March 27, 2025 13:30, SP2 416-2

ABSTRACT:
Partial differential equations (PDEs) with random inputs are widely studied in uncertainty quantification. If the random input field is represented as a series expansion, computing PDE response statistics requires solving high-dimensional integrals of the PDE output over a sequence of stochastic parameters. In practical computations, one typically needs to discretize the problem in several ways: truncating the infinite-dimensional input field to a finite-dimensional representation, spatial discretization of the PDE using, e.g., finite elements, and approximating high-dimensional integrals using cubatures such as quasi–Monte Carlo (QMC) methods.

QMC methods have been extensively studied for uniform and lognormal parameterizations of the input field. In these cases, the random input field is a real analytic function of the parameters. However, recent interest has shifted toward uncertainty quantification for PDEs with Gevrey-regular inputs. The Gevrey class contains infinitely smooth functions that satisfy a growth condition on the higher-order partial derivatives, but which are nonetheless not analytic in general.

In this talk, we analyze Gevrey-regular parameterizations of input random fields with generalized Gaussian distributions, including potentially fat-tailed cases.