Prior representations of random fields for stochastic multiscale modeling

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. © 2013 The Authors.