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Uncertainty quantification in neural networks gained a lot of attention in the past years. The most popular approaches, Bayesian neural networks (BNNs), Monte Carlo dropout, and deep ensembles have one thing in common: they are all based on…

Machine Learning · Computer Science 2020-10-06 Sina Däubener , Asja Fischer

Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is…

Computer Vision and Pattern Recognition · Computer Science 2022-12-12 Neslihan Kose , Ranganath Krishnan , Akash Dhamasia , Omesh Tickoo , Michael Paulitsch

Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the…

Machine Learning · Computer Science 2023-11-29 Yuichi Kajiura , Jorge Espin , Dong Zhang

The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each…

Machine Learning · Statistics 2018-03-02 Hiroyuki Hanada , Toshiyuki Takada , Jun Sakuma , Ichiro Takeuchi

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature…

Machine Learning · Computer Science 2023-08-14 Daniel Ries , Joshua Michalenko , Tyler Ganter , Rashad Imad-Fayez Baiyasi , Jason Adams

Machine learning interatomic potentials (MLIPs) enable accurate atomistic modelling, but reliable uncertainty quantification (UQ) remains elusive. In this study, we investigate two UQ strategies, ensemble learning and D-optimality, within…

Materials Science · Physics 2025-08-06 Fei Shuang , Zixiong Wei , Kai Liu , Wei Gao , Poulumi Dey

To facilitate robust and trustworthy deployment of large language models (LLMs), it is essential to quantify the reliability of their generations through uncertainty estimation. While recent efforts have made significant advancements by…

Computation and Language · Computer Science 2025-07-22 Rui Li , Jing Long , Muge Qi , Heming Xia , Lei Sha , Peiyi Wang , Zhifang Sui

Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…

Machine Learning · Computer Science 2023-09-06 Ruihan Zhang , Peixin Zhang , Jun Sun

Countless research works of deep neural networks (DNNs) in the task of credit card fraud detection have focused on improving the accuracy of point predictions and mitigating unwanted biases by building different network architectures or…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

Computational Physics · Physics 2024-12-16 Jorge F. Urbán , Petros Stefanou , José A. Pons

Despite the increasing demand for safer machine learning practices, the use of Uncertainty Quantification (UQ) methods in production remains limited. This limitation is exacerbated by the challenge of validating UQ methods in absence of UQ…

Machine Learning · Computer Science 2025-03-03 Arthur Pignet , Chiara Regniez , John Klein

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret…

Machine Learning · Computer Science 2024-11-14 Rebecca Nevin , Aleksandra Ćiprijanović , Brian D. Nord

Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted…

While Deep Neural Networks (DNNs) achieve state-of-the-art accuracy in various applications, they often fall short in accurately estimating their predictive uncertainty and, in turn, fail to recognize when these predictions may be wrong.…

Machine Learning · Computer Science 2020-07-22 Ankur Mallick , Chaitanya Dwivedi , Bhavya Kailkhura , Gauri Joshi , T. Yong-Jin Han

Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconstruction of turbulent flow fields from sparse data. However,…

Machine Learning · Computer Science 2026-04-21 Khemraj Shukla , Zongren Zou , Theo Kaeufer , Michael Triantafyllou , George Em Karniadakis

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…

Machine Learning · Computer Science 2025-12-22 Zhaoqian Gao , Min Yanga

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…

Numerical Analysis · Mathematics 2023-12-07 Siddhartha Mishra , Roberto Molinaro

In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken…

Machine Learning · Computer Science 2025-04-01 E. V. Aretos , D. G. Sotiropoulos

To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon…

Machine Learning · Computer Science 2023-07-21 Wenxuan Ma , Xing Yan , Kun Zhang

Uncertainty quantification in neural network promises to increase safety of AI systems, but it is not clear how performance might vary with the training set size. In this paper we evaluate seven uncertainty methods on Fashion MNIST and…

Machine Learning · Computer Science 2021-11-19 Matias Valdenegro-Toro