Model exploration for approximation of complex, high-dimensional problems - WMM9AM23

Goal(s)

The goal of this lecture is to address the difficult problem of approximating high-dimensional functions, meaning functions of a large number of parameters. The first part of the lecture is devoted to interpolation techniques via polynomial functions or via gaussian processes. In the second part, we present two methods for reducing the dimension of the input parameters space, namely the Sliced Inverse Regression and the Ridge Function Recovery.

Content(s)

Many industrial applications invole expensive computational codes which can take weeks or months to run. It is typical for weather prediction, in aerospace sector or in the civil engineering field. There is here an important (economic) challenge to reduce the computational cost by constructing a surrogate for the input-to-output relationship.
Since only a few number of model runs is affordable, dedicated tools have been developed to exploit this type of "not-so-big" data sets. This lecture focuses on some of the most recent advances in that direction.

Basic knowledge in probability and statistics