[论文解读] SE(3)-equivariant prediction of molecular wavefunctions and electronic densities

Oliver T. Unke, Mihail Bogojeski+4 more|arXiv (Cornell University)|Jun 4, 2021

Machine Learning in Materials Science参考文献 29被引用 25

一句话总结

PhiSNet 学习 SE(3)-等变波函数和电子密度，以端到端方式导出观测量，相较于从头计算方法取得巨大的准确度提升和显著的加速，并成功实现对更高层理论的迁移学习。

ABSTRACT

Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent approaches attempt to learn the electronic wavefunction (or density) as a central quantity of atomistic systems, from which all other observables can be derived. This is complicated by the fact that wavefunctions transform non-trivially under molecular rotations, which makes them a challenging prediction target. To solve this issue, we introduce general SE(3)-equivariant operations and building blocks for constructing deep learning architectures for geometric point cloud data and apply them to reconstruct wavefunctions of atomistic systems with unprecedented accuracy. Our model achieves speedups of over three orders of magnitude compared to ab initio methods and reduces prediction errors by up to two orders of magnitude compared to the previous state-of-the-art. This accuracy makes it possible to derive properties such as energies and forces directly from the wavefunction in an end-to-end manner. We demonstrate the potential of our approach in a transfer learning application, where a model trained on low accuracy reference wavefunctions implicitly learns to correct for electronic many-body interactions from observables computed at a higher level of theory. Such machine-learned wavefunction surrogates pave the way towards novel semi-empirical methods, offering resolution at an electronic level while drastically decreasing computational cost. Additionally, the predicted wavefunctions can serve as initial guess in conventional ab initio methods, decreasing the number of iterations required to arrive at a converged solution, thus leading to significant speedups without any loss of accuracy or robustness.

研究动机与目标

• 以预测分子波函数（而非固定属性）来按需导出观测量为动机。
• 为几何点云开发 SE(3)-等变神经构件，以预测哈密顿量。
• 构建 PhiSNet，使其输出具有精确旋转等变性的哈密顿量矩阵。
• 展示与先前最先进方法的准确性和效率提升。
• 展示从低级到高级量子化学数据的迁移学习路径。

提出的方法

• 为点云上的深度学习引入 SE(3)-等变运算。
• 构建 PhiSNet，使其从等变的原子表示输出哈密顿量块。
• 使用张量积展开和 Clebsch-Gordan 系数在哈密顿量块中强制等变性。
• 通过分块组装预测哈密顿量的对角和非对角块。
• 在 DFT (PBE/def2-SVP) 的 KS/重叠矩阵上训练，并与 SchNOrb 进行比较。
• 通过对 HF 推导的模型进行微调以预测 CCSD(T) 观测值来展示迁移学习。

实验结果

研究问题

• RQ1 SE(3)-等变神经网络结构是否能够准确预测分子波函数和电子密度？
• RQ2 直接预测哈密顿量是否能够实现能量和力的端到端高精度推导？
• RQ3 与先前的最先进（SchNOrb）及从头计算方法相比，能达到何种精度和速度提升？
• RQ4 在低级理论上预训练的模型能否经微调捕捉到高级电子相关效应？
• RQ5 预测的波函数是否可作为有效的初始猜测，以加速传统量子化学计算？

主要发现

• PhiSNet 在多种分子中相对于 SchNOrb，在 K、S、ε、ψ 的预测误差上实现高达两个数量级的降低。
• PhiSNet 相对于从头的 DFT 计算在速度上超过三个数量级。
• 该模型保持严格的 SE(3) 等变性，所需参数更少、收敛速度比非等变对手更快。
• 迁移学习使得 HF 级模型通过学习哈密顿量修正而被修正到 CCSD(T) 级观测值。
• 预测的波函数可实现能量和力的端到端推导，并可作为加速传统量子化学方法的良好初始猜测。