The paper describes the philosophy, design, functionality, and usage of the Python software
toolbox Chaospy for performing uncertainty quantification via polynomial chaos expansions …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

This work proposes and analyzes a stochastic collocation method for solving elliptic partial
differential equations with random coefficients and forcing terms. These input data are …

Learning approximations to smooth target functions of many variables from finite sets of
pointwise samples is an important task in scientific computing and its many applications in …

Uncertainties have become a major concern in integrated circuit design. In order to avoid the
huge number of repeated simulations in conventional Monte Carlo flows, this paper presents …

Stochastic collocation methods for approximating the solution of partial differential equations
with random input data (eg, coefficients and forcing terms) suffer from the curse of …

Shannon-type expected information gain can be used to evaluate the relevance of a
proposed experiment subjected to uncertainty. The estimation of such gain, however, relies …

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE
with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional …

Polynomial approximations constructed using a least-squares approach form a ubiquitous
technique in numerical computation. One of the simplest ways to generate data for least …

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for
computing statistics of the solution of a PDE with random data. MISC is a combination …