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Deploying deep learning models in safety-critical applications remains a very challenging task, mandating the provision of assurances for the dependable operation of these models. Uncertainty quantification (UQ) methods estimate the model's…

Machine Learning · Computer Science 2024-01-23 Daniel Bethell , Simos Gerasimou , Radu Calinescu

Bayesian neural networks (BNN) can estimate the uncertainty in predictions, as opposed to non-Bayesian neural networks (NNs). However, BNNs have been far less widely used than non-Bayesian NNs in practice since they need iterative NN…

Machine Learning · Computer Science 2022-02-15 Namuk Park , Taekyu Lee , Songkuk Kim

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

For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…

Machine Learning · Computer Science 2022-11-21 Lixiang Zhang , Jia Li

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional…

Machine Learning · Computer Science 2025-12-02 Adriel Sosa Marco , John Daniel Kirwan , Alexia Toumpa , Simos Gerasimou

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…

Machine Learning · Statistics 2023-09-07 Sanket Jantre , Nathan M. Urban , Xiaoning Qian , Byung-Jun Yoon

Recurrent neural networks (RNNs) have shown promising performance for language modeling. However, traditional training of RNNs using back-propagation through time often suffers from overfitting. One reason for this is that stochastic…

Computation and Language · Computer Science 2017-04-25 Zhe Gan , Chunyuan Li , Changyou Chen , Yunchen Pu , Qinliang Su , Lawrence Carin

Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…

Machine Learning · Computer Science 2024-01-17 Soyed Tuhin Ahmed

Traditional neural networks provide deterministic predictions without inherent uncertainty estimates. While Bayesian Neural Networks (BNNs) offer a principled approach to uncertainty quantification, their computational complexity limits…

Machine Learning · Statistics 2026-05-25 Rouaa Hoblos , Noura Dridi , Noureddine Zerhouni , Zeina Al Masry

Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…

Machine Learning · Statistics 2024-10-22 Ziyu Wang , Chris Holmes

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

We are interested in estimating the uncertainties of deep neural networks, which play an important role in many scientific and engineering problems. In this paper, we present a striking new finding that an ensemble of neural networks with…

Machine Learning · Computer Science 2022-12-05 Jayaraman J. Thiagarajan , Rushil Anirudh , Vivek Narayanaswamy , Peer-Timo Bremer

Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art…

Machine Learning · Computer Science 2025-11-18 Ramzi Dakhmouche , Adrien Letellier , Hossein Gorji

Deep neural networks (DNNs) have achieved state-of-the-art performances in many important domains, including medical diagnosis, security, and autonomous driving. In these domains where safety is highly critical, an erroneous decision can…

Machine Learning · Computer Science 2019-06-12 Aryan Mobiny , Hien V. Nguyen , Supratik Moulik , Naveen Garg , Carol C. Wu

State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible…

Computational Physics · Physics 2018-10-17 Rohit Tripathy , Ilias Bilionis

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

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a…

Machine Learning · Statistics 2025-10-20 Frank Shih , Zhenghao Jiang , Faming Liang

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…

Machine Learning · Statistics 2021-10-05 Theodore Papamarkou , Jacob Hinkle , M. Todd Young , David Womble

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…

Machine Learning · Computer Science 2024-03-15 Tim Rensmeyer , Oliver Niggemann

Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…

Computation · Statistics 2018-04-25 Thomas A. Catanach , James L. Beck
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