The recent development of machine learning (ML) and Deep Learning (DL) increases the
opportunities in all the sectors. ML is a significant tool that can be applied across many …

This paper presents a review of the current state-of-the-art of numerical methods for
stochastic computations. The focus is on efficient high-order methods suitable for practical …

Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

The@ first graduate-level textbook to focus on fundamental aspects of numerical methods
for stochastic computations, this book describes the class of numerical methods based on …

This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …

We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial
differential equations (PDEs). The method extracts a reduced basis from a collection of high …

Recently there has been a growing interest in designing efficient methods for the solution of
ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin …

In this paper we propose and analyze a stochastic collocation method to solve elliptic partial
differential equations with random coefficients and forcing terms (input data of the model) …

The Dakota toolkit provides a flexible and extensible interface between simulation codes
and iterative analysis methods. Dakota contains algorithms for optimization with gradient …