With the datasets of the density distributions calculated by Skyrme density functional theories, we elaborated deep neural networks to generate the density profile and provide a table of related hyperparameters set for similar applications of other structural models. In the process of machine learning with the objective/target functions that normalized mean square error and Kullback–Leibler divergence (cross entropy), there is a turning point showing the transition from the Fermi-like distribution to the realistic Skyrme distribution, while this property is transcended when Pearson ${\chi }^2$ divergence is employed. A training program of about 35 minutes with only about $5\text{\%}-10\text{\%}$ nuclei ($200-300$) is sufficient to describe the nucleon density distributions of all the nuclear chart within 2% relative error. We obtain similar results employing different datasets calculated by different Skyrme density functional theories. We further investigate the extrapolation properties, which show that an addition of 15 nucleons is acceptable. Based on the results, we propose a mixed dataset approach and a retraining approach in order to go beyond a single physical structure model.

利用 Skyrme 密度泛函理论计算的密度分布数据集，我们详细阐述了深度神经网络来生成密度剖面，并为其他结构模型的类似应用提供相关超参数集的表。在使用归一化均方误差和 Kullback-Leibler 散度（交叉熵）的目标/目标函数进行机器学习的过程中，有一个转折点显示了从 Fermi-like 分布到现实 Skyrme 分布的转变，而这个属性当皮尔逊超越时${\chi }^2$发散被使用。大约 35 分钟的训练计划$5\text{\%}-10\text{\%}$ 核（$200-300$) 足以描述所有核图的核子密度分布在 2% 的相对误差内。我们使用由不同 Skyrme 密度泛函理论计算的不同数据集获得了类似的结果。我们进一步研究了外推特性，这表明添加 15 个核子是可以接受的。基于结果，我们提出了一种混合数据集方法和一种再训练方法，以超越单一的物理结构模型。