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

Forum topic · 小凯 · 2026-06-30

Summary

This arXiv paper (2606.28287) by Phong Dang, Evander Espinoza, and Xiaoliang Wan explores 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. Rather than pursuing high-precision prediction, the authors build interpretable, symmetry-based models from the SU(3) and SU(4) Casimir operators: Feature-Informed NN (FINN) for point predictions, Gaussian-Informed NN (GINN) with uncertainty quantification, and Wigner-Informed NN (WINN), 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. SU(4) operators alone cut the root-mean-square error 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. Despite its compact form, WINN achieves the lowest validation RMSE of 0.430 MeV, competitive with state-of-the-art nuclear mass models.

Paper Overview

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

Abstract (Full Translation)

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, and by roughly 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, 0.430 MeV -- competitive with state-of-the-art mass models.

Key Takeaways

SU(4) and SU(3) Casimir operators, known from ab initio studies of light nuclei, retain predictive power for global nuclear binding energies.
Three interpretable NN models introduced: FINN (point prediction), GINN (uncertainty quantification), WINN (compact operator-based mass formula).
SU(4) features reduce RMSE by ~50% on train/test and ~20% on inference versus a liquid-drop baseline.
WINN achieves a validation RMSE of 0.430 MeV, competitive with leading nuclear mass models despite its compact form.
Trained on AME2016; validated on nuclei new to AME2020.

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