Bayesian mixture density networks for evaluating neutron-induced fission charge yields
Phys. Rev. C 112, 014607 – Published 2 July, 2025
DOI: https://doi.org/10.1103/gd8l-zzmy
Abstract
Background: Predicting neutron-induced fission charge yields poses substantial challenges due to the complex, nonequilibrium nature of the fission process and the limited availability of detailed experimental data over a broad range of energies. Reliable modeling is essential for applications in reactor engineering, isotope production, and fundamental nuclear physics.
Purpose: This work aims to develop a robust probabilistic machine learning framework capable of accurately predicting neutron-induced fission charge yields under conditions of data scarcity. By incorporating methods that handle both epistemic (model-related) and aleatoric (data-inherent) uncertainties, the approach strives to represent physical phenomena such as odd-even effects and energy-dependent yields while providing realistic confidence intervals.
Method: A Bayesian mixture density network (BMDN) is introduced, combining three probabilistic components: (1) Gaussian process regression (GPR) to augment sparse datasets with synthetic samples and associated uncertainties; (2) Bayesian neural network (BNN) layers with an integrated attention mechanism that treats model parameters as random variables, capturing epistemic uncertainty through variational inference; and (3) a mixture density network (MDN) output layer that models charge yields as mixtures of Gaussian distributions, accommodating multimodal patterns and aleatoric uncertainty.
Results: The BMDN reproduces charge yield distributions for nuclei within the training set and generalizes effectively to previously unseen systems like . It accurately reflects odd-even staggering and energy dependence, with uncertainty intervals that correspond to both model confidence and intrinsic data variability. Comparisons against experimental data and semiempirical calculations demonstrate strong agreement with observed trends. While incorporating a white noise kernel in GPR enhances noise realism, it can soften subtle structural details, emphasizing the importance of balancing noise modeling with feature retention.
Conclusions: The presented approach provides a flexible, uncertainty-aware framework for predicting fission charge yields under sparse data conditions. By uniting GPR, BNN layers, and MDN outputs, the BMDN offers meaningful probabilistic insights and can guide future efforts toward more comprehensive datasets and improved theoretical models. Its adaptability makes it a promising tool for enhancing nuclear data evaluations, informing design choices in fission-related technologies, and advancing fundamental understanding of the fission process.
