Basic Framework and Main Methods of Uncertainty Quantification

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Explainable AI for cybersecurity automation, intelligence and trustworthiness in digital twin: Methods, taxonomy, challenges and prospects

Sarker, I. H., Janicke, H., Mohsin, A., Gill, A. Q., & Maglaras, L. A. (2024) · ICT Express · doi:10.1016/j.icte.2024.05.007 · Cited by 227 · see citing works

A hybrid science‐guided machine learning approach for modeling chemical processes: A review

Sharma, N., & Liu, Y. A. (2022) · AIChE Journal · doi:10.1002/aic.17609 · Cited by 196 · see citing works

A Novel Approach to Uncertainty Quantification in Groundwater Table Modeling by Automated Predictive Deep Learning

Shahri, A. A., Shan, C., & Larsson, S. (2022) · Natural Resources Research · doi:10.1007/s11053-022-10051-w · Cited by 181 · see citing works

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Wang, C., Qiang, X., Xu, M., & Wu, T. (2022) · Symmetry · doi:10.3390/sym14061219 · Cited by 143 · see citing works

Defects and uncertainties of adhesively bonded composite joints

Omairey, S., Jayasree, N., & Kazilas, M. (2021) · SN Applied Sciences · doi:10.1007/s42452-021-04753-8 · Cited by 124 · see citing works

A Survey of Uncertainty Quantification in Machine Learning for Space Weather Prediction

Siddique, T., Mahmud, M. S., Keesee, A. M., Ngwira, C. M., & Connor, H. K. (2022) · Geosciences · doi:10.3390/geosciences12010027 · Cited by 64 · see citing works

Machine Learning-Based Process Optimization in Biopolymer Manufacturing: A Review

Malashin, I. P., Martysyuk, D., Тынченко, В. С., Gantimurov, A., Семиколенов, А. В., Nelyub, V., & Бородулин, А. С. (2024) · Polymers · doi:10.3390/polym16233368 · Cited by 66 · see citing works

Credibility assessment of in silico clinical trials for medical devices

Pathmanathan, P., Aycock, K., Badal, A., Bighamian, R., Bodner, J., Craven, B. A., & Niederer, S. (2024) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1012289 · Cited by 62 · see citing works

A study of uncertainties in groundwater vulnerability modelling using Bayesian model averaging (BMA)

Gharekhani, M., Nadiri, A. A., Khatibi, R. H., Sadeghfam, S., & Moghaddam, A. A. (2021) · Journal of Environmental Management · doi:10.1016/j.jenvman.2021.114168 · Cited by 62 · see citing works

Uncertainty quantification for structural response field with ultra-high dimensions

Cao, L., & Zhao, Y. (2024) · International Journal of Mechanical Sciences · doi:10.1016/j.ijmecsci.2024.109110 · Cited by 47 · see citing works

Eddy Current Measurement for Planar Structures

Xia, Z., Huang, R., Chen, Z., Yu, K., Zhang, Z., Avila, J. R. S., & Yin, W. (2022) · Sensors · doi:10.3390/s22228695 · Cited by 44 · see citing works

Quantification of Uncertainty and Its Applications to Complex Domain for Autonomous Vehicles Perception System

Wang, K., Wang, Y., Liu, B., & Chen, J. (2023) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2023.3256459 · Cited by 42 · see citing works

Sequential-based non-probabilistic reliability optimization for composite aircraft wing considering aero-structural coupling constraints

Wang, L., Tian, K., & Luo, Z. (2025) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2025.118323 · Cited by 33 · see citing works

Fast Estimation of Metallic Pipe Properties Using Simplified Analytical Solution in Eddy-Current Testing

Xia, Z., Yan, J., Huang, R., Lu, M., Cui, Z., Peyton, A. J., Yin, W., & Yang, W. (2022) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2022.3224516 · Cited by 30 · see citing works

A Review of Uncertainty-Based Multidisciplinary Design Optimization Methods Based on Intelligent Strategies

Wang, C., Fan, H., & Qiang, X. (2023) · Symmetry · doi:10.3390/sym15101875 · Cited by 18 · see citing works

Solving coupled differential equation groups using PINO-CDE

Ding, W., He, Q., Tong, H., Wang, Q., & wang, P. Y. (2023) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2023.111014 · Cited by 18 · see citing works

Physics-based reduced order modeling for uncertainty quantification of guided wave propagation using Bayesian optimization

Drakoulas, G. I., Gortsas, T. V., & Polyzos, D. K. (2024) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2024.108531 · Cited by 15 · see citing works

Modelling of a continuous veneer drying unit of industrial scale and model-based ANOVA of the energy efficiency

Gradov, D. V., Yusuf, Y. O., Ojalainen, J., Suuronen, J., Eskola, R., Roininen, L., & Koiranen, T. (2021) · Energy · doi:10.1016/j.energy.2021.122673 · Cited by 14 · see citing works

Optimized Scenario for Estimating Suspended Sediment Yield Using an Artificial Neural Network Coupled with a Genetic Algorithm

Yadav, A., Hasan, M. K., Joshi, D., Kumar, V., Aman, A. H. M., Alhumyani, H. A., Alzaidi, M. S., & Mishra, H. (2022) · Water · doi:10.3390/w14182815 · Cited by 13 · see citing works

Uncertainty analysis of rudder shaft thermal conditions on the flutter characteristics of the hypersonic control surface

Ye, K., Qin, L., Ye, Z., Yang, D., & Dong, B. (2024) · Aerospace Science and Technology · doi:10.1016/j.ast.2024.109721 · Cited by 12 · see citing works

Time-Dependent Behavior of Callovo-Oxfordian Claystone for Nuclear Waste Disposal: Uncertainty Quantification from In-Situ Convergence Measurements

Do, D., Tran, N.-T., Hoxha, D., Vu, M., & Armand, G. (2022) · Sustainability · doi:10.3390/su14148465 · Cited by 10 · see citing works

Leveraging Industry 4.0: Deep Learning, Surrogate Model, and Transfer Learning with Uncertainty Quantification Incorporated into Digital Twin for Nuclear System

Rahman, M. M., Khan, A. H., Anowar, S., Al-Imran, M., Verma, R., Kumar, D., Kobayashi, K., & Alam, S. B. (2022) · Springer eBooks · doi:10.1007/978-3-030-72322-4_192-1 · Cited by 12 · see citing works

Sampling-efficient surrogate modeling for sensitivity analysis of brake squeal using polynomial chaos expansion

Mohamed, H., Schöner, C., & Jekel, D. (2025) · Results in Engineering · doi:10.1016/j.rineng.2025.104649 · Cited by 10 · see citing works

Utilizing Computational Modelling to Bridge the Gap between In Vivo and In Vitro Degradation Rates for Mg-xGd Implants

AlBaraghtheh, T., Hermann, A., Shojaei, A., Willumeit‐Römer, R., Cyron, C. J., & Zeller‐Plumhoff, B. (2023) · Corrosion and Materials Degradation · doi:10.3390/cmd4020014 · Cited by 9 · see citing works

The inclusion of uncertainty in circularity transition modeling: A case study on wind turbine blade end-of-life management

Walzberg, J., Hanes, R. J., Ghosh, T., Key, A., Potter, K., & Eberle, A. L. (2023) · Sustainable Energy Technologies and Assessments · doi:10.1016/j.seta.2023.103569 · Cited by 8 · see citing works

Bayesian Hierarchical Modelling for Uncertainty Quantification in Operational Thermal Resistance of LED Systems

Dvorzak, M., Magnien, J., Kleb, U., Kraker, E., & Mücke, M. (2022) · Applied Sciences · doi:10.3390/app121910063 · Cited by 8 · see citing works

Designing Evolving Cyber-Physical-Social Systems: Computational Research Opportunities

Allen, J. K., Nellippallil, A. B., Ming, Z., Milisavljevic-Syed, J., & Mistree, F. (2023) · Journal of Computing and Information Science in Engineering · doi:10.1115/1.4062883 · Cited by 8 · see citing works

Uncertainty Quantification of the Short‐ and Long‐Term Behavior of COx Claystone and Reliability Analysis of the IL‐LLW Repository's Concrete Liner Based on In Situ Convergence Data

Do, D., Vu, M., Nguyen, T. T., Hoxha, D., & Armand, G. (2025) · International Journal for Numerical and Analytical Methods in Geomechanics · doi:10.1002/nag.3949 · Cited by 6 · see citing works

Combination of Bayesian and artificial neuronal networks to quantify uncertainty of the short- and long-term behavior of Callovo-Oxfordian claystone

Hieu, P. Q., Thach, T. T., Do, D., Vu, M., Hoxha, D., & Armand, G. (2025) · Environmental Earth Sciences · doi:10.1007/s12665-025-12635-0 · Cited by 5 · see citing works

Calibration, Sensitivity and Uncertainty Analysis of Complex Ecological Models—A Review

Malchow, A.-K., & Hartig, F. (2026) · Ecology Letters · doi:10.1111/ele.70375 · Cited by 5 · see citing works

Uncertainty Quantification for Epidemic Risk Management: Case of SARS-CoV-2 in Morocco

Hammadi, L., Raillani, H., Ndiaye, B. M., Badria, A., Ballouti, A. E., Jidane, S., Belyamani, L., & de Cursi, E. S. (2023) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph20054102 · Cited by 4 · see citing works

Digital Twins for Marine Operations: From Surface to Deep Water

Van, M., Edwards, C. B., Tran-Thanh, L., & Bonney, M. S. (2023) · UK-RAS white papers · doi:10.31256/wp2023.6 · Cited by 4 · see citing works

Parameterized Reduced-Order Models for Probabilistic Analysis of Thermal Protection System Based on Proper Orthogonal Decomposition

Zhang, K., Yao, J., Wenxiang, Z., Cao, Z., Li, T., & Xin, J. (2024) · Aerospace · doi:10.3390/aerospace11040269 · Cited by 3 · see citing works

A Toolbox for Design of Experiments for Energy Systems in Co-Simulation and Hardware Tests

Schwarz, J. S., Perez, L. E. R., Pham, M. C., Heussen, K., & Tran, Q. T. (2024) · Open Source Modelling and Simulation of Energy Systems (OSMSES) · doi:10.1109/osmses62085.2024.10668967 · Cited by 3 · see citing works

Best Practices in Developing a Workflow for Uncertainty Quantification for Modeling the Biodegradation of Mg‐Based Implants

AlBaraghtheh, T., Willumeit‐Römer, R., & Zeller‐Plumhoff, B. (2024) · Advanced Science · doi:10.1002/advs.202403543 · Cited by 3 · see citing works

Probabilistic framework for the calibration of mean wind profiles in urban areas

Picozzi, V., Sepe, V., Avossa, A. M., & Ricciardelli, F. (2025) · Journal of Building Engineering · doi:10.1016/j.jobe.2025.112720 · Cited by 3 · see citing works

Aerodynamic Performance Uncertainty Analysis and Optimization of a Conventional Axisymmetric Vehicle Based on Parallel Polynomial Chaos Expansions

Peng, X., Zhu, H., Xu, D., Xiao, M., Wang, W., & Cai, G. (2022) · Aerospace · doi:10.3390/aerospace9080396 · Cited by 3 · see citing works

Towards uncertainty and sensitivity analysis for modal parameters identification during ice–structure interaction

Wang, C., Nord, T. S., Ziemer, G., & Li, G. (2023) · Ocean Engineering · doi:10.1016/j.oceaneng.2023.114224 · Cited by 3 · see citing works

SiTAR: Situated Trajectory Analysis for In-the-Wild Pose Error Estimation

Scargill, T., Chen, Y., Hu, T., & Gorlatova, M. A. (2023) · Proceedings - International Symposium on Mixed and Augmented Reality, ISMAR · doi:10.1109/ismar59233.2023.00043 · Cited by 3 · see citing works

Uncertainty Modelling in Performability Prediction for Safety-Critical Systems

Ahamad, S., & Gupta, R. (2024) · Arabian Journal for Science and Engineering · doi:10.1007/s13369-024-08891-0 · Cited by 3 · see citing works

Enhancing Estimation of Fine Particulate Matter Chemical Composition across North America by Including Geophysical A Priori Information in Deep Learning with Uncertainty Quantification

Shen, S., van Donkelaar, A., Jacobs, N., Li, C., & Martin, R. V. (2026) · ACS ES&T Air · doi:10.1021/acsestair.5c00251 · Cited by 3 · see citing works

Sequential Monte Carlo with likelihood tempering and parallel implementation for uncertainty quantification

Maruchi, T., Yajima, T., & Kawajiri, Y. (2026) · AIChE Journal · doi:10.1002/aic.70319 · Cited by 2 · see citing works

Analysis of Safety Factors for Crack Initiation in Adhesive Joints by Uncertainty Quantification Analysis

Hach, M., Hopfe, J., Spitzer, S., & Weißgraeber, P. (2025) · ce/papers · doi:10.1002/cepa.3321 · Cited by 1 · see citing works

Hybrid uncertainty quantification in rotor dynamics using nonparametric probability approach

Feng, W., Cao, X., Liu, B., Liu, Z., Liu, J., & Zhang, K. (2026) · Applied Mathematical Modelling · doi:10.1016/j.apm.2026.116777 · Cited by 1 · see citing works

Uncertainty in Composite Damage Modeling and Finite Element Model Updating: A Survey

Santana, P. B., Gomes, H. M., Ferreira, A. J. M., & Tita, V. (2026) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-026-10744-y · Cited by 1 · see citing works

Leveraging Industry 4.0: Deep Learning, Surrogate Model, and Transfer Learning with Uncertainty Quantification Incorporated into Digital Twin for Nuclear System

Rahman, M. A., Khan, A. H., Anowar, S., Al-Imran, M., Verma, R., Kumar, D., Kobayashi, K., & Alam, S. B. (2023) · Springer eBooks · doi:10.1007/978-3-030-97940-9_192 · Cited by 1 · see citing works

Understanding Social Feedback in Biological Collectives with Smoothed Model Checking

Klein, J., & Petrov, T. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-19759-8_12

A Hybrid Science‐Guided Machine Learning Approach for Modeling Chemical and Polymer Processes

Liu, Y. A., & Sharma, N. (2023) · Wiley eBooks · doi:10.1002/9783527843831.ch11 · Cited by 5 · see citing works

A Model for Dealing with Epistemic Uncertainties in Agile Software Project ManagementPreprint

Barbosa, J. F., de Farias, I. H., Marinho, M., & de Moura, H. P. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4848407

Numerical Solution Method of PDE Based on Neural Network and Feynman-Kac Formula

Yu, J., Lin, J., & Gu, Z. (2025) · Highlights in Science Engineering and Technology · doi:10.54097/f77bmp67

Quantifying uncertainties related to reverse logistics implementation: state of the art

Dnaya, S., Adiba, E. B. E. I., & Yaagoubi, A. E. (2025) · International Conference on Optimization and Applications (ICOA) · doi:10.1109/icoa66896.2025.11236938

Computational physiological modeling for lung-specific ventilation and perfusion management in ex vivo lung perfusion

Imholz, D., Braithwaite, S. A., Blankman, P., Oppersma, E., de Jongh, F. H., de Heer, L. M., Luijk, B., Bühre, W., Donker, D. W., & van Loon, L. M. (2026) · Frontiers in Physiology · doi:10.3389/fphys.2025.1724724

Uncertainty Quantification

Jones, G., & Leyde, B. P. (2026) · Springer eBooks · doi:10.1007/978-3-032-09180-2_4

Uncertainty Quantification: Theory, Implementation, and Applications

Smith, R. C. (2013) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611973228 · Cited by 1,179 · see citing works

Introduction to Uncertainty Quantification

Sullivan, T. J. (2015) · Texts in applied mathematics · doi:10.1007/978-3-319-23395-6 · Cited by 436 · see citing works

Introduction to Uncertainty Quantification (UQ)

Flener, P. (2015)

Uncertainty Quantification Toolkit (UQTk)

Debusschere, B., Sargsyan, K., Safta, C., & Chowdhary, K. (2015) · Springer eBooks · doi:10.1007/978-3-319-11259-6_56-1 · Cited by 21 · see citing works