相关论文: On the Selection of Random Field Evaluation Points…

Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications…

We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…

We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…

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…

A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and exactness of spatial quantities…

In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness…

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

Randomized quasi-Monte Carlo (RQMC) sampling can bring orders of magnitude reduction in variance compared to plain Monte Carlo (MC) sampling. The extent of the efficiency gain varies from problem to problem and can be hard to predict. This…

Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…

We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…

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…

We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal…

This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…

This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…

In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…

We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor…

Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically…

Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution.…