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

2026-06-26

AI Summary

This study investigates whether Wigner SU(4) and Elliott SU(3) symmetries govern binding energy systematics across the entire nuclear chart, beyond light and medium-mass nuclei. To this end, the authors develop interpretable neural network models—such as WINN—that explicitly incorporate ab initio symmetry principles via SU(3) and SU(4) Casimir operators as foundational physical ingredients in a global nuclear mass model. Evaluated on the AME2020 dataset, WINN achieves a root-mean-square error of 0.430 MeV, demonstrating that SU(4) symmetry alone substantially enhances predictive accuracy. The model further uncovers novel phenomena: restoration of symmetry near the neutron drip line and pronounced quartic-term contributions in the superheavy region, highlighting the pivotal role of these symmetries in extreme nuclear domains.

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, and by about a fifth on extrapolation, relative to the liquid-drop baseline -- showing that Wigner's symmetry carries predictive information beyond bulk properties. Despite its compact form, WINN reaches the lowest validation RMSE, 0.430 MeV -- competitive with state-of-the-art mass models -- which we read less as a benchmark than as evidence that its symmetry basis captures important physics. WINN further reveals i) an enhancement of the quadratic SU(4) Casimir near the neutron dripline, signaling restoration of Wigner's symmetry, and ii) an unexpected gain of the quartic operator in the superheavy region. We thereby elevate emergent symmetries from the hidden order within individual nuclei to a governing principle of the whole nuclear chart.

Problem

• nuclear symmetries
• nuclear masses
• SU(3)
• SU(4)
• ab initio modeling

Innovation

• interpretable neural networks
• nuclear symmetries
• SU(4) Casimir operators
• ab initio nuclear theory
• nuclear mass modeling