The Role of Nuclear Data Sensitivities in Prompt α-Eigenvalue Predictions of Delayed Critical Benchmarks

Abstract

Alpha (α) eigenvalues, which describe the logarithmic time derivative of the neutron population in a multiplying system, are integral to time-dependent behavior and diagnostic applications. However, uncertainties in the evaluated nuclear data can significantly impact the accuracy of transport simulations for such quantities. This work explores the use of machine learning models to predict two key outputs, α-eigenvalues and keff bias, using input features derived from α-eigenvalue sensitivities to nuclear data. The criticality safety benchmark models used in this study come from the International Handbook of Evaluated Criticality Safety Benchmark Experiments. Three models, random forest, XGBoost, and NGBoost, are trained on both energy-resolved and energy-summed α sensitivities. For the α-eigenvalue bias prediction, NGBoost achieved the highest R 2 (0.9476) using energy-resolved features, while XGBoost performed best using summed sensitivities. In contrast, when predicting the keff bias, all the models showed moderate predictive capability (best R 2 ≈ 0.72), as the mapping from the static α-sensitivities to the static keff bias was less direct. SHAP (SHapley Additive exPlanations) analysis was used to interpret the model predictions. Across both prediction tasks, the features associated with neutron capture [H-1 (n, γ)], uranium scattering reactions (such as 235 U elastic/inelastic), and actinide capture/fission reactions (such as 239 Pu and 234 U) were consistently identified as the most impactful. This highlights the key role of specific nuclear reactions and energy ranges in shaping both time-dependent and steady-state criticality behavior. These results demonstrated that α-sensitivities, despite being computed for time-dependent metrics, can provide valuable insights for predicting both α-eigenvalues and the keff bias. Moreover, machine learning models offer a promising pathway for uncovering important nuclear data dependencies and guiding future data evaluation efforts.