Probabilistic Machine Learning Framework for Predicting Critical Heat Flux in Uniformly Heated Vertical Tubes with Uncertainty Quantification
Abstract
Critical heat flux (CHF) defines the limiting boundary condition of heat transfer in evaporative systems. Numerous empirical correlations and models have been proposed over the past decades to predict CHF under subcooled and saturated flow conditions. However, these conventional approaches are often limited by their dependence on empirical constants and their validity within narrow operating conditions or specific working fluids, resulting in significant prediction deviations outside those conditions. Moreover, recently developed machine learning models mainly include deterministic (mean value) prediction. To address this limitation, unified machine learning frameworks—Bayesian neural network (BNN) and Natural Gradient Boosting (NGBoost)—have been developed using 24 579 experimental data points (Nuclear Regulatory Commission database) to predict mean value as well as prediction uncertainty. The models utilize 80% of data points for training and 20% for testing. The performance of the developed models is evaluated by employing mean predicted/measured (P/M) CHF values, standard deviation of predicted/measured CHF values, root-mean-square percentage error, mean absolute percentage error, and coefficient of determination (R2), along with 95% confidence interval (CI)-based uncertainty quantification. Both models capture around the 95% (94.7% for BNN and 93.9% for NGBoost) of experimental (test dataset) data points within the 95% CI. Moreover, developed models have shown an improved performance on the test, total, and unseen dataset compared to the widely used lookup table, except for the case when NGBoost is used to predict the unseen dataset. Finally, SHAP-based (SHapley Additive exPlanations) interpretability analysis revealed that higher vapor quality, pressure, and heated length negatively influence CHF predictions, which is consistent with the physics behind CHF.
Recommended Citation
A. Mondal and S. L. Sharma, "Probabilistic Machine Learning Framework for Predicting Critical Heat Flux in Uniformly Heated Vertical Tubes with Uncertainty Quantification," Nuclear Technology, Taylor and Francis Group; Taylor and Francis; American Nuclear Society, Jan 2026.
The definitive version is available at https://doi.org/10.1080/00295450.2026.2629142
Department(s)
Nuclear Engineering and Radiation Science
Keywords and Phrases
Bayesian neural network (BNN); critical heat flux (CHF); Machine learning (ML); Natural Gradient Boosting (NGBoost); probabilistic models; uncertainty quantification (UQ)
International Standard Serial Number (ISSN)
1943-7471; 0029-5450
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Taylor and Francis Group; Taylor and Francis; American Nuclear Society, All rights reserved.
Publication Date
01 Jan 2026
