|Title||Approximate solutions of lagrange multipliers for information-theoretic random field models|
|Publication Type||Journal Article|
|Year of Publication||2015|
|Authors||B Staber, and J Guilleminot|
|Journal||Siam/Asa Journal on Uncertainty Quantification|
|Pagination||599 - 621|
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 [J. Guilleminot and C. Soize, Multiscale Model. Simul., 11 (2013), pp. 840-870]. 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.
|Short Title||Siam/Asa Journal on Uncertainty Quantification|