用于电子密度预测的等变流匹配

中文摘要 AI 辅助

机器学习代理模型已被越来越多地用于降低密度泛函理论（DFT）计算成本，以替代第一性原理计算。在该领域中，预测实空间电子密度可为自洽场（SCF）过程提供可扩展且可迁移的初始化。然而，当前方法面临一个明显的困境：基于网格的架构计算成本高昂，而基组方法无法捕捉系数空间中固有的结构相关性。为此，我们开发了OrbFlow，一种SE(3)等变生成模型，通过流匹配预测高斯型轨道（GTO）系数。OrbFlow保留了紧凑的原子中心基组的效率，同时用在整个系数空间上学习的概率路径替代逐点回归。它通过两阶段轨迹课程进行训练，以减轻数值积分过程中的离散化漂移。OrbFlow在QM9上达到了最先进的精度，与先前最佳模型相比，密度误差降低了13.6%，并且在MD基准的每个分子上，与共享其基组的最强先前方法相比，误差降低了51%至63%。预测的密度还将SCF迭代次数最多减少了68%，并可零样本迁移到未见过的交换关联泛函，且无需任何SCF计算即可恢复偶极矩和四极矩，精度在DFT参考值的百分之几以内。

英文摘要

Machine learning surrogates for density functional theory (DFT) have been increasingly used to reduce the cost of first-principles calculations. In this arena, predicting real-space electron densities offers a scalable and transferable initialization for self-consistent field (SCF) procedures. However, current methods face a clear dilemma. That is, grid-based architectures incur a high computational cost, while basis-set methods fail to capture the structural correlations inherent in the coefficient space. Here, we develop OrbFlow, an $\mathrm{SE}(3)$-equivariant generative model that predicts Gaussian-type orbital (GTO) coefficients via flow matching. OrbFlow retains the efficiency of a compact atom-centered basis while replacing pointwise regression with a learned probability path over the full coefficient space. It is trained through a two-phase trajectory curriculum that mitigates discretization drift during numerical integration. OrbFlow achieves state-of-the-art accuracy on QM9, reducing density error by 13.6% relative to the previous best model, and reduces error by 51% to 63% on every molecule of the MD benchmark relative to the strongest prior method sharing its basis. The predicted density also cuts SCF iterations by up to 68% with zero-shot transfer to unseen exchange-correlation functionals and recovers dipole and quadrupole moments to within a few percent of DFT references without any SCF calculation.

发表机构

• Texas A&M University（德克萨斯农工大学）

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