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Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…

Machine Learning · Computer Science 2019-12-06 Peter Grönquist , Tal Ben-Nun , Nikoli Dryden , Peter Dueben , Luca Lavarini , Shigang Li , Torsten Hoefler

Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks…

Machine Learning · Computer Science 2022-07-05 Romain Egele , Romit Maulik , Krishnan Raghavan , Bethany Lusch , Isabelle Guyon , Prasanna Balaprakash

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…

Machine Learning · Computer Science 2023-02-08 Apostolos F Psaros , Xuhui Meng , Zongren Zou , Ling Guo , George Em Karniadakis

Bringing deep neural networks (DNNs) into safety critical applications such as automated driving, medical imaging and finance, requires a thorough treatment of the model's uncertainties. Training deep neural networks is already resource…

Computer Vision and Pattern Recognition · Computer Science 2022-05-31 Julian Burghoff , Robin Chan , Hanno Gottschalk , Annika Muetze , Tobias Riedlinger , Matthias Rottmann , Marius Schubert

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

Chemical Physics · Physics 2024-05-17 Matthias Kellner , Michele Ceriotti

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is…

Machine Learning · Computer Science 2021-01-11 Florian Wenzel , Jasper Snoek , Dustin Tran , Rodolphe Jenatton

Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…

Machine Learning · Computer Science 2020-10-27 Jeremiah Zhe Liu , Zi Lin , Shreyas Padhy , Dustin Tran , Tania Bedrax-Weiss , Balaji Lakshminarayanan

Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models…

Machine Learning · Computer Science 2020-11-20 Omer Achrack , Raizy Kellerman , Ouriel Barzilay

The widespread use of Deep Neural Networks (DNNs) has recently resulted in their application to challenging scientific visualization tasks. While advanced DNNs demonstrate impressive generalization abilities, understanding factors like…

Graphics · Computer Science 2024-08-13 Atul Kumar , Siddharth Garg , Soumya Dutta

Uncertainty estimation bears the potential to make deep learning (DL) systems more reliable. Standard techniques for uncertainty estimation, however, come along with specific combinations of strengths and weaknesses, e.g., with respect to…

Machine Learning · Computer Science 2022-05-02 Joachim Sicking , Maram Akila , Jan David Schneider , Fabian Hüger , Peter Schlicht , Tim Wirtz , Stefan Wrobel

Ensemble learning is a standard approach to building machine learning systems that capture complex phenomena in real-world data. An important aspect of these systems is the complete and valid quantification of model uncertainty. We…

Machine Learning · Computer Science 2019-11-12 Jeremiah Zhe Liu , John Paisley , Marianthi-Anna Kioumourtzoglou , Brent Coull

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

Machine Learning · Computer Science 2025-12-16 Wenchong He , Zhe Jiang , Tingsong Xiao , Zelin Xu , Yukun Li

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Analysis of PDEs · Mathematics 2019-09-04 Dongkun Zhang , Lu Lu , Ling Guo , George Em Karniadakis

Deep neural networks have become the default choice for many of the machine learning tasks such as classification and regression. Dropout, a method commonly used to improve the convergence of deep neural networks, generates an ensemble of…

Machine Learning · Statistics 2019-04-11 Tal Kachman , Michal Moshkovitz , Michal Rosen-Zvi

For many practical, high-risk applications, it is essential to quantify uncertainty in a model's predictions to avoid costly mistakes. While predictive uncertainty is widely studied for neural networks, the topic seems to be under-explored…

Machine Learning · Computer Science 2021-04-05 Andrey Malinin , Liudmila Prokhorenkova , Aleksei Ustimenko

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Machine Learning · Computer Science 2026-02-18 Aurora Grefsrud , Nello Blaser , Trygve Buanes

Deep Neural Networks (DNN) are increasingly used as components of larger software systems that need to process complex data, such as images, written texts, audio/video signals. DNN predictions cannot be assumed to be always correct for…

Software Engineering · Computer Science 2022-12-15 Michael Weiss , Paolo Tonella

Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…

Machine Learning · Computer Science 2023-05-19 Luigi Sbailò , Luca M. Ghiringhelli

Deep neural networks (DNNs) have become the technology of choice for realizing a variety of complex tasks. However, as highlighted by many recent studies, even an imperceptible perturbation to a correctly classified input can lead to…

Machine Learning · Computer Science 2022-07-27 Guy Amir , Tom Zelazny , Guy Katz , Michael Schapira

Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture…

Machine Learning · Computer Science 2022-12-21 Maximiliano A. Sacco , Juan J. Ruiz , Manuel Pulido , Pierre Tandeo