Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
This article provides a survey of recent research efforts on the application of quasi-Monte
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …
Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications
In this paper, the potential benefits of quasi-Monte Carlo (QMC) methods for uncertainty
propagation are assessed via two applications: a numerical case study and a realistic and …
propagation are assessed via two applications: a numerical case study and a realistic and …
Message-Passing Monte Carlo: Generating low-discrepancy point sets via graph neural networks
Discrepancy is a well-known measure for the irregularity of the distribution of a point set.
Point sets with small discrepancy are called low discrepancy and are known to efficiently fill …
Point sets with small discrepancy are called low discrepancy and are known to efficiently fill …
[图书][B] Randomized quasi-Monte Carlo: An introduction for practitioners
P L'Ecuyer - 2018 - Springer
We survey basic ideas and results on randomized quasi-Monte Carlo (RQMC) methods,
discuss their practical aspects, and give numerical illustrations. RQMC can improve …
discuss their practical aspects, and give numerical illustrations. RQMC can improve …
Quantum quasi-Monte Carlo technique for many-body perturbative expansions
High order perturbation theory has seen an unexpected recent revival for controlled
calculations of quantum many-body systems, even at strong coupling. We adapt integration …
calculations of quantum many-body systems, even at strong coupling. We adapt integration …
Algorithm 958: Lattice builder: A general software tool for constructing rank-1 lattice rules
P L'ecuyer, D Munger - ACM Transactions on Mathematical Software …, 2016 - dl.acm.org
We introduce a new software tool and library named Lattice Builder, written in C++, that
implements a variety of construction algorithms for good rank-1 lattice rules. It supports …
implements a variety of construction algorithms for good rank-1 lattice rules. It supports …
Higher order quasi--Monte Carlo integration for holomorphic, parametric operator equations
We analyze the convergence of higher order quasi--Monte Carlo (QMC) quadratures of
solution functionals to countably parametric, nonlinear operator equations with distributed …
solution functionals to countably parametric, nonlinear operator equations with distributed …
A Randomised Lattice Rule Algorithm with Pre-determined Generating Vector and Random Number of Points for Korobov Spaces with
D Nuyens, L Wilkes - International Conference on Monte Carlo and Quasi …, 2022 - Springer
In previous work, we showed that a lattice rule with a pre-determined generating vector but
random number of points can achieve the near optimal convergence of O (n-α-1/2+ ϵ), ϵ> 0 …
random number of points can achieve the near optimal convergence of O (n-α-1/2+ ϵ), ϵ> 0 …
Inchworm quasi Monte Carlo for quantum impurities
The inchworm expansion is a promising approach to solving strongly correlated quantum
impurity models due to its reduction of the sign problem in real and imaginary time …
impurity models due to its reduction of the sign problem in real and imaginary time …
A tool for custom construction of QMC and RQMC point sets
P L'Ecuyer, P Marion, M Godin… - … Conference on Monte …, 2020 - Springer
Abstract We present LatNet Builder, a software tool to find good parameters for lattice rules,
polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and …
polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and …