The recently developed Deep Potential [Phys. Rev. Lett. 120 (2018) 143001 [27]] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality and symmetry properties of each component of the network. In this paper, we leverage its network structure to effectively represent the mapping from the atomic configuration to the electron density in Kohn-Sham density function theory (KS-DFT). By directly targeting at the self-consistent electron density, we demonstrate that the adapted network architecture, called the Deep Density, can effectively represent the self-consistent electron density as the linear combination of contributions from many local clusters. The network is constructed to satisfy the translation, rotation, and permutation symmetries, and is designed to be transferable to different system sizes. We demonstrate that using a relatively small number of training snapshots, with each snapshot containing a modest amount of data-points, Deep Density achieves excellent performance for one-dimensional insulating and metallic systems, as well as systems with mixed insulating and metallic characters. We also demonstrate its performance for real three-dimensional systems, including small organic molecules, as well as extended systems such as water (up to 512 molecules) and aluminum (up to 256 atoms).

最近开发的深层电势 [Phys. 牧师莱特。120 (2018) 143001 [27]] 是一种使用深度神经网络表示一般原子间势的强大方法。Deep Potential 的成功取决于对网络每个组件的局部性和对称性属性的正确处理。在本文中，我们利用其网络结构来有效地表示 Kohn-Sham 密度函数理论 (KS-DFT) 中从原子配置到电子密度的映射。通过直接针对自洽电子密度，我们证明了称为深度密度的自适应网络架构可以有效地将自洽电子密度表示为来自许多局部簇的贡献的线性组合。构建网络以满足平移、旋转和置换对称性，并被设计为可转移到不同的系统大小。我们证明，使用相对较少的训练快照，每个快照包含适量的数据点，Deep Density 在一维绝缘和金属系统以及具有混合绝缘和金属特征的系统上实现了出色的性能。我们还展示了它在真实三维系统中的性能，包括有机小分子，以及扩展系统，如水（最多 512 个分子）和铝（最多 256 个原子）。以及具有混合绝缘和金属特性的系统。我们还展示了它在真实三维系统中的性能，包括有机小分子，以及扩展系统，如水（最多 512 个分子）和铝（最多 256 个原子）。以及具有混合绝缘和金属特性的系统。我们还展示了它在真实三维系统中的性能，包括有机小分子，以及扩展系统，如水（最多 512 个分子）和铝（最多 256 个原子）。