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Enhanced Multilevel Monte Carlo Method Applied to FDTD for Probability Distribution Estimation
IEEE Transactions on Antennas and Propagation, 2023Multilevel Monte Carlo (MLMC) method, enhanced by a smoothing technique based on kernel density estimation (KDE), is coupled with the finite-difference time-domain (FDTD) algorithm in order to estimate the probability distribution of any quantity of ...
Xiaojie Zhu +3 more
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Numerical Methods for Partial Differential Equations, 2023
A second‐order, multilevel Monte Carlo ensemble, and hybridizable discontinuous Galerkin (MLMCE‐HDG) method is proposed to solve the stochastic parabolic partial differential equations (SPDEs).
Meng Li, Xianbing Luo
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A second‐order, multilevel Monte Carlo ensemble, and hybridizable discontinuous Galerkin (MLMCE‐HDG) method is proposed to solve the stochastic parabolic partial differential equations (SPDEs).
Meng Li, Xianbing Luo
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Multilevel monte carlo for cortical circuit models
Journal of Computational Neuroscience, 2022Multilevel Monte Carlo (MLMC) methods aim to speed up computation of statistics from dynamical simulations. MLMC is easy to implement and is sometimes very effective, but its efficacy may depend on the underlying dynamics. We apply MLMC to networks of spiking neurons and assess its effectiveness on prototypical models of cortical circuitry under ...
Zhuo-Cheng Xiao, Kevin K. Lin
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Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need
International Conference on Machine LearningWe 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 (MC).
Shangda Yang +6 more
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Journal of Computational Physics, 2020
In this work we introduce and analyze a novel multilevel Monte Carlo (MLMC) estimator for the accurate approximation of central moments of system outputs affected by uncertainties. Central moments play a central role in many disciplines to characterize a
Sebastian Krumscheid +2 more
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In this work we introduce and analyze a novel multilevel Monte Carlo (MLMC) estimator for the accurate approximation of central moments of system outputs affected by uncertainties. Central moments play a central role in many disciplines to characterize a
Sebastian Krumscheid +2 more
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Accelerated Multilevel Monte Carlo With Kernel‐Based Smoothing and Latinized Stratification
Water Resources Research, 2020Heterogeneity and a paucity of measurements of key material properties undermine the veracity of quantitative predictions of subsurface flow and transport.
S. Taverniers, S. Bosma, D. Tartakovsky
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Adaptive Multilevel Monte Carlo Simulation
2011This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values depending on the solution to an Ito stochastic differential equation. The work (Michael Giles. Oper. Res.
Håkon Hoel +3 more
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Multilevel summation and Monte Carlo simulations
Journal of Molecular Liquids, 2006The Multilevel Summation method for the estimation of the potential energy of a many-body system (for cases of long-range isotropic and dipole–dipole interparticle interactions) is developed. The method is implemented in the frame of the Monte Carlo version proposed by Hetenyi et al. [B. Hetenyi, K. Bernacki, B.J. Berne, J. Chem. Phys. 117 (2002) 8203.
A. Brandt +3 more
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A filtered multilevel Monte Carlo method for estimating the expectation of discretized random fields
arXiv.org, 2023Jérémy Briant +7 more
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