Generation of non-Gaussian tensor-valued random fields using an ISDE-based algorithm

Johann Guilleminot (1) , Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

A random generator is constructed for non-Gaussian tensorvalued random fields. Specifically, it focuses on the generation of the class of Prior Algebraic Stochastic Models associated with elliptic operators, for which the family of first-order marginal probability distributions is constructed using the MaxEnt principle. The strategy essentially relies on the definition of a family of diffusion processes, the invariant measures of which coincide with the target system of first-order marginal probability distributions. Those processes are defined as the unique stationary solutions of a family of Ito stochastic differential equations, the definition of which involves the construction of a family of normalized Wiener processes. The definition of the later allows spatial dependencies to be generated and the algorithm turns out to be very efficient for high probabilistic dimensions, it does not suffer from the curse of dimensionnality that is inherently exhibited by Gaussian chaos expansions, for instance. The algorithm is finally validated through the generation of a matrix-valued non-Gaussian random field.

Mots clés: uncertainty quantification; random generator; non-Gaussian tensor-valued random fields; ISDE approach; adaptive Verlet scheme

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

Johann Guilleminot, Christian Soize. Generation of non-Gaussian tensor-valued random fields using an ISDE-based algorithm. ICOSSAR 2013, 11th International Conference on Structural Safety and Reliability, Columbia University, Jun 2013, New-York, United States. pp.1-6. ⟨hal-00806416⟩