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Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when…

Computational Engineering, Finance, and Science · Computer Science 2025-02-04 Saurabh Deshpande , Hussein Rappel , Mark Hobbs , Stéphane P. A. Bordas , Jakub Lengiewicz

Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to…

Machine Learning · Statistics 2026-01-27 Philipp Reiser , Javier Enrique Aguilar , Anneli Guthke , Paul-Christian Bürkner

Understanding which concepts models can and cannot represent has been fundamental to many tasks: from effective and responsible use of models to detecting out of distribution data. We introduce Gaussian process probes (GPP), a unified and…

Machine Learning · Computer Science 2023-11-07 Zi Wang , Alexander Ku , Jason Baldridge , Thomas L. Griffiths , Been Kim

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…

Numerical Analysis · Mathematics 2020-10-16 Mahadevan Ganesh , Stuart C Hawkins , Alexandre Tartakovsky , Ramakrishna Tipireddy

In this paper an efficient and reliable method for stochastic yield estimation is presented. Since one main challenge of uncertainty quantification is the computational feasibility, we propose a hybrid approach where most of the Monte Carlo…

Computational Engineering, Finance, and Science · Computer Science 2020-10-12 Mona Fuhrländer , Sebastian Schöps

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Machine Learning · Computer Science 2021-01-07 Laura Swiler , Mamikon Gulian , Ari Frankel , Cosmin Safta , John Jakeman

Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…

Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn…

Materials Science · Physics 2024-08-21 Jin Dai , Santosh Adhikari , Mingjian Wen

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

Dynamical Systems · Mathematics 2007-05-23 Yu Zou , Ioannis G. Kevrekidis

Decision-making in manufacturing often involves optimizing key process parameters using data collected from simulation experiments. Gaussian processes are widely used to surrogate the underlying system and guide optimization. Uncertainty…

Applications · Statistics 2025-07-30 Yezhuo Li , Qiong Zhang , Madhura Limaye , Gang Li

Gaussian process (GP) surrogates are the default tool for emulating expensive computer experiments, but cubic cost, stationarity assumptions, and Gaussian predictive distributions limit their reach. We propose Generative Bayesian…

Machine Learning · Computer Science 2026-02-26 Nick Polson , Vadim Sokolov

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

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be…

Machine Learning · Computer Science 2024-05-15 Longze Li , Jiang Chang , Aleksandar Vakanski , Yachun Wang , Tiankai Yao , Min Xian

Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top-of-atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and…

Atmospheric and Oceanic Physics · Physics 2022-04-06 Michael F. Howland , Oliver R. A. Dunbar , Tapio Schneider

The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…

Computation · Statistics 2023-03-24 Ziyu Xie , Farah Alsafadi , Xu Wu

Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…

Artificial Intelligence · Computer Science 2021-06-15 Dongxia Wu , Liyao Gao , Xinyue Xiong , Matteo Chinazzi , Alessandro Vespignani , Yi-An Ma , Rose Yu

Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…

Numerical Analysis · Mathematics 2023-09-08 Sergei Manzhos , Manabu Ihara

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…

Methodology · Statistics 2023-05-04 Moses Y-H. Chan , Matthew Plumlee , Stefan M. Wild

Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…

Statistics Theory · Mathematics 2025-10-28 Toni Karvonen , François Bachoc

Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…

Machine Learning · Statistics 2025-12-16 Haoyu Li , Isaac J Michaud , Ayan Biswas , Han-Wei Shen