Mathematical and Algorithmic Aspects of Uncertainty Quantification.    June 3-10, 2015

General Information

Lecture 1, 3/6/2015 (14-18) Introduction and motivation; random fields (14-18) Slides part I
Lecture 2, 4/6/2015 (9-13) Monte Carlo and Quasi Monte Carlo methods Slides part II (only first part)

Slides part III
Lecture 3, 5/6/2015 (9-13) MultiLevel Monte Carlo; polynomial approximation in 1D Slides part II (second part)

MLMC in compressible aerodynamics (Talk Pisaroni at IWUQCFD 2015)

Slides part IV (only first part)
Lab 1, 5/6/2015 (14-18) Monte Carlo and Quasi Monte Carlo integration of functions Lab1 assignment (execise 1) Sobol Matlab toolkit (downloaded from
Lecture 4, 8/6/2015 (9-13) Multivariate polynomial approximation; discrete L^2 projection Slides part IV (second part)
Lab 2, 8/6/2015 (15-17) Generation of Gaussian random fields; MC and QMC of second order boundary value problem with random coefficients Lab1 assignment (exercise 2) FEM solver for exercise 2
Lecture 5, 9/6/2015 (14-18) Multivariate polynomial approximation; sparse interpolation; stochastic Galerkin Slides part IV (third part)

Adaptive sparse grids in subsurface flow modeling (Talk Tamellini at SIAM-CSE2015)
Lecture 6, 10/6/2015 (9-10) Global sensitivity analysis; Hyperbolic problems Slides sensitivity analysis

Slides part V
Lab 3, 10/6/2015 (10-13) Polynomial approximation by sparse grids and discrete least squares for second order boundary value problem with random coefficients Lab2 assignment

Assignments for final evaluation
Sparse grids Matlab toolkit