differential equations with an unknown coefficient that is spatially varying over a certain domain. We propose an identification procedure that combines neural classification, zonation, function interpolation, and optimization search. There are at least two major advantages of this approach: classification capability without a priori assumptions regarding zone shape, zone number, and zone configuration of unknown parameters, and incorporation of uncertainty in the observation data into the identification procedure. We consider aquifer parameter identification as an example.