A parameter identification problem in stochastic homogenization

• Main Authors: Legoll Frédéric, Minvielle William, Obliger Amaël, Simon Marielle
• Format: Article
• Language: English
• Published: EDP Sciences 2015-01-01
• Series: ESAIM: Proceedings and Surveys
• Online Access: http://dx.doi.org/10.1051/proc/201448008

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.