Mathematical models are widely used in physics and engineering applications as predictive tools. However, in many situations, the input parameters of the model are uncertain due to either a lack of knowledge or an intrinsic variability of the system. Examples are the study of subsurface phenomena, biological tissues, complex materials, whose properties are often heterogeneous, not perfectly characterized and, possibly, changing in time in an uncertain way.

In this line of research we consider the case in which the uncertainty can be described reasonably well in a probabilistic setting and we focus on the problem of effectively propagating it from the input parameters to the output quantities of interest of the mathematical model. In particular we focus on non-intrusive numerical methods that imply solving the problem for a well chosen set of input parameters and make inference on the statistical properties of the output quantities based on the corresponding evaluations.

- Raul Tempone (KAUST)
- Mohammad Motamed (KAUST)
- Fabio Nobile (EPFL & Politecnico di Milano)
- Ivo Babuska (UT Austin, TX)
- Lorenzo Tamellini (Politecnico di Milano)
- Giovani Migliorati (Politecnico di Milano)
- Joakim Beck (UCL, London, UK)

- M. Motamed, F. Nobile and R. Tempone.
**A****Stochastic Collocation Method fo the Second Order Wave Equation with a Discontinuous Random Speed****.**Journal of Numerische Mathematik, Volume 123, Issue 3 (2013), Page 493-536 - J. Beck, F. Nobile, L. Tamellini and R. Tempone.
**On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods.**Mathematical Models and Methods in Applied Sciences (M3AS), vol. 22, num. 9, p. 1250023.1-1250023.33, 2012. - Q. Long, M. Scavino, R. Tempone and S. Wang.
**Fast Estimation of Expected Information Gains for Bayesian Experimental Designs Based on****Laplace Approximations****.**Computer Methods in Applied Mechanics and Engineering. Accepted, 2012 J. Back, F. Nobile, L. Tamellini and R. Tempone,

**Stochastic Spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison.**Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, Volume 76, 43-62, 2011.-
**A Stochastic Collocation method for elliptic Partial DifferentialEquations with Random Input Data.**SIAM Review, Volume 52, Issue 2, 317-355, 2010.