Related papers: Multilevel Monte Carlo Metamodeling for Variance F…
For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte…
We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An…
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…
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…
This paper proposes a new multilevel Monte Carlo (MLMC) method for the ergodic SDEs which do not satisfy the contractivity condition. By introducing the change of measure technique, we simulate the path with contractivity and add the…
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…
Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…
We present in this paper a hybrid, Multi-Level Monte Carlo (MLMC) method for solving the neutral particle transport equation. MLMC methods, originally developed to solve parametric integration problems, work by using a cheap, low fidelity…
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…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
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…
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…
This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…
Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency…
The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
Multi-model Monte Carlo methods, such as multi-level Monte Carlo (MLMC) and multifidelity Monte Carlo (MFMC), allow for efficient estimation of the expectation of a quantity of interest given a set of models of varying fidelities. Recently,…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…