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초록

We propose NuPINN-CAL, a physics-informed neural network designed to directly predict nuclear proton density distributions, rho p(r), from the fundamental nuclear identifiers (Z, N). Unlike conventional Skyrme-Hartree-Fock (Skyrme-HF) and energy-density functional approaches, NuPINN-CAL explicitly embeds two key nuclear-physics constraints (proton-number conservation and charge-radius consistency) into its learning objective. A novel constraint-aware learning strategy dynamically balances these physics constraints with Skyrme-HF priors, ensuring stable and interpretable training even in small-data regimes.Benchmarking on 120 magic and semi-magic nuclei, NuPINN-CAL achieves a root-mean-square deviation of 0.022 fm in charge radii, representing a similar to 33% improvement over Skyrme-HF predictions. Beyond numerical accuracy, the model demonstrates strong generalization to open-shell systems. These results validate the central hypothesis that (Z, N) uniquely determines rho p(r) as a deterministic and physically consistent mapping, highlighting NuPINN-CAL as a robust, interpretable, and data-efficient paradigm for next-generation nuclear density modeling.

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