Data-driven bubble transport prediction and uncertainty quantification in lead-cooled fast reactor based on attentional feature fusion

Core voiding caused by steam generator tube rupture (SGTR) is a critical safety concern for pool-type lead-cooled fast reactors (LFR). Assessing its risk requires an accurate prediction of bubble transport in LFR during SGTR. However, physics-based predictions of bubble transport are usually computationally expensive. This work employed a data-driven method to predict bubble transport within the European Lead-cooled System during SGTR accidents. The neural network-based model tackled the issue of heterogeneous input features using learnable feature embeddings and attentional feature fusion (AFF). The specifically selected rectified linear unit 1 (ReLU1) and the modified Softmax activation eliminated non-physical outputs. As the prediction model is used in safety-critical applications, the deep ensembles (DE) method quantified the epistemic uncertainty. Combining the attentional feature fusion and the modified Softmax activation yielded the best model accuracy with a root mean squared error of 6.03×10⁻³ and a mean absolute error of 3.56×10⁻³, which was statistically validated. The sensitivity analysis suggests that learnable feature embeddings properly encode the characteristics of input features. The all-in-one approach, which used the modified Softmax activation to correlate output features, yielded significant covariance estimates. Although the univariate uncertainty distribution evaluation suggests that further calibration is required (the expected calibration error exceeds 0.1), predictive uncertainty can still benefit model robustness by indicating model trustworthiness. The proposed method can predict bubble distributions during SGTR in real time, leaving a sufficient time window for further core-voiding risk assessments. © 2026 Elsevier Ltd.