Kohn-Sham density functional theory (KS-DFT) has found widespread application
in accurate electronic structure calculations. However, it can be
computationally demanding especially for large-scale simulations, motivating
recent efforts toward its machine-learning (ML) acceleration. We propose a
neural network self-consistent fields (NeuralSCF) framework that establishes
the Kohn-Sham density map as a deep learning objective, which encodes the
mechanics of the Kohn-Sham equations. Modeling this map with an
SE(3)-equivariant graph transformer, NeuralSCF emulates the Kohn-Sham
self-consistent iterations to obtain electron densities, from which other
properties can be derived. NeuralSCF achieves state-of-the-art accuracy in
electron density prediction and derived properties, featuring exceptional
zero-shot generalization to a remarkable range of out-of-distribution systems.
NeuralSCF reveals that learning from KS-DFT's intrinsic mechanics significantly
enhances the model's accuracy and transferability, offering a promising
stepping stone for accelerating electronic structure calculations through
mechanics learning.

通过机械学习加速，我们提出了一种神经网络自洽场 (NeuralSCF) 框架，其以 Kohn-Sham 密度 (density) 映射为深度学习目标，模拟了 Kohn-Sham 方程的自洽迭代，获得电子密度并衍生其他性质，从而在电子密度预测和衍生性质上实现了最先进的准确度，并在分布外系统上具有出色的零样本泛化能力，表明从 KS-DFT 的内在机理中学习明显提高了模型的准确性和可转移性，为通过机械学习加速电子结构计算提供了有希望的基石。

神经 SCF：用于密度泛函理论的神经网络自洽场

NeuralSCF: Neural network self-consistent fields for density functional  theory

This work studies machine learning for electron density prediction, which is
fundamental for understanding chemical systems and density functional theory
(DFT) simulations. To this end, we introduce the Gaussian plane-wave neural
operator (GPWNO), which operates in the infinite-dimensional functional space
using the plane-wave and Gaussian-type orbital bases, widely recognized in the
context of DFT. In particular, both high- and low-frequency components of the
density can be effectively represented due to the complementary nature of the
two bases. Extensive experiments on QM9, MD, and material project datasets
demonstrate GPWNO's superior performance over ten baselines.

通过引入高斯平面波神经算子 (GPWNO)，本研究探讨了机器学习用于电子密度预测的方法，该方法对理解化学系统和密度泛函理论 (DFT) 模拟是基本重要的。经过对 QM9，MD 和材料项目数据集的广泛实验，表明 GPWNO 相对于其他十个基准模型具有出色的性能。