Related papers: A multilevel Monte Carlo method for computing fail…
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…
We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designed to operate optimally within memory and CPU-time…
We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
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…
Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…
We present a novel variant of the multi-level Monte Carlo method that effectively utilizes a reserved computational budget on a high-performance computing system to minimize the mean squared error. Our approach combines concepts of the…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
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…
The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any…
Engineering risk is concerned with the likelihood of failure and the scenarios when it occurs. The sensitivity of failure probability to change in system parameters is relevant to risk-informed decision making. Computing sensitivity is at…
A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Convergence of the method is proved and its convergence rate studied. Results in high dimension for different kind of non-linearities show…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…
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…