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

    Peiwen Zai1,*, Wei Cheng1,2, and Feng-Shou Zhang1,3,4,†

    • 1The Key Laboratory of Beam Technology of Ministry of Education, School of Physics and Astronomy, Beijing Normal University, Beijing 100875, China
    • 2Advanced Institute of Natural Sciences, Beijing Normal University at Zhuhai, Zhuhai 519087, China
    • 3Institute of Radiation Technology, Beijing Academy of Science and Technology, Beijing 100875, China
    • 4Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China

    • *Contact author: pewenz@mail.bnu.edu.cn
    • †Contact author: fszhang@bnu.edu.cn

    Phys. Rev. C 114, 034334 – Published 29 September, 2026

    DOI: https://doi.org/10.1103/cm8z-l3m8

    Abstract

    Machine-learning approaches can improve nuclear mass modeling, 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 multilayer perceptron (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.

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