# Direct and Inverse Problems for PDEs with Random Coefficients - Abstract

**Nouy, Anthony**

*Preconditioners for parameter-dependent equations and goal-oriented model order reduction*

We consider large systems of parameter-dependent equations, e.g. arising from the discretization of stochastic PDEs. We propose an interpolation of matrix inverse based on a projection of the identity matrix with respect to the Frobenius norm. The use of randomized linear algebra allow for handling large matrices. Adaptive interpolation strategies are then proposed for different objectives in the context of projection-based model reduction methods: the improvement of residual-based error estimators, the improvement of the projection on a given reduced approximation space, or the recycling of computations for sampling based model reduction methods.