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We introduce a novel approach for calibrating uncertainty quantification (UQ) tailored for multi-modal large language models (LLMs). Existing state-of-the-art UQ methods rely on consistency among multiple responses generated by the LLM on…

Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods…

Machine Learning · Computer Science 2023-10-31 Hao Sun , Boris van Breugel , Jonathan Crabbe , Nabeel Seedat , Mihaela van der Schaar

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

The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive…

Machine Learning · Computer Science 2024-01-02 Deepak Akhare , Tengfei Luo , Jian-Xun Wang

The advent of fabrication techniques such as additive manufacturing has focused attention on the considerable variability of material response due to defects and other microstructural aspects. This variability motivates the development of…

Data Analysis, Statistics and Probability · Physics 2019-06-26 Francesco Rizzi , Mohammad Khalil , Reese E. Jones , Jeremy A. Templeton , Jakob T. Ostien , Brad L. Boyce

This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can…

Systems and Control · Electrical Eng. & Systems 2026-05-26 Ethan R. Burnett , Spencer Boone

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…

Probability · Mathematics 2016-05-20 Houman Owhadi , Clint Scovel , Timothy John Sullivan , Mike McKerns , Michael Ortiz

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

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

Uncertainty Quantification (UQ) has gained traction in an attempt to improve the interpretability and robustness of machine learning predictions. Specifically (medical) biosignals such as electroencephalography (EEG), electrocardiography…

Signal Processing · Electrical Eng. & Systems 2025-06-06 Ivo Pascal de Jong , Andreea Ioana Sburlea , Matias Valdenegro-Toro

Robust optimization is a method for optimization under uncertainties in engineering systems and designs for applications ranging from aeronautics to nuclear. In a robust design process, parameter variability (or uncertainty) is incorporated…

Computation · Statistics 2022-10-17 Richa Verma , Dinesh Kumar , Kazuma Kobayashi , Syed Alam

It is critical that machine learning (ML) model predictions be trustworthy for high-throughput catalyst discovery approaches. Uncertainty quantification (UQ) methods allow estimation of the trustworthiness of an ML model, but these methods…

Machine Learning · Computer Science 2023-02-07 Cameron Gruich , Varun Madhavan , Yixin Wang , Bryan Goldsmith

Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models require uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training…

Machine Learning · Computer Science 2022-11-01 Ya Ju Fan , Jonathan E. Allen , Kevin S. McLoughlin , Da Shi , Brian J. Bennion , Xiaohua Zhang , Felice C. Lightstone

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…

Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative…

Machine Learning · Computer Science 2023-11-21 Zongren Zou , Xuhui Meng , George Em Karniadakis

Reliable uncertainty quantification (UQ) in machine learning (ML) regression tasks is becoming the focus of many studies in materials and chemical science. It is now well understood that average calibration is insufficient, and most studies…

Machine Learning · Statistics 2024-01-25 Pascal Pernot

This study presents a comprehensive framework for uncertainty quantification (UQ) and design optimization of plasma etching in semiconductor manufacturing. The framework is demonstrated using experimental measurements of etched depth…

Popular Physics · Physics 2025-11-10 Yongsu Jung , Minji Kang , Muyoung Kim , Min Sup Choi , Hyeong-U Kim , Jaekwang Kim

With increasing computational demand, Neural-Network (NN) based models are being developed as pre-trained surrogates for different thermohydraulics phenomena. An area where this approach has shown promise is in developing higher-fidelity…

Fluid Dynamics · Physics 2024-12-13 Cody Grogan , Som Dutta , Mauricio Tano , Somayajulu L. N. Dhulipala , Izabela Gutowska

Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision, natural language processing, and…

Machine Learning · Computer Science 2022-08-26 Zongren Zou , Xuhui Meng , Apostolos F Psaros , George Em Karniadakis

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