Related papers: h- and p-refined Multilevel Monte Carlo Methods fo…
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…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically…
In this paper we develop a very efficient approach to the Monte Carlo estimation of the expected value of partial perfect information (EVPPI) that measures the average benefit of knowing the value of a subset of uncertain parameters…
This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types 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…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of…
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…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of numerical solutions in…
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…
This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…
Sampling-based approaches are widely used in systems without analytic models to estimate risk or find optimal control. However, gathering sufficient data in such scenarios can be prohibitively costly. On the other hand, in many situations,…
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…