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This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…

Numerical Analysis · Mathematics 2021-09-30 Philipp A. Guth , Andreas Van Barel

Uncertainty propagation of large scale discrete supply chains can be prohibitive when a large number of events occur during the simulated period and discrete event simulations (DES) are costly. We present a time bucket method to approximate…

Computation · Statistics 2019-01-17 Nai-Yuan Chiang , Yinqing Lin , Quan Long

Multilevel Monte Carlo (MLMC) is a flexible and effective variance reduction technique for accelerating reliability assessments of complex power system. Recently, data-driven surrogate models have been proposed as lower-level models in the…

Machine Learning · Computer Science 2025-07-31 Ruiqi Zhang , Simon H. Tindemans

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…

Numerical Analysis · Mathematics 2023-09-06 Michael B Giles

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…

This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…

Computational Engineering, Finance, and Science · Computer Science 2024-09-30 Piotr Wolszczak , Pawel Lonkwic , Americo Cunha , Grzegorz Litak , Szymon Molski

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…

Computational Physics · Physics 2020-08-12 Subhayan De

Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…

Computational Finance · Quantitative Finance 2025-10-23 Alexandre Boumezoued , Adel Cherchali , Vincent Lemaire , Gilles Pagès , Mathieu Truc

We consider the problem of estimating a nested structure of two expectations taking the form $U_0 = E[\max\{U_1(Y), \pi(Y)\}]$, where $U_1(Y) = E[X\ |\ Y]$. Terms of this form arise in financial risk estimation and option pricing. When…

Computational Finance · Quantitative Finance 2023-08-16 Abdul-Lateef Haji-Ali , Jonathan Spence

We propose a control variate multilevel Monte Carlo method for the kinetic BGK model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carlo technique with the computation of the optimal control…

Numerical Analysis · Mathematics 2020-04-17 Jingwei Hu , Lorenzo Pareschi , Yubo Wang

Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced…

Computational Engineering, Finance, and Science · Computer Science 2023-01-10 Matteo Croci , Vegard Vinje , Marie E. Rognes

We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to…

Numerical Analysis · Mathematics 2026-04-08 Giulia Bertaglia , Walter Boscheri , Lorenzo Pareschi

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…

Optimization and Control · Mathematics 2017-11-08 Andreas Van Barel , Stefan Vandewalle

In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where…

Numerical Analysis · Mathematics 2021-02-05 Lorenzo Pareschi , Torsten Trimborn , Mattia Zanella

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…

Numerical Analysis · Mathematics 2024-12-12 Anastasia Istratuca , Aretha Teckentrup

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…

Numerical Analysis · Mathematics 2016-11-30 Petr Plecháč , Erik von Schwerin

Monte Carlo and Active Subspace Identification methods are combined with first- and second-order adjoint sensitivities to perform (forward) uncertainty quantification analysis of the thermo-acoustic stability of two annular combustor…

Fluid Dynamics · Physics 2016-10-12 Luca Magri , Michael Bauerheim , Franck Nicoud , Matthew Juniper

We present an analysis of multilevel Monte Carlo techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients ({\em cross-sections}) are heterogenous random fields. To do this,…

Numerical Analysis · Mathematics 2020-01-15 Ivan G. Graham , Matthew J. Parkinson , Robert Scheichl

Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response.…

Dynamical Systems · Mathematics 2024-07-08 Zhenwei Xu , Roshan S. Kaundinya , Shobhit Jain , George Haller

The recently developed method Lasso Monte Carlo (LMC) for uncertainty quantification is applied to the characterisation of spent nuclear fuel. The propagation of nuclear data uncertainties to the output of calculations is an often required…

Computational Physics · Physics 2023-09-04 Arnau Albà , Andreas Adelmann , Dimitri Rochman