A parameter identification problem in stochastic homogenization

Frédéric Legoll; William Minvielle; Amaël Obliger; Marielle Simon

doi:10.1051/proc/201448008

Geodesic

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A parameter identification problem in stochastic homogenization

Frédéric Legoll ^1,² ; William Minvielle ^3,² ; Amaël Obliger ^4,⁵ ; Marielle Simon ⁶

¹ Laboratoire Navier, École Nationale des Ponts et Chaussées, Université Paris-Est, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France;
² INRIA Rocquencourt, MATHERIALS research-team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
³ CERMICS, École Nationale des Ponts et Chaussées, Université Paris-Est, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France;
⁴ Sorbonne Universités, UPMC Univ. Paris 06, UMR 8234 PHENIX, 75005 Paris, France;
⁵ ANDRA, Parc de la Croix-Blanche, 1-7, rue Jean-Monnet, 92298 Châtenay-Malabry, France
⁶ UMPA, UMR-CNRS 5669, ENS Lyon, 46 allée d’Italie, 69007 Lyon, France;

ESAIM. Proceedings, Tome 48 (2015), pp. 190-214.

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Résumé

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.

DOI : 10.1051/proc/201448008

Affiliations des auteurs :

Frédéric Legoll ^{1, 2} ; William Minvielle ^{3, 2} ; Amaël Obliger ^{4, 5} ; Marielle Simon ⁶

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     title = {A parameter identification problem in stochastic homogenization},
     journal = {ESAIM. Proceedings},
     pages = {190--214},
     publisher = {mathdoc},
     volume = {48},
     year = {2015},
     doi = {10.1051/proc/201448008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201448008/}
}

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Frédéric Legoll; William Minvielle; Amaël Obliger; Marielle Simon. A parameter identification problem in stochastic homogenization. ESAIM. Proceedings, Tome 48 (2015), pp. 190-214. doi : 10.1051/proc/201448008. http://geodesic.mathdoc.fr/articles/10.1051/proc/201448008/

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