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Predicting fuel assembly bow in pressurized water reactors requires solving tightly coupled fluid-structure interaction problems, whose direct simulations can be computationally prohibitive, making large-scale uncertainty quantification…

Applications · Statistics 2026-01-27 Ali Abboud , Josselin Garnier , Bertrand Leturcq , Stanislas de Lambert

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

As machine learning (ML) models are increasingly deployed in high-stakes domains, trustworthy uncertainty quantification (UQ) is critical for ensuring the safety and reliability of these models. Traditional UQ methods rely on specifying a…

Machine Learning · Statistics 2025-05-14 Abhineet Agarwal , Michael Xiao , Rebecca Barter , Omer Ronen , Boyu Fan , Bin Yu

Uncertainty Quantification (UQ) is essential for the reliable application of computational models in engineering and science. Among surrogate modeling techniques, Gaussian Process Regression (GPR) is particularly valuable for its…

Computation · Statistics 2025-12-15 Jinglai Li , Hongqiao Wang

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…

Optimization and Control · Mathematics 2019-10-16 David Métivier , Marc Vuffray , Sidhant Misra

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…

Computational Engineering, Finance, and Science · Computer Science 2021-03-31 Marc Rocas , Alberto García-González , Xabier Larrayoz , Pedro Díez

We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…

Chaotic Dynamics · Physics 2023-11-02 George Papadakis , Kyriakos D. Kantarakias

This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are available. A tried and tested technique is to build surrogates of the objective and the…

Optimization and Control · Mathematics 2022-08-18 Charles Audet , Sébastien Le Digabel , Renaud Saltet

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…

Machine Learning · Statistics 2025-09-11 Marzieh Ajirak , Anand Ravishankar , Petar M. Djuric

Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An…

Machine Learning · Statistics 2023-06-28 Stephen Guth , Alireza Mojahed , Themistoklis P. Sapsis

We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal…

Computational Engineering, Finance, and Science · Computer Science 2020-05-20 Niklas Georg , Dimitrios Loukrezis , Ulrich Römer , Sebastian Schöps

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…

Quantum Physics · Physics 2013-12-17 Kevin C. Young , Matthew D. Grace

Slurry transportation via pipelines is essential for global industries, offering efficiency and environmental benefits. Specifically, the precise calibration of physical parameters for transporting raw phosphate material to fertilizer…

Fluid Dynamics · Physics 2024-06-13 Marwane Elkarii , Radouan Boukharfane , Nabil El Moçayd

Epistemic uncertainty quantification (UQ) identifies where models lack knowledge. Traditional UQ methods, often based on Bayesian neural networks, are not suitable for pre-trained non-Bayesian models. Our study addresses quantifying…

Machine Learning · Computer Science 2024-04-17 Hanjing Wang , Qiang Ji

Image-based computational fluid dynamics (CFD) modeling enables derivation of hemodynamic information, which has become a paradigm in cardiovascular research and healthcare. Nonetheless, the predictive accuracy largely depends on precisely…

Fluid Dynamics · Physics 2021-07-20 Han Gao , Xueyu Zhu , Jian-Xun Wang

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…

Machine Learning · Statistics 2023-11-13 Ziyi Huang , Henry Lam , Haofeng Zhang

The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…

Numerical Analysis · Mathematics 2019-06-21 Adi Ditkowski , Gadi Fibich , Amir Sagiv

The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a…

Methodology · Statistics 2016-04-27 C. V. Mai , M. D. Spiridonakos , E. N. Chatzi , B. Sudret

Quantum machine learning (QML) presents potential for early industrial adoption, yet limited access to quantum hardware remains a significant bottleneck for deployment of QML solutions. This work explores the use of classical surrogates to…

In this paper, we study the stochastic collocation (SC) methods for uncertainty quantification (UQ) in hyperbolic systems of nonlinear partial differential equations (PDEs). In these methods, the underlying PDEs are numerically solved at a…

Numerical Analysis · Mathematics 2025-06-19 Alina Chertock , Arsen S. Iskhakov , Safa Janajra , Alexander Kurganov