Related papers: Modern Monte Carlo Methods for Efficient Uncertain…
The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
We present a "module-based hybrid" Uncertainty Quantification (UQ) framework for general nonlinear multi-physics simulation. The proposed methodology, introduced in [\hyperlink{ref1}{1}], supports the independent development of each…
In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…
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…
Trustworthy deployment of ML models requires a proper measure of uncertainty, especially in safety-critical applications. We focus on uncertainty quantification (UQ) for classification problems via two avenues -- prediction sets using…
Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…
Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal…
Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…
We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that are modeled using the Richards' equation. We propose a stochastic extension for the empirical models that are…
Uncertainty quantification (UQ) in computational chemistry (CC) is still in its infancy. Very few CC methods are designed to provide a confidence level on their predictions, and most users still rely improperly on the mean absolute error as…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…
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…
This article presents a novel approach, named MCMP (Monte Carlo Motion Planning), to the problem of motion planning under uncertainty, i.e., to the problem of computing a low-cost path that fulfills probabilistic collision avoidance…
In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the…
Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning,…
Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are…
Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios…