{"id":741,"date":"2023-10-23T10:44:49","date_gmt":"2023-10-23T14:44:49","guid":{"rendered":"https:\/\/ne.ncsu.edu\/artisans\/?page_id=741"},"modified":"2025-11-26T04:08:44","modified_gmt":"2025-11-26T09:08:44","slug":"uq-of-ml","status":"publish","type":"page","link":"https:\/\/ne.ncsu.edu\/artisans\/research\/uq-of-ml\/","title":{"rendered":"UQ of ML"},"content":{"rendered":"\n
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Research Topics<\/strong><\/h4>\n\n\n\n

Inverse Uncertainty Quantification (UQ)<\/a>
Integration of Prior Knowledge, Inverse UQ and Quantitative Validation<\/a>
Uncertainty Quantification of Machine Learning (ML)<\/a>
Deep Generative Modeling (DGM)<\/a>
<\/a>Cognitive Operator Readiness Assistant (CORA)
<\/a>UQ and ML for Nuclear Forensics and Non-proliferation<\/a><\/p>\n<\/div><\/div>\n\n\n\n

Uncertainty Quantification of ML<\/strong><\/h4>\n\n\n\n

ML-based models are subject to approximation uncertainties when they are used to make predictions. Such uncertainty exists even within the training domain because the training data can be sparse. We summarize the sources of uncertainties for ML models into the following five categories. (1) Data noise \u2013 noises in training data from either physical simulation models or experiments can lead to ML uncertainty. (2) Data coverage \u2013 few and\/or gappy data that has incomplete coverage of the training domain can cause ML uncertainty. (3) Extrapolation \u2013 generalization of the ML models to the extrapolated domains outside of the training domain can result in large uncertainties. (4) Imperfect model \u2013 when a ML model\u2019s architecture is not properly defined, e.g., the model is too simple or too complex with respect to the data. (5) Training process \u2013 issues such as random initialization, convergence to local minima, hyperparameter tuning, posterior inference for Bayesian neural nets, etc. can lead to ML uncertainty. A combination of various sources of uncertainties can greatly affect the accuracy of ML models. Unlike the uncertainty sources in physics-based modeling (data, numerical, model, parameter and code), these sources are usually not well-separated from each other. Ensuring robustness especially in the context of extrapolation is a grand challenge.<\/p>\n\n\n

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Our research on UQ of ML focuses on pursuing new research ideas based on Monte Carlo Dropout (MCD), Deep Ensembles (DE) and Bayesian neural network (BNN) to quantify the prediction uncertainties in deep neural networks (DNNs), as they have the greatest potential for SciML applications in nuclear engineering. We are developing novel approaches that can efficiently implement the variational Bayesian methods for BNN, as well as performing systematic benchmark studies for different UQ methods. We will also focus on developing gradient-based Bayesian inference methods to train BNNs. The Hamiltonian Monte Carlo (HMC) algorithm is a type of MCMC algorithm designed for drawing samples from probability distributions by computing the gradient of the Hamiltonian equations in the direction of high-probability regions, leading to better convergence of MCMC sampling. We will develop efficient HMC-enhanced MCMC exploration of the posterior distributions of BNN parameters, for both steady-state and transient problems in representative nuclear engineering applications.<\/p>\n\n\n\n

Relevant publications:<\/mark><\/strong><\/p>\n\n\n\n

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  1. Wu, X., Moloko, L., Bokov, P., Delipei, G., Kaizer, J., and Ivanov, K. (2025). Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need? Nuclear Science and Engineering
    https:\/\/doi.org\/10.1080\/00295639.2025.2552500<\/a><\/li>\n\n\n\n
  2. Akins, A., Kultgen, D., Wu, X., and Heifetz, A. (2025). Uncertainty Quantification through Monte Carlo Dropout for Multi-Modal Anomaly Detection in a Liquid Sodium Purification System. Nuclear Technology
    https:\/\/doi.org\/10.1080\/00295450.2025.2518613<\/a><\/li>\n\n\n\n
  3. Furlong, A., Alsafadi, F., Palmtag, S., Godfrey, A., and Wu, X. (2025). Data-Driven Prediction and Uncertainty Quantification of PWR Crud-Induced Power Shift Using Convolutional Neural Networks. Energy, 316:134447.
    https:\/\/doi.org\/10.1016\/j.energy.2025.134447<\/a><\/li>\n\n\n\n
  4. Moloko, L., Bokov, P., Wu, X., and Ivanov, K. (2024). Clustering and uncertainty analysis to improve the machine learning-based predictions of SAFARI-1 control follower assembly axial neutron flux profiles. Annals of Nuclear Energy, 206:110630
    https:\/\/doi.org\/10.1016\/j.anucene.2024.110630<\/a><\/li>\n\n\n\n
  5. Moloko, L., Bokov, P., Wu, X., and Ivanov, K. (2023). Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks. Annals of Nuclear Energy, 188:109813
    https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0306454923001329<\/a><\/li>\n\n\n\n
  6. Yaseen, M. and Wu, X. (2023). Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models. Nuclear Science and Engineering, 197:947\u2013966
    https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00295639.2022.2123203<\/a><\/li>\n<\/ol>\n\n\n\n

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    Uncertainty Quantification of ML ML-based models are subject to approximation uncertainties when they are used to make predictions. Such uncertainty exists even within the training…<\/p>\n","protected":false},"author":365,"featured_media":0,"parent":22,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-landing.php","meta":{"_acf_changed":false,"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-741","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/pages\/741","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/users\/365"}],"replies":[{"embeddable":true,"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/comments?post=741"}],"version-history":[{"count":8,"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/pages\/741\/revisions"}],"predecessor-version":[{"id":1576,"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/pages\/741\/revisions\/1576"}],"up":[{"embeddable":true,"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/pages\/22"}],"wp:attachment":[{"href":"https:\/\/ne.ncsu.edu\/artisans\/wp-json\/wp\/v2\/media?parent=741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}