Related papers: An introduction to uncertainty quantification for …
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Reliable uncertainty quantification is a first step towards building explainable, transparent, and accountable artificial intelligent systems. Recent progress in Bayesian deep learning has made such quantification realizable. In this paper,…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk…
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…
Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…
Quality-Diversity optimisation (QD) has proven to yield promising results across a broad set of applications. However, QD approaches struggle in the presence of uncertainty in the environment, as it impacts their ability to quantify the…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
The prediction of thermo-mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters. Such materials occur e.g. in historic buildings, and the durability…
Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…
The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties,…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…
In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…
Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point,…
This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve…
In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power,…
The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and…