Nuclear mass is a fundamental observable value that reflects nuclear structure and stability, and plays a key role in nuclear physics and astrophysics. Most of the existing neural network research focuses on predicting the binding energy or neutron/proton separation energy alone, little attention is paid to the physical correlations between these observable quantities. A physical information-based artificial neural network (ANN) is developed based on the relativistic point-coupling model PCK-PK1 to systematically predict nuclear binding energy and single/double neutron/proton separation energy, while maintaining the physical self-consistency of the predictions. To evaluate the influence of introducing separation-energy constraints, different combinations of loss function weights are used to train the networks, enabling a comparison between networks without separation-energy constraints (such as ANN1) and those containing such constraints (such as ANN3).

The neural network significantly improves the overall prediction accuracy of binding energy compared with the PCF-PK1 model. Without separation-energy constraints, ANN1 already achieves high precision for binding energy (RMSE \approx 0.147 MeV) and separation energy (RMSE \approx 0.158–0.185 MeV). Incorporating the separation-energy constraints into 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. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00239.