用图神经网络建模电子密度，实现高精度且可扩展的量子化学计算。
Learning Equivariant Non-Local Electron Density Functionals
- 将电子密度转为原子中心点云，用等变图网络捕捉分子尺度相互作用。
- 在MD17和QM9上相比传统方法降低35%~50%误差，训练数据效率更高。
- 适合需要高效准确力场的分子模拟研究者，尤其擅长小样本和大分子外推。
密度泛函理论的精度依赖于对交换关联（XC）泛函中非局部贡献的近似。现有机器学习与人工设计的近似存在精度不足、可扩展性差或依赖昂贵参考数据的问题。为此，我们提出基于等变图神经网络的新型非局部XC泛函——等变图交换关联（EG-XC）。不同于以往依赖半局部泛函或固定尺寸密度描述符的方法，我们将电子密度压缩为SO(3)等变的核中心点云，以高效捕捉原子尺度的非局部相互作用。通过在此点云上应用等变图网络，实现了可扩展且高精度的分子范围相互作用建模。训练EG-XC时，仅需能量目标并通过自洽场求解器反向传播。实验表明，EG-XC在MD17数据集上能准确重构‘金标准’CCSD(T)能量；在3BPA的分布外构象上，相对MAE降低35%至50%。在QM9上，其数据效率优异，表现优于在五倍更多分子及更大体系上训练的力场，相同训练集下平均MAE降低51%。
原文摘要 · Abstract (English)
The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy, limited scalability, or dependence on costly reference data. To address these issues, we introduce Equivariant Graph Exchange Correlation (EG-XC), a novel non-local XC functional based on equivariant graph neural networks (GNNs). Where previous works relied on semi-local functionals or fixed-size descriptors of the density, we compress the electron density into an SO(3)-equivariant nuclei-centered point cloud for efficient non-local atomic-range interactions. By applying an equivariant GNN on this point cloud, we capture molecular-range interactions in a scalable and accurate manner. To train EG-XC, we differentiate through a self-consistent field solver requiring only energy targets. In our empirical evaluation, we find EG-XC to accurately reconstruct `gold-standard' CCSD(T) energies on MD17. On out-of-distribution conformations of 3BPA, EG-XC reduces the relative MAE by 35% to 50%. Remarkably, EG-XC excels in data efficiency and molecular size extrapolation on QM9, matching force fields trained on 5 times more and larger molecules. On identical training sets, EG-XC yields on average 51% lower MAEs.
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