In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty
quantification of physical/biological systems described by ordinary or partial differential …

We address shape uncertainty quantification for the two-dimensional Helmholtz
transmission problem, where the shape of the scatterer is the only source of uncertainty. In …

A stochastically enriched spectral finite element method (StSFEM) is developed to solve
wave propagation problems in random media. This method simultaneously includes all …

摘要不确定性量化(Uncertainty Quantification, UQ) 是近年来国际上热门的研究课题,
其应用领域包括水文学, 流体力学, 数据同化, 天气预测等等. 由于UQ 问题中的大量随机参数 …

A new stochastic method, integrating spline dimensional decomposition (SDD) and
isogeometric analysis (IGA), is proposed for solving stochastic boundary-value problems …

We develop a fast method for optimally designing experiments in the context of statistical
seismic source inversion. In particular, we efficiently compute the optimal number and …

Stochastic quantities of interest are expanded in generalized polynomial chaos expansions
using stochastic Galerkin methods. An application to hyperbolic differential equations does …

We consider the very challenging problem of efficient uncertainty quantification for acoustic
wave propagation in a highly heterogeneous, possibly layered, random medium …

In this work, we apply the MG/OPT framework to a multilevel-in-sample-space discretization
of optimization problems governed by PDEs with uncertain coefficients. The MG/OPT …