# Product units in gated recurrent units improve nuclear-mass prediction

Source: [Product units in gated recurrent units improve nuclear-mass prediction](<https://www.sota2.com/research/paper/6a264c9590966ade919bea6d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-26T05:00:12.659Z

Authors: Ziyuan Li, Paulo S.A. Freitas, John W. Clark, Babette Dellen

Published: 2026-06-05T03:25:50.000Z

## Abstract

The prediction of masses of atomic nuclei using machine learning can complement theoretical models and advance the exploration of poorly known domains of the nuclear chart. We propose a machine learning technique based on gated recurrent units (GRU), which have demonstrated competitive performance in nuclear-mass prediction by exploiting long-term dependencies. By integrating multiplicative interactions and product-unit transformations within recurrent units, we report significant improvements in nuclear-mass prediction. Computations are performed in the complex domain to jointly capture amplitude and phase dynamics. For interpolation and temporal-extrapolation tasks based on the atomic mass evaluation (AME2016 and AME2020), the complex additive-multiplicative product-unit gated recurrent unit (AM-PU-GRU) model consistently achieves the lowest prediction errors, with an interpolation RMSE of 0.227 $\\pm$ 0.004 MeV and an extrapolation RMSE of 0.179 $\\pm$ 0.015 MeV. These results surpass other state-of-the-art machine learning models and also outperform the real-valued GRU baseline and product-unit ablation variants, while remaining robust to different theoretical priors, including WS4 and SEMF. Our findings establish complex-valued product-unit recurrent networks as a new benchmark for sequence-based nuclear-mass prediction.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Nuclear mass prediction on AME 2020](<https://www.sota2.com/research/sota/nuclear-mass-prediction-on-ame-2020.md>): Nuclear mass prediction; AME 2020; ExtRMSE: 0.179.

- [Nuclear mass prediction on AME 2016](<https://www.sota2.com/research/sota/nuclear-mass-prediction-on-ame-2016.md>): Nuclear mass prediction; AME 2016; IntRMSE: 0.253.

- [Nuclear mass excess prediction on AME Experiment I 2020 (interpolation)](<https://www.sota2.com/research/sota/nuclear-mass-excess-prediction-on-ame-experiment-i-2020-interpolation.md>): Nuclear mass excess prediction; AME Experiment I 2020 (interpolation); IntRMSE (MeV): 0.227.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.06866>)

[PDF](<https://arxiv.org/pdf/2606.06866.pdf>)