| Summary: | 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, including
homogenized coefficients. 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 when some small
statistical noise is present in the system.
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