Uncertainty quantification in high-dimensional parametric PDEs via compressed sensing
jeudi 15 février 2018, 15h30 - 16h30
In this talk I will review the basic problems stemming in high-dimensional parametric and stochastic PDEs. I will introduce an efficient method for computing numerical solutions to such problems which combines a weighted version of standard compressed sensing with a multi-level approach. By exploiting the analytic dependence on the parameters of a class parametric PDEs, we can show convergence rates for non-linear sparse approximation of polynomial chaos expansions that beat the so-called curse of dimensionality. I will give a theoretical analysis in terms of (uniform) approximation rates and computations as well as numerical examples illustrating our theory.
This is based on joint work with Holger Rauhut (RWTH Aachen) and Christoph Schwab (ETHZ).