Adaptive wavelets for uncertainty  quantification in dynamical systems
July 19, 2012
2:30 p.m.
Denis Dreano
Abstract
The behavior of dynamical systems is often modeled as the solution to a system of differential equations. Most of the time, the parameters such as the initial conditions, the boundary conditions, the physical constants or the geometry are not well known. Spectral methods for uncertainty quantification study the effects of randomness on dynamical systems. The solution to the randomized set of equations is a stochastic process which is approximated using a Galerkin approach.
Usually, a Polynomial Chaos basis is used for the projection. However, such basis may be inefficient when the solution nature can change quickly with the values of the parameters. In that case, a local basis like wavelets may be useful. Here we investigate the construction of wavelets which are adapted to the probability density function of the parameters