UQ for PDEs with Gaussian random field inputs

Jakob Zech (U Heidelberg)

Apr 04. 2022, 16:20 — 17:10

We establish summability results for coefficient sequences of Wiener-Hermite polynomial chaos expansions for countably-parametric solutions of linear elliptic and parabolic partial differential equations with Gaussian random field inputs. Our proof technique is based on the holomorphic extension of solution maps, and thus allows a unified ``differentiation-free'' sparsity analysis applicable also to posterior densities in Bayesian inverse problems. We present dimension-independent convergence rates of high-dimensional deterministic numerical approximation schemes such as single-level and multi-level versions of anisotropic sparse-grid Hermite-Smolyak interpolation and quadrature in both forward and inverse uncertainty quantification. Additionally, we provide expression rate bounds for neural network approximations of the response surfaces to the parametric PDEs.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Adaptivity, High Dimensionality and Randomness (Workshop)
Carsten Carstensen (HU Berlin)
Albert Cohen (Sorbonne U, Paris)
Michael Feischl (TU Vienna)
Christoph Schwab (ETH Z├╝rich)