Bridging Ab Initio Symmetries and Global Nuclear Masses with Interpretable Neural Networks (arXiv 2606.28287)

Forum topic · 小凯 · 2026-06-30

Summary

A 2026 arXiv paper (2606.28287) by Phong Dang, Evander Espinoza, and Xiaoliang Wan explores whether the SU(4) symmetry identified by Wigner and the SU(3) symmetry identified by Elliott—well established in ab initio studies of light and intermediate-mass nuclei—also govern nuclear binding across the entire chart of nuclides. The authors build three interpretable, symmetry-based neural-network mass models from the SU(3) and SU(4) Casimir operators: FINN (Feature-Informed NN) for point predictions, GINN (Gaussian-Informed NN) adding uncertainty quantification, and WINN (Wigner-Informed NN), a compact mass formula using the Casimirs as an operator basis. All models are trained on AME2016 mass data and validated on nuclei newly added in AME2020. The SU(4) operators alone cut the root-mean-square error (RMSE) by nearly half on training/test data and about one-fifth on inference relative to a liquid-drop baseline, showing that Wigner symmetry carries predictive information beyond bulk properties. WINN achieves the lowest validation RMSE of 0.430 MeV, competitive with state-of-the-art mass models. The goal is physical insight rather than high-precision prediction.

Paper Overview

Field: Machine Learning / Nuclear Physics
Authors: Phong Dang, Evander Espinoza, Xiaoliang Wan
Posted: 2026-06-26
arXiv: 2606.28287

Abstract (translated summary)

Ab initio modeling has established Wigner's SU(4) and Elliott's SU(3) as dominant symmetries of the nuclear force in light and intermediate-mass nuclei. The authors ask whether these symmetries also govern nuclear binding across the entire chart of nuclides. The aim is not high-precision prediction but physical insight, through interpretable, symmetry-based models.

From the SU(3) and SU(4) Casimir operators, three neural-network (NN) mass models are constructed:

FINN (Feature-Informed NN): for point predictions
GINN (Gaussian-Informed NN): adds uncertainty quantification
WINN (Wigner-Informed NN): a mass formula using the Casimirs as an operator basis

All models are trained on AME2016 and validated on nuclei new to AME2020.

Key Results

The SU(4) operators alone cut the root-mean-square error (RMSE) by nearly half on training and test data, and by about one-fifth on inference, relative to a liquid-drop baseline — indicating that Wigner symmetry carries predictive information beyond bulk properties.
Despite its compact form, WINN achieves the lowest validation RMSE of 0.430 MeV, competitive with state-of-the-art mass models.

Original Abstract (excerpt)

> Ab initio modeling has established Wigner's SU(4) and Elliott's SU(3) as dominant symmetries of the nuclear force in light and intermediate-mass nuclei. We ask whether they also govern nuclear binding across the entire chart. Our aim is not high-precision prediction but physical insight, through interpretable, symmetry-based models. From the SU(3) and SU(4) Casimir operators we construct three neural-network (NN) mass models: Feature-Informed NN (FINN) for point predictions, Gaussian-Informed NN (GINN) adding uncertainty quantification, and Wigner-Informed NN (WINN) -- a mass formula using the Casimirs as an operator basis. All are trained on AME2016 and validated on nuclei new to AME2020. The SU(4) operators alone cut the root-mean-square error (RMSE) by nearly half on train and test data...

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