A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A 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.


Published in:
SIAM/ASA Journal on uncertainty Quantification, 8, 1, 414-450
Year:
2020
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 Record created 2018-05-31, last modified 2020-04-27

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