Related papers: Modern Monte Carlo Variants for Uncertainty Quanti…
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief…
Uncertainty quantification (UQ) is crucial in safety-critical applications such as medical image segmentation. Total uncertainty is typically decomposed into data-related aleatoric uncertainty (AU) and model-related epistemic uncertainty…
Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving…
In this study, we develop a probabilistic approach to map the parametric uncertainty to the output state uncertainty in first-order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two-phase transport in…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…
In mathematics there is a wide class of knot invariants that may be expressed in the form of multiple line integrals computed along the trajectory C describing the spatial conformation of the knot. In this work it is addressed the problem…
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 investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible,…
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…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007)…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
We present a novel technique to incorporate precision calculations from quantum chromodynamics into fully differential particle-level Monte-Carlo simulations. By minimizing an information-theoretic quantity subject to constraints, our…
This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in…
We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…
We have developed an Uncertainty Quantification process for multistep pipelines and applied it to the ACORN particle tracking pipeline. All our experiments are made using the TrackML open dataset. Using the Monte Carlo Dropout method, we…
We evaluate uncertainty quantification (UQ) methods for deep learning applied to liquid argon time projection chamber (LArTPC) physics analysis tasks. As deep learning applications enter widespread usage among physics data analysis, neural…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…
We discuss the efficiency of Monte Carlo methods in solving continuum radiative transfer problems. The sampling of the radiation field and convergence of dust temperature calculations in the case of optically thick clouds are both studied.…
We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of…