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Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…

Verification solutions for uncertainty quantification are presented for time dependent transport problems where $c$, the scattering ratio, is uncertain. The method of polynomial chaos expansions is employed for quick and accurate…

In the critical task of making generative models trustworthy and robust, methods for Uncertainty Quantification (UQ) have begun to show encouraging potential. However, many of these methods rely on rigid heuristics that fail to generalize…

Faithful uncertainty quantification (UQ) is paramount in high stakes climate prediction. Deep ensembles, or ensembles of probabilistic neural networks, are state of the art for UQ in machine learning (ML) and are growing increasingly…

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…

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…

Determining process-structure-property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process-structure and structure-property linkages. In this work, we…

Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine…

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a…

Uncertainty Quantification (UQ) workloads are becoming increasingly common in science and engineering. They involve the submission of thousands or even millions of similar tasks with potentially unpredictable runtimes, where the total…

Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an…

Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are…

Machine learning methods are increasingly widely used in high-risk settings such as healthcare, transportation, and finance. In these settings, it is important that a model produces calibrated uncertainty to reflect its own confidence and…

While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…

Trustworthy depression prediction based on deep learning, incorporating both predictive reliability and algorithmic fairness across diverse demographic groups, is crucial for clinical application. Recently, achieving reliable depression…

In the Part 1 of the present paper the performance of several different low and high-order finite-volume methods were assessed by investigating how well they can capture the turbulent spectra of a compressible flow where small smooth…

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…

This work presents novel extensions for combining two frameworks for quantifying both aleatoric (i.e., irreducible) and epistemic (i.e., reducible) sources of uncertainties in the modeling of engineered systems. The data-consistent (DC)…