Reliable Uncertainty Estimation for Machine-Learned Multigroup Cross Sections Without Retraining

Abstract

Uncertainty quantification in machine learning models is essential for nuclear energy applications. While machine learning models can make both uncertainty and point predictions, these models are often significantly more difficult to train jointly than models that make point predictions alone. Split conformal prediction is a family of methods for computing distribution-free prediction intervals by calculating nonconformity scores corresponding to a target quantile in a calibration dataset. Although conformal prediction only guarantees marginal coverage, normalizing nonconformity scores enables predictive interval widths to be calculated on a per-sample basis, providing an approximation to conditional coverage. In this work, we connect uncertainty predicting neural networks to pre-trained networks that estimate shielding factors in multigroup neutron cross sections. We train the uncertainty models on the same OpenMC data used by the pre-trained models, whose weights and biases remain fixed. The outputs of the uncertainty models are the standard deviations of the residual, separated into contributions from the model and tally uncertainty. Their corresponding variances are combined in quadrature to provide a normalizing factor for conformal prediction, providing interval widths that are adaptive on a per-sample basis. Baselines for comparison are established using Mondrian conformal prediction, and by using the ground truth OpenMC uncertainties as normalizers in the conformal framework. We use predicted uncertainty interval widths and the severity of predictions that overshoot the interval widths as bases for comparing our normalizer with the baselines. We find that our method dramatically reduces both interval widths and the degree to which predictions fall outside these widths.