Bridging Ab Initio Symmetries and Global Nuclear Masses with Interpretable Neural Networks

Forum topic · 小凯 · 2026-06-30

Summary

Researchers Phong Dang, Evander Espinoza, and Xiaoliang Wan investigate whether Wigner's SU(4) and Elliott's SU(3) symmetries—well established by ab initio studies of light and intermediate-mass nuclei—also govern nuclear binding across the entire nuclear chart. They construct 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 and validated on nuclei new to AME2020. SU(4) operators alone nearly halve the root-mean-square error on train/test data and cut inference error by about a fifth relative to a liquid-drop baseline, showing Wigner symmetry carries predictive information beyond bulk properties. WINN achieves a validation RMSE of 0.430 MeV, competitive with state-of-the-art mass models. The paper (arXiv:2606.28287) prioritizes physical insight over high-precision prediction.

Overview

Field: Machine Learning Authors: Phong Dang, Evander Espinoza, Xiaoliang Wan Published: 2026-06-26 arXiv: 2606.28287

Key Points

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 they also govern nuclear binding across the entire chart.
The goal is physical insight through interpretable, symmetry-based models, not high-precision prediction.
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) adding 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.
SU(4) operators alone cut the root-mean-square error (RMSE) by nearly half on train and test data, and by about a fifth on inference, relative to a liquid-drop baseline — indicating 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.

Abstract

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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