A parameter identification problem in stochastic homogenization

TL;DR

This paper addresses the challenge of parameter identification in stochastic homogenization of porous media by proposing a least-squares approach, demonstrating the effectiveness of Newton's method in the one-dimensional case with noisy data.

Contribution

It introduces a least-squares formulation for inverse parameter identification in stochastic homogenization and analyzes the selection of macroscopic observables for unique parameter determination.

Findings

Newton algorithm effectively determines parameters with small noise

Focus on one-dimensional case for computational efficiency

Method shows robustness against statistical noise

Abstract

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.