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Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many…

Methodology · Statistics 2024-06-19 Joy N. Mueller , Khachik Sargsyan , Craig J. Daniels , Habib N. Najm

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

Machine Learning · Statistics 2025-07-22 Xiaoping Du

While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision.…

Machine Learning · Computer Science 2026-05-22 Pedro C. Vieira , Pedro Ribeiro , Viacheslav Borovitskiy

The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Le Fang , Wangkun Xu , Fei Teng

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…

Machine Learning · Computer Science 2021-10-27 Alexander Henkes , Ismail Caylak , Rolf Mahnken

Post-hoc explanation methods have become a critical tool for understanding black-box classifiers in high-stakes applications. However, high-performing classifiers are often highly nonlinear and can exhibit complex behavior around the…

Machine Learning · Computer Science 2024-03-05 Davin Hill , Aria Masoomi , Max Torop , Sandesh Ghimire , Jennifer Dy

Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…

Machine Learning · Computer Science 2026-04-01 Johannes Exenberger , Sascha Ranftl , Robert Peharz

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…

Machine learning applications require fast and reliable per-sample uncertainty estimation. A common approach is to use predictive distributions from Bayesian or approximation methods and additively decompose uncertainty into aleatoric…

Machine Learning · Computer Science 2026-02-10 H. Martin Gillis , Isaac Xu , Thomas Trappenberg

This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available…

Numerical Analysis · Mathematics 2024-02-09 Nick Pepper , Francesco Montomoli , Kyriakos Kantarakias

While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…

Machine Learning · Computer Science 2020-04-08 Fredrik K. Gustafsson , Martin Danelljan , Thomas B. Schön

Deep generative models, while revolutionizing fields like image and text generation, largely operate as opaque ``black boxes'', hindering human understanding, control, and alignment. While methods like sparse autoencoders (SAEs) show…

Machine Learning · Computer Science 2026-04-03 Lingjing Kong , Shaoan Xie , Guangyi Chen , Yuewen Sun , Xiangchen Song , Eric P. Xing , Kun Zhang

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…

Machine Learning · Statistics 2026-02-10 Anchit Jain , Stephen Bates

Knowledge Graphs are pivotal for semantic data integration. The real-world data they model is often inherently uncertain. Within knowledge graphs, uncertainty manifests in three distinct levels: imprecise attribute values, probabilistic…

Artificial Intelligence · Computer Science 2026-05-19 Jingcheng Wu

We introduce a novel framework for AI-generated image detection through epistemic uncertainty, aiming to address critical security concerns in the era of generative models. Our key insight stems from the observation that distributional…

Computer Vision and Pattern Recognition · Computer Science 2025-11-04 Jun Nie , Yonggang Zhang , Tongliang Liu , Yiu-ming Cheung , Bo Han , Xinmei Tian

Evaluations of generative AI models often collapse nuanced behaviour into a single number computed for a single decoding configuration. Such point estimates obscure tail risks, demographic disparities, and the existence of multiple…

Artificial Intelligence · Computer Science 2026-01-23 Yanan Long

Epistemic uncertainty is crucial for safety-critical applications and data acquisition tasks. Yet, we find an important phenomenon in deep learning models: an epistemic uncertainty collapse as model complexity increases, challenging the…

Machine Learning · Computer Science 2025-05-27 Andreas Kirsch

Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…

Methodology · Statistics 2017-03-17 N. Fajraoui , S. Marelli , B. Sudret

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based…

Machine Learning · Computer Science 2025-07-21 Jon Vadillo , Roberto Santana , Jose A. Lozano , Marta Kwiatkowska

Probabilistic knowledge graph embeddings represent entities as distributions, using learned variances to quantify epistemic uncertainty. We identify a fundamental limitation: these variances are relation-agnostic, meaning an entity receives…

Machine Learning · Computer Science 2026-01-05 Chorok Lee
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