Related papers: A Massively Parallel Implementation of Multilevel …
This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…
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 coefficients. It considers, and contrasts, the uniform…
Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC$^2$) are two methods…
We introduce a new high-performance design for parallelism within the Quantum Monte Carlo code QMCPACK. We demonstrate that the new design is better able to exploit the hierarchical parallelism of heterogeneous architectures compared to the…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive.…
In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel…
We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…
We propose and analyze deterministic multilevel approximations for Bayesian inversion of operator equations with uncertain distributed parameters, subject to additive Gaussian measurement data. The algorithms use a multilevel (ML) approach…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combination of optimal coupling transformations between coarse…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form…
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
In the field of computational finance, one is commonly interested in the expected value of a financial derivative whose payoff depends on the solution of stochastic differential equations (SDEs). For multi-dimensional SDEs with…