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

Forum topic · 小凯 · 2026-06-30

Summary

This paper (arXiv 2606.28287, by Phong Dang, Evander Espinoza, and Xiaoliang Wan) investigates whether Wigner's SU(4) and Elliott's SU(3) symmetries—established by ab initio modeling as dominant features of the nuclear force in light and intermediate-mass nuclei—also govern nuclear binding across the entire chart of nuclides. The authors construct three interpretable, symmetry-based neural-network mass models from the SU(3) and SU(4) Casimir operators: Feature-Informed NN (FINN) for point predictions, Gaussian-Informed NN (GINN) adding uncertainty quantification, and Wigner-Informed NN (WINN), a compact mass formula using the Casimirs as an operator basis. All models are trained on AME2016 and validated on nuclei new to AME2020. The SU(4) operators alone reduce the root-mean-square error (RMSE) by nearly half on train and test data and 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. The work emphasizes physical insight and interpretability over pure high-precision prediction.

Overview

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

Abstract (English, from source)

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...

Key Points

Three NN mass models built from SU(3)/SU(4) Casimir operators: FINN (point predictions), GINN (adds uncertainty quantification), WINN (compact mass formula using Casimirs as an operator basis).
Training set: AME2016; validation: nuclei new in AME2020.
SU(4) operators alone cut RMSE by nearly half on train/test data and by about one fifth on inference, relative to a liquid-drop baseline — 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 despite its compact form.
The goal is physical insight via interpretable, symmetry-based models rather than high-precision prediction alone.

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