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原子核质量是反映核结构与稳定性的重要物理量，在核结构研究与天体核物理过程中均具有关键作用。目前，基于神经网络的研究多集中于结合能或中子、质子分离能的单一预测，较少关注结合能与分离能之间的物理约束关系。本研究基于相对论平均场点耦合模型PCF-PK1，结合神经网络对原子核结合能以及单、双中子和单、双质子分离能进行了系统预测。在训练过程中引入分离能约束，以保持结合能与分离能之间的物理自洽性。结果表明，神经网络能够显著提升结合能的整体预测精度。其中，在特定损失函数权重组合下，结合能的预测均方根偏差可达到0.140 MeV。进一步分析发现，在保持物理自洽性的前提下，引入分离能约束能够同时对结合能和分离能的预测结果实现小幅优化。支撑本研究成果的数据集可在科学数据银行https://doi.org/10.57760/sciencedb.j00213.00239中访问获取.（为便于审稿，我们同时提供了审稿期间可访问的私有链接： https://www.scidb.cn/s/bqyemq。）Abstract Nuclear masses are fundamental observables that reflect nuclear structure and stability, playing a key role in nuclear physics and astrophysical processes. Most existing neural network studies focus on predicting either binding energies or neutron/proton separation energies individually, with limited attention to the physical correlations between these observables. Based on the relativistic point-coupling model PCF-PK1, a physics-informed artificial neural network (ANN) was developed to systematically predict nuclear binding energies along with single- and double-neutron/proton separation energies, while preserving the physical self-consistency of the predictions. To assess the impact of incorporating separation-energy constraints, networks were trained with varying loss function weight combinations, enabling a comparison between networks without separation-energy constraints (e.g., ANN1) and those including such constraints (e.g., ANN3).
The neural network significantly improves the overall prediction accuracy of binding energies compared with the PCF-PK1 model. Without separation-energy constraints, ANN1 already achieves high precision for binding energies (RMSE ≈ 0.147 MeV) and separation energies (RMSE ≈ 0.158– 0.185 MeV). Incorporating separation-energy constraints in ANN3 results in a slight improvement in overall prediction accuracy. The binding energy predictions improve by approximately 4.6%, while the separation energy predictions increase by 8.9–12.0%. The improvement is particularly noticeable for nuclei where the deviations of ANN1 predictions from experimental values exceed 0.2 MeV. Supporting datasets are publicly accessible at the Science Data Bank (https://doi.org/10.57760/sciencedb.j00213.00239). To facilitate the review process, a private access link is provided for reviewers during the review period (https://www.scidb.cn/s/bqyemq).-
Keywords:
- Nuclear mass /
- Neural network /
- Separation energy
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