Ensembles of physics-enhanced neural networks for the prediction of critical heat flux in nuclear reactors and the quantification of its uncertainty

The Critical Heat Flux (CHF) is a physical phenomenon that may cause the deterioration of the heat transfer in the core of nuclear reactors, potentially leading to core damage. Its accurate prediction is therefore a crucial issue in nuclear reactor safety. To this aim, various empirical and mechanistic models have been proposed to estimate the CHF across various flow regimes and conditions, which however present some drawbacks: i) data scarcity in some parts of the input domain; ii) no information about prediction uncertainties; iii) difficult explainability and interpretability of the results. To address these issues, ensembles of Physics-Enhanced Neural Networks (PENNs) are considered to predict the CHF as a function of relevant physical input variables (e.g., pipe heated length and diameter, pressure, mass flux, outlet quality). Two different frameworks to integrate physics and data-driven NN-based strategies are here compared for the first time, to the best of the author’s knowledge. In the first, fixed-structure (prior) baseline models (i.e., the Groeneveld Look-Up Table-LUT and the mechanistic Liu model) are constructed relying on the existing knowledge on the physical phenomenon of interest, which serves as a reference solution; then, NN ensembles are employed to capture unknown, unexplored information from the mismatch (i.e., the residuals) between the real CHF values and the estimates produced by the knowledge-based models. In the second, the LUT and the mechanistic Liu model are directly implemented in the NN loss function for effective (physics- and data-driven) ensemble training. A case study is carried out with an extensive CHF database (published by the U.S. Nuclear Regulatory Commission with measurements in vertical uniformly-heated water-cooled cylindrical tubes) to demonstrate: i) the improved performance of the PENN-based approaches as compared to traditional knowledge-based models; ii) the PENN superior generalization capabilities over standalone data-driven NNs in the presence of small-sized datasets (i.e., a few tens or hundreds points); iii) the possibility to build robustness in the CHF predictions by bootstrap and PENN weights random reinitialization for quantifying uncertainty and estimating prediction intervals.