Qin Xinming, Li Jielan, Hu Wei, Yang Jinlong
Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
J Phys Chem A. 2020 Dec 3;124(48):10066-10074. doi: 10.1021/acs.jpca.0c06019. Epub 2020 Nov 17.
The interpolative separable density fitting (ISDF) is an efficient and accurate low-rank decomposition method to reduce the high computational cost and memory usage of the Hartree-Fock exchange (HFX) calculations with numerical atomic orbitals (NAOs). In this work, we present a machine learning K-means clustering algorithm to select the interpolation points in ISDF, which offers a much cheaper alternative to the expensive QR factorization with column pivoting (QRCP) procedure. We implement this K-means-based ISDF decomposition to accelerate hybrid functional calculations with NAOs in the HONPAS package. We demonstrate that this method can yield a similar accuracy for both molecules and solids at a much lower computational cost. In particular, K-means can remarkably reduce the computational cost of selecting the interpolation points by nearly two orders of magnitude compared to QRCP, resulting in a speedup of ∼10 times for ISDF-based HFX calculations.
插值可分离密度拟合（ISDF）是一种高效且准确的低秩分解方法，用于降低使用数值原子轨道（NAO）进行哈特里 - 福克交换（HFX）计算时的高计算成本和内存使用量。在这项工作中，我们提出了一种机器学习K均值聚类算法来选择ISDF中的插值点，它为使用列主元QR分解（QRCP）过程这种昂贵方法提供了一种成本低得多的替代方案。我们在HONPAS软件包中实现了这种基于K均值的ISDF分解，以加速使用NAO的杂化泛函计算。我们证明，该方法在计算成本低得多的情况下，对分子和固体都能产生相似的精度。特别是，与QRCP相比，K均值可以将选择插值点的计算成本显著降低近两个数量级，从而使基于ISDF的HFX计算加速约10倍。
