Physics-structured cooperative neural network for baseline-free nuclear mass modeling

Abstract

Machine learning approaches can improve nuclear mass modelling, but the most accurate strategies often depend on a theoretical mass baseline or hand-crafted physics features. We test whether a modular architecture encoding selected nuclear-structure priors improves baseline-free direct prediction and yields informative branch diagnostics. The Cooperative Neural Network (CoNN) implements this approach through four form-constrained branches: a smooth macroscopic network, discrete embeddings, a two-dimensional regional grid, and a parity-aware network. It extracts complementary patterns from (Z, N) through these branches and sums their outputs to predict binding energies without a theoretical mass-model baseline. Thus, the model retains physics priors while reducing its reliance on engineered input features. On AME2020, CoNN reaches a root-mean-square deviation (RMSD) of 0.269 MeV for 3558 nuclei, compared with 0.836 MeV for a parameter-matched unstructured MLP. It also gives RMSDs of 0.419 MeV on a held-out interpolation subset and 0.728 MeV on 122 nuclei newly measured since AME2016. The learned branch outputs show recognizable physical patterns, including embedding shell-kink signatures at major magic numbers and odd-even staggering along isotopic chains. These results identify architecture-level priors as a practical route to baseline-free mass prediction, with learned components that help diagnose both nuclear-structure patterns and extrapolation limits.

Substantially revised version; 12 pages, 9 figures, 4 tables. Revised title; expanded methodology, analyses, and model diagnostics