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Monte Carlo simulation is often used for the reliability assessment of power systems, but it converges slowly when the system is complex. Multilevel Monte Carlo (MLMC) can be applied to speed up computation without compromises on model…
Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…
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…
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…
Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…
Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper…
This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…
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.…
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.…
The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of…
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…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower…
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…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
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…
Active learning is a promising paradigm to reduce the labeling cost by strategically requesting labels to improve model performance. However, existing active learning methods often rely on expensive acquisition function to compute,…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…
Machine Learning (ML) algorithms are increasingly used as surrogate models to increase the efficiency of stochastic reliability analyses in geotechnical engineering. This paper presents a highly efficient ML aided reliability technique that…