Related papers: An introduction to uncertainty quantification for …

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…

Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…

In the last few decades, uncertainty quantification (UQ) methods have been used widely to ensure the robustness of engineering designs. This chapter aims to detail recent advances in popular uncertainty quantification methods used in…

While generative models have become increasingly prevalent across various domains, fundamental concerns regarding their reliability persist. A crucial yet understudied aspect of these models is the uncertainty quantification surrounding…

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over…

The aim of the paper is to demonstrate the use of the Galerkin method for some kind of Volterra equations, determininistic and stochastic as well. The paper consists of two parts: the theoretical and numerical one. In the first part we…

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been…

We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…

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…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

This paper provides a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more in this area. It exploits many very simple examples, which are understandable to undergraduates, to…

The high dynamics and heterogeneous interactions in the complicated urban systems have raised the issue of uncertainty quantification in spatiotemporal human mobility, to support critical decision-makings in risk-aware web applications such…

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…

We introduce the first method of uncertainty quantification in the domain of Kolmogorov-Arnold Networks, specifically focusing on (Higher Order) ReLUKANs to enhance computational efficiency given the computational demands of Bayesian…

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…