## Section:
New Results2>
### Uncertainty Quantification3>

Participants : RĂ©mi Abgrall, Pietro Congedo [Corresponding member] , Gianluca Geraci, Mario Ricchiuto.

We developed two research lines: the first one focused on the computation of high-order statistics, the second one is related to the formulation of a global framework in the coupled physical/stochastic space. First, we proposed a formulation in order to compute the decomposition of high-order statistics. The idea is to compute the most influential parameters for high orders permitting to improve the sensitivity analysis. Second objective is to illustrate the correlation between the high-order functional decomposition and the PC-based techniques, thus displaying how to compute each term from a numerical point of view. Secondly, Basing on the Harten multiresolution framework in the stochastic space, we proposed a method allowing an adaptive refinement/derefinement in both physical and stochastic space for time dependent problems. As a consequence, an higher accuracy is obtained with a lower computational cost with respect to classical non-intrusive approaches, where the adaptivity is performed in the stochastic space only. Performances of this algorithm are tested on scalar Burgers equation and Euler system of equations, comparing with the classical Monte Carlo and Polynomial Chaos techniques.

Application of some of these techniques to tsunami simulations have been conducted.