Variance reduction in stochastic homogenization : proof of concept, using antithetic variables

Réduction de variance en homogénéisation stochastique : l'exemple des variables antithétiques

Ronan Costaouec (1, 2) , Claude Le Bris (1, 2) , Frédéric Legoll (2, 3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes

We show that we can reduce the variance in a simple problem of stochastic homogenization using the classical technique of antithetic variables. The setting, and the presentation, are deliberately kept elementary. We point out the main issues, show some illustrative results, and demonstrate, both theoretically and numerically, the efficiency of the approach on simple cases.

Mots clés: variance reduction; antithetic variables; stochastic homogenization

Domaines: Analyse numérique [math.NA]

Ronan Costaouec, Claude Le Bris, Frédéric Legoll. Variance reduction in stochastic homogenization : proof of concept, using antithetic variables. [Research Report] RR-7207, Inria. 2010, pp.1-21. ⟨inria-00457946⟩