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Bayesian Inference of Multiscale Differential Equations

Thursday, August 22, 2019
4:00pm to 5:00pm
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Annenberg 213
Bayesian Inference of Multiscale Differential Equations
Giacomo Garegnani, Doctoral Assistant, Numerical Analysis and Computational Mathematics, École polytechnique fédérale de Lausanne,

Inverse problems involving differential equations defined on multiple scales naturally arise in several engineering applications. The computational cost due to discretization of multiscale equations can be reduced employing homogenization methods, which allow for cheaper computations. Nonetheless, homogenization techniques introduce a modelling error, which has to be taken into account when solving inverse problems. In this presentation, we consider the treatment of the homogenization error in the framework of inverse problems involving either an elliptic PDE or a Langevin diffusion process. In both cases, theoretical results involving the limit of oscillations of vanishing amplitude are provided, and computational techniques for dealing with the modelling error are presented.

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