MATHICSE Technical Report : A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A new strategy based on numerical homogenization and Bayesian techniques for solvingmultiscale inverse problems is introduced. We consider a class of elliptic problems which vary ata microscopic scale, and we aim at recovering the highly oscillatory tensor from measurements ofthe fine scale solution at the boundary, using a coarse model based on numerical homogenizationand model order reduction. We provide a rigorous Bayesian formulation of the problem, takinginto account different possibilities for the choice of the prior measure. We prove well-posednessof the effective posterior measure and, by means of G-convergence, we establish a link betweenthe effective posterior and the fine scale model. Several numerical experiments illustrate theefficiency of the proposed scheme and confirm the theoretical findings.


Year:
May 29 2018
Publisher:
Écublens, MATHICSE
Keywords:
Note:
MATHICSE Technical Report Nr. 09.2018
Laboratories:




 Record created 2019-09-27, last modified 2019-12-05

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