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In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
Knowing the uncertainty associated with the output of a deep neural network is of paramount importance in making trustworthy decisions, particularly in high-stakes fields like medical diagnosis and autonomous systems. Monte Carlo Dropout…
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…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
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,…
We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under uncertainty. EVSI is defined as a nested expectation in which…
Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Quantifying the impact of the model uncertainty on the given operational objectives…
We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain…
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…
Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC)…
Simulation-based optimal design techniques are a convenient tool for solving a particular class of optimal design problems. The goal is to find the optimal configuration of factor settings with respect to an expected utility criterion. This…
Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…
We 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…
Uncertainty approximation in text classification is an important area with applications in domain adaptation and interpretability. One of the most widely used uncertainty approximation methods is Monte Carlo (MC) Dropout, which is…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually,…
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…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…