Abdulle, AssyrDi Blasio, Andrea2018-05-312018-05-312018-05-31202010.1137/18M1187891https://infoscience.epfl.ch/handle/20.500.14299/146668A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly oscillatory tensor from measurements of the fine scale solution at the boundary, using a coarse model based on numerical homogenization and model order reduction. We provide a rigorous Bayesian formulation of the problem, taking into account different possibilities for the choice of the prior measure. We prove well-posedness of the effective posterior measure and, by means of G-convergence, we establish a link between the effective posterior and the fine scale model. Several numerical experiments illustrate the efficiency of the proposed scheme and confirm the theoretical findings.Inverse problemsBayesian regulatizationHomogenizationMultiscale methodstext::journal::journal article::research article