Related papers: Multilevel Quasi-Monte Carlo for Optimization unde…
There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains functions that are infinitely smooth with a growth condition on the…
A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It…
In this study, we consider the development of tailored quasi-Monte Carlo (QMC) cubatures for non-conforming discontinuous Galerkin (DG) approximations of elliptic partial differential equations (PDEs) with random coefficients. We consider…
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…
Parametric regularity of discretizations of flux vector fields satisfying a balance law is studied under some assumptions on a random parameter that links the flux with an unknown primal variable (often through a constitutive law). In the…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption,…
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…
Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…
In many models used in engineering and science, material properties are uncertain or spatially varying. For example, in geophysics, and porous media flow in particular, the uncertain permeability of the material is modelled as a random…
Methods for generating sequences of surrogates approximating fine scale models of two-phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest (QoIs). For…
By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…
Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…
By adopting a Multilevel Monte Carlo (MLMC) framework, we show that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the thousands typically…
Building on previous research which generalized multilevel Monte Carlo methods using either sparse grids or Quasi-Monte Carlo methods, this paper considers the combination of all these ideas applied to elliptic PDEs with finite-dimensional…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
We explore the application of the quasi-Monte Carlo (QMC) method in deep backward dynamic programming (DBDP) (Hure et al. 2020) for numerically solving high-dimensional nonlinear partial differential equations (PDEs). Our study focuses on…