Bridging Ab Initio Symmetries and Global Nuclear Masses with Interpretable Neural Networks
2026-06-26 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study whether certain symmetries, known from light and medium nuclei, also explain how all nuclei across the periodic table hold together. They build neural network models based on these symmetries to predict nuclear masses and find that using Wigner's SU(4) symmetry notably improves prediction accuracy beyond simple models. Their best model, which uses symmetry-based formulas, performs well compared to advanced methods and highlights physical patterns near nuclear stability limits. This suggests these symmetries are fundamental principles explaining nuclear binding broadly, not just in specific cases.
Wigner's SU(4) symmetryElliott's SU(3) symmetrynuclear bindingCasimir operatorsneural networksmass modelsliquid-drop modelnuclear driplinesuperheavy nucleiAME nuclear mass evaluations
Authors
Phong Dang, Evander Espinoza, Xiaoliang Wan, Michela Negro, Jerry P. Draayer, Feng Pan, Tomas Dytrych, Daniel Langr, David Kekejian
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.