  In porous media physics, calibrating model parameters through experiments is
a challenge. This process is plagued with errors that come from modelling,
measurement and computation of the macroscopic observables through random
homogenization -- the forward problem -- as well as errors coming from the
parameters fitting procedure -- the inverse problem. In this work, we address
these issues by considering a least-square formulation to identify parameters
of the microscopic model on the basis on macroscopic observables. In
particular, we discuss the selection of the macroscopic observables which we
need to know in order to uniquely determine these parameters. To gain a better
intuition and explore the problem without a too high computational load, we
mostly focus on the one-dimensional case. We show that the Newton algorithm can
be efficiently used to robustly determine optimal parameters, even if some
small statistical noise is present in the system.

Optimization and Control;Analysis of PDEs;Numerical Analysis