Prior representations of random fields for stochastic multiscale modeling

Johann Guilleminot (1) , Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

In this presentation, we will present and discuss some of the most recent contributions to the construction of Prior Algebraic Stochastic Models (PASM) for non-Gaussian tensor-valued random fields. We will first motivate the need of such prior models accounting, not only for mathematical constraints, but also for physically sounded constraints such as local anisotropy. In a second step, we will expose a methodology that aims at constructing such probabilistic models. Computational issues related to random generation will be addressed as well. Finally, we will exemplify both the approach and the algorithms by considering the modeling of mesoscopic elasticity tensor random fields, for which information associated with a stochastic anisotropy measure must be taken into account.

Mots clés: Random fields; non-Gaussian; multiscale modeling; uncertainty quantification

Domaines: Mécanique [physics.med-ph]; Matériaux; Probabilités [math.PR]; Statistiques [math.ST]

Johann Guilleminot, Christian Soize. Prior representations of random fields for stochastic multiscale modeling. IUTAM Symposium on Multiscale Problems in Stochastic Mechanics, Jun 2012, Karlsruhe, Germany. pp.1-6. ⟨hal-00734151v2⟩