We incorporate in the Kohn-Sham self consistent equation a trained
neural-network projection from the charge density distribution to the
Hartree-exchange-correlation potential $n \rightarrow V_{\rm Hxc}$ for possible
numerical approach to the exact Kohn-Sham scheme. The potential trained through
a newly developed scheme enables us to evaluate the total energy without
explicitly treating the formula of the exchange-correlation energy. With a case
study of a simple model we show that the well-trained neural-network $V_{\rm
Hxc}$ achieves accuracy for the charge density and total energy out of the
model parameter range used for the training, indicating that the property of
the elusive ideal functional form of $V_{\rm Hxc}$ can approximately be
encapsulated by the machine-learning construction. We also exemplify a factor
that crucially limits the transferability--the boundary in the model parameter
space where the number of the one-particle bound states changes--and see that
this is cured by setting the training parameter range across that boundary. The
training scheme and insights from the model study apply to more general
systems, opening a novel path to numerically efficient Kohn-Sham potential.

通过将经过训练的神经网络投影到电荷密度分布上，得到 Hartree-exchange-correlation potential $n ightarrow V_{m Hxc}$，从而实现对精确 Kohn-Sham 方案的可能数值逼近。与一个简单模型进行研究表明，良好训练的神经网络 $V_{m Hxc}$ 可以精确评估电荷密度和总能量，其精度超出了用于训练的模型参数范围，说明机器学习构建可以近似地封装理想的 $V_{m Hxc}$ 功能形式的属性。同时表明，一种在模型参数空间边界处具有重要限制的因素可以通过设置跨越该界限的培训参数范围来解决。该研究对于更一般的体系适用，并为数值有效的 Kohn-Sham 电位开辟了一条新的途径。