Related papers: A Flexible Uncertainty Quantification Framework fo…

Despite the popularity of Convolutional Neural Networks (CNN), the problem of uncertainty quantification (UQ) of CNN has been largely overlooked. Lack of efficient UQ tools severely limits the application of CNN in certain areas, such as…

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…

Functional uncertainty quantification (FunUQ) was recently proposed to quantify uncertainties in models and simulations that originate from input functions, as opposed to parameters. This paper extends FunUQ to quantify uncertainties…

In complex physical process characterization, such as the measurement of the regression rate for solid hybrid rocket fuels, where both the observation data and the model used have uncertainties originating from multiple sources, combining…

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account…

Uncertainty Quantification (UQ) is a booming discipline for complex computational models based on the analysis of robustness, reliability and credibility. UQ analysis for nonlinear crash models with high dimensional outputs presents…

Large Language Models (LLMs) excel in text generation, reasoning, and decision-making, enabling their adoption in high-stakes domains such as healthcare, law, and transportation. However, their reliability is a major concern, as they often…

Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite…

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…

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…

We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method…

Uncertainties from model parameters and model discrepancy from small-scale models impact the accuracy and reliability of predictions of large-scale systems. Inadequate representation of these uncertainties may result in inaccurate and…

With increasing deployment of machine learning systems in various real-world tasks, there is a greater need for accurate quantification of predictive uncertainty. While the common goal in uncertainty quantification (UQ) in machine learning…

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for…

An uncertainty quantification framework is developed for Eulerian-Lagrangian models of particle-laden flows, where the fluid is modeled through a system of partial differential equations in the Eulerian frame and inertial particles 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…