Abstract:
This talk is concerned with the development of probabilistic reduced order models facilitating uncertainty quantification in partial differential equations with random and spatially varying coefficients. In particular, Poisson’s equation with a random, heterogeneous conductivity field is investigated. Following the Bayesian paradigm, the reduced order model is searched for within a space that comprises solely physically plausible models. This may be achieved by means of a spatial coarse-graining procedure and it is favorable in the sense that the number of expensive fine model evaluations required for training is minimized. So far, coarse representations of the heterogeneous fine scale material parameter field were constrained to be isotropic. This work aims at improving the accuracy of the reduced order model by allowing for anisotropic representations.