Machine Learning Methods for Predicting Mean and Uncertainty in Nodal Cross-Section Libraries

This study presents a comparative analysis of regression techniques for modeling few-group cross-section libraries as a function of state parameters, with prediction targets that include both mean values and covariance matrices to represent aleatoric uncertainty from nuclear data perturbations. Beyond absolute accuracy, the primary focus is convergence performance: whether the prediction error decreases monotonically as the number of unique training samples Nbranch increases. The results show that the convergence behavior differs substantially across the methods. In particular, the transformed neural network model exhibits inconsistent, nonmonotonic convergence with respect to Nbranch, indicating limited robustness. In contrast, the transformed polynomial regression (tp-PR) model shows stable convergence and achieves the best performance at the largest training set (Nbranch = 1024) with a kinf error of 0.015%. A comparison of the predicted and reference keff distributions further shows that the tp-PR model was able to reproduce uncertainty induced by nuclear data uncertainty.