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K-means clustering, as a classic unsupervised machine learning algorithm, isthe key step to select the interpolation sampling points in interpolativeseparable density fitting (ISDF) decomposition. Real-valued K-means clusteringfor accelerating the ISDF decomposition has been demonstrated for large-scalehybrid functional enabled \textit{ab initio} molecular dynamics (hybrid AIMD)simulations within plane-wave basis sets where the Kohn-Sham orbitals arereal-valued. However, it is unclear whether such K-means clustering works forcomplex-valued Kohn-Sham orbitals. Here, we apply the K-means clustering intohybrid AIMD simulations for complex-valued Kohn-Sham orbitals and use animproved weight function defined as the sum of the square modulus ofcomplex-valued Kohn-Sham orbitals in K-means clustering. Numerical resultsdemonstrate that this improved weight function in K-means clustering algorithmyields smoother and more delocalized interpolation sampling points, resultingin smoother energy potential, smaller energy drift and longer time steps forhybrid AIMD simulations compared to the previous weight function used in thereal-valued K-means algorithm. In particular, we find that this improvedalgorithm can obtain more accurate oxygen-oxygen radial distribution functionsin liquid water molecules and more accurate power spectrum in crystal silicondioxide compared to the previous K-means algorithm. Finally, we describe amassively parallel implementation of this ISDF decomposition to acceleratelarge-scale complex-valued hybrid AIMD simulations containing thousands ofatoms (2,744 atoms), which can scale up to 5,504 CPU cores on modernsupercomputers.

Complex-valued K-means clustering of interpolative separable density  fitting algorithm for large-scale hybrid functional enabled \textit{ab  initio} molecular dynamics simulations within plane waves