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The standard technique for measurement of random uncertainties of star formation histories (SFHs) is the bootstrap Monte Carlo, in which the color-magnitude diagram (CMD) is repeatedly resampled. The variation in SFHs measured from the…

Classifiers based on neural networks (NN) often lack a measure of uncertainty in the predicted class. We propose a method to estimate the probability mass function (PMF) of the different classes, as well as the covariance of the estimated…

In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms.…

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…

Nuclear physics seeks to describe both bound and unbound states within a unified predictive framework. While coordinate-space Quantum Monte Carlo (QMC) methods have successfully computed bound states for systems with $A \leq 12$, their…

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Based on Monte Carlo approach and conventional error analysis theory, taking the heaviest doubly magic nucleus $^{208}$Pb as an example, we firstly evaluate the propagated uncertainties of universal potential parameters for three typical…

This study is devoted to the construction of a multifidelity Monte Carlo (MFMC) method for the uncertainty quantification of a nonlocal, non-mass-conserving Cahn-Hilliard model for phase transitions with an obstacle potential. We are…

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate…

Propagating nuclear uncertainties to nucleosynthesis simulations is key to understand the impact of theoretical uncertainties on the predictions, especially for processes far from the stability region, where nuclear properties are scarcely…

The high precision and conformity of intensity-modulated particle therapy (IMPT) comes at the cost of susceptibility to treatment uncertainties in particle range and patient set-up. Dose uncertainty quantification and mitigation, which is…

Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in…

We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing. We focus on the mono-energetic 1D…

The conductance of two Anderson impurity models, one with two-fold and another with four-fold degeneracy, representing two types of quantum dots, is calculated using a world-line quantum Monte Carlo (QMC) method. Extrapolation of the…

Computational chemistry has come a long way over the course of several decades, enabling subatomic level calculations particularly with the development of Density Functional Theory (DFT). Recently, machine-learned potentials (MLP) have…

Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable…

Quantum Monte Carlo methods find fruitful application in large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in a fluctuating one-body field;…

We use quantum Monte Carlo methods in the framework of the interacting nuclear shell model to calculate the statistical properties of nuclei at finite temperature and/or excitation energies. With this approach we can carry out realistic…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…