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This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…

Quantum Physics · Physics 2026-03-30 Ryan Bennink , Olena Burkovska , Konstantin Pieper , Jorge Ramirez , Elaine Wong

For safe and reliable deployment in the real world, autonomous agents must elicit appropriate levels of trust from human users. One method to build trust is to have agents assess and communicate their own competencies for performing given…

Robotics · Computer Science 2022-06-22 Aastha Acharya , Rebecca Russell , Nisar R. Ahmed

Uncertainty quantification for complex deep learning models is increasingly important as these techniques see growing use in high-stakes, real-world settings. Currently, the quality of a model's uncertainty is evaluated using…

Machine Learning · Computer Science 2021-12-15 Benjamin Kompa , Jasper Snoek , Andrew Beam

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Machine Learning · Computer Science 2024-04-22 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Machine Learning · Computer Science 2023-06-27 Lisa Wimmer , Yusuf Sale , Paul Hofman , Bern Bischl , Eyke Hüllermeier

Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…

Computation · Statistics 2026-05-19 Anderson V. Pires , Maliki Moustapha , Stefano Marelli , Bruno Sudret

A scientometric analysis of Monte Carlo simulation and Monte Carlo codes has been performed over a set of representative scholarly journals related to radiation physics. The results of this study are reported and discussed. They document…

Computational Physics · Physics 2010-12-16 Maria Grazia Pia , Tullio Basaglia , Zane W. Bell , Paul V. Dressendorfer

This extended abstract briefly summarizes ongoing research activity on the evaluation and experimental validation of physics methods for photon and electron transport. The analysis includes physics models currently implemented in Geant4 as…

Safety evaluation of self-driving technologies has been extensively studied. One recent approach uses Monte Carlo based evaluation to estimate the occurrence probabilities of safety-critical events as safety measures. These Monte Carlo…

Methodology · Statistics 2019-07-19 Zhiyuan Huang , Mansur Arief , Henry Lam , Ding Zhao

In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…

Data Analysis, Statistics and Probability · Physics 2017-12-07 Paul N. Patrone , Anthony J. Kearsley , Andrew M. Dienstfrey

Estimating uncertainty of machine learning models is essential to assess the quality of the predictions that these models provide. However, there are several factors that influence the quality of uncertainty estimates, one of which is the…

Machine Learning · Computer Science 2022-11-03 Yuko Kato , David M. J. Tax , Marco Loog

Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper…

Computational Engineering, Finance, and Science · Computer Science 2014-09-18 Zheng Zhang , Ibrahim , M. Elfadel , Luca Daniel

Deep learning based methods for automatic organ segmentation have shown promise in aiding diagnosis and treatment planning. However, quantifying and understanding the uncertainty associated with model predictions is crucial in critical…

Image and Video Processing · Electrical Eng. & Systems 2023-08-16 Jadie Adams , Shireen Y. Elhabian

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and…

Computational Physics · Physics 2018-01-08 Markus Wallerberger , Emanuel Gull

The primary focus of Monte Carlo simulation is to identify and quantify risk related to uncertainty and variability in spreadsheet model inputs. The stress of Monte Carlo simulation often reveals logical errors in the underlying spreadsheet…

Software Engineering · Computer Science 2010-01-26 Hilary L. Emmett , Lawrence I. Goldman

Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…

Other Computer Science · Computer Science 2019-04-03 Juan M. Durán , Nico Formanek

Future neutrino-oscillation experiments are expected to bring definite answers to the questions of neutrino-mass hierarchy and violation of charge-parity symmetry in the lepton sector. To realize this ambitious program it is necessary to…

High Energy Physics - Phenomenology · Physics 2017-05-15 Artur M Ankowski , Camillo Mariani

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

Machine Learning · Computer Science 2025-08-19 Freddie Bickford Smith , Jannik Kossen , Eleanor Trollope , Mark van der Wilk , Adam Foster , Tom Rainforth

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…

Quantum Physics · Physics 2026-04-13 Giovanni Chesi , Lorenzo Maccone

Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…

Machine Learning · Computer Science 2024-06-28 Matias Valdenegro-Toro , Ivo Pascal de Jong , Marco Zullich