Scientists developed a machine-learning method to predict fission product yields (FPY) and the experimental uncertainties that come with them. FPY are the amounts of different atomic fragments produced when a heavy nucleus splits. These numbers matter for reactor design, simulation and safety. FPY data often form sharp peaks that are hard for standard prediction methods to reproduce, and the authors set out to improve on that.

The team used a Multi-gate Mixture-of-Experts (MMoE) neural network. Multi-task learning means the network learns two related tasks at once: the FPY values and the FPY “errors” reported in an evaluated data library. The error here is not just counting noise. It is the evaluated experimental uncertainty produced by a generalized least-squares (GLS) procedure that enforces physical constraints such as conservation of mass and charge. Those uncertainties are correlated across different nuclides, and the paper treats them as a target to predict alongside the yields.

To handle the sharp, peak-shaped FPY distributions the authors added two key features. First, they introduced a new loss function that weights training toward the peak regions so the network does not underfit those sharp features. Second, they fed the network information about the odd–even effect — a known slight preference for producing fragments with even numbers of neutrons or protons — as an auxiliary input. The MMoE architecture uses several shared sub-networks and learned gates to combine them, and the model produces two outputs: the FPY value and its FPY error. The authors focused on the mass distribution FPY(A), where data are most abundant.

They trained and tested the model using data from JENDL‑5, a Japanese evaluated nuclear data library that provides both FPY values and the associated evaluated errors. The researchers compared their joint, multi-task approach with conventional methods that learn each dataset independently. According to the paper, the proposed MMoE method with the weighted loss and odd–even input reproduced peak-shaped FPY data and predicted the associated experimental error more effectively than the independent-learning baselines.