**Date: **19 June 2019

**Time: **12:45 - 13:30 (Lunch available from 12:35)

**Room:** RA 1501 (Ravelijn)

**Speaker:** Olivier Zahm

## Title: Gradient-based dimension reduction for uncertainty quantification problems

**Abstract:**

Uncertainty Quantification (UQ) aims at characterizing and quantifying the impact of some input parameters of interest, generally modelled as random variables, onto the outcome of a computational model. The goal could be for instance to estimate the mean behaviour of a system or its probability of failure. Often the model is too expensive to evaluate so that the UQ analysis is realized on a surrogate model, meaning an approximation that allows fast evaluations of the input-to-output relashionship. However, approximation of multivariate functions is a difficult task when the number of input parameters is large. Identifying the directions where the function does not vary significantly is a key preprocessing step to reduce the complexity of the approximation algorithms.

In this talk, we propose and analyze gradient-based methods that permit to detect such a low-dimensional structure. The methodology consists in minimizing an upper-bound of the approximation error obtained using Poincaré-type inequalities. We show the connection with standard screening techniques used in Global Sensitivity Analysis. We then explain how this methodology naturally extends to nonlinear dimension reduction, e.g. when the function is not constant along a subspace but along a low-dimensional manifold.