Statistical inference for partial differential equations*

Abstract

Many physical phenomena are modeled by parametrized PDEs. The poor knowledge on the involved parameters is often one of the numerous sources of uncertainties on these models. Some of these parameters can be estimated, with the use of real world data. The aim of this mini-symposium is to introduce some of the various tools from both statistical and numerical communities to deal with this issue. Parametric and non-parametric approaches are developed in this paper. Some of the estimation procedures require many evaluations of the initial model. Some interpolation tools and some greedy algorithms for model reduction are therefore also presented, in order to reduce time needed for running the model.