Approximate solutions of Lagrange multipliers for information-theoretic random field models

B Staber (1) , Johann Guilleminot (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

This work is concerned with the construction of approximate solutions for the Lagrange multipliers involved in information-theoretic non-Gaussian random field models. Specifically, representations of physical fields with invariance properties under some orthogonal transformations are considered. A methodology for solving the optimization problems raised by entropy maximization (for the family of first-order marginal probability distributions) is first presented and exemplified in the case of elasticity fields exhibiting fluctuations in a given symmetry class. Results for all classes ranging from isotropy to orthotropy are provided and discussed. The derivations are subsequently used for proving a few properties that are required in order to sample the above models by solving a family of stochastic differential equations – along the lines of the algorithm constructed in [9]. The results thus allow for forward simulations of the probabilistic models in stochastic boundary value problems, as well as for a reduction of the computational cost associated with model calibration through statistical inverse problems.

Mots clés: Elasticity; information-theoretic stochastic model; maximum entropy principle; random field; stochastic elliptic boundary value problem; uncertainty quantification

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

B Staber, Johann Guilleminot. Approximate solutions of Lagrange multipliers for information-theoretic random field models. SIAM/ASA Journal on Uncertainty Quantification, 2015, pp.1-23. ⟨hal-01166830⟩