相关论文: Improved Efficiency of Multilevel Monte Carlo for …

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many…

Stochastic PDEs of Fluctuating Hydrodynamics are a powerful tool for the description of fluctuations in many-particle systems. In this paper, we develop and analyze a Multilevel Monte Carlo (MLMC) scheme for the Dean--Kawasaki equation, a…

Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…

This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for L\'evy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain…

We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look-ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo…

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…

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…

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…

In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…

This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

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…

This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…

In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms.…

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…

We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…

The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…

In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation (SPDE). It is assumed that one can only estimate…

We introduce three related but distinct improvements to multilevel Monte Carlo (MLMC) methods for the solution of systems of stochastic differential equations (SDEs). Firstly, we show that when the payoff function is twice continuously…