Complex-Valued K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Large-Scale Hybrid...

Area of Science:

• Computational Chemistry
• Materials Science
• Machine Learning

Background:

• K-means clustering is vital for interpolative separable density fitting (ISDF) in electronic structure calculations.
• Existing methods using real-valued K-means are effective but limited for complex-valued orbitals.
• Accelerating large-scale hybrid ab initio molecular dynamics (hybrid AIMD) simulations is crucial.

Purpose of the Study:

• To adapt K-means clustering for complex-valued Kohn-Sham orbitals in hybrid AIMD simulations.
• To improve the accuracy and efficiency of ISDF decomposition.
• To enable larger and more complex molecular dynamics simulations.

Main Methods:

• Proposed an improved weight function for K-means clustering using the sum of the square modulus of complex-valued orbitals.
• Applied the enhanced K-means algorithm to ISDF decomposition in hybrid AIMD.
• Implemented a massively parallel version for large-scale simulations.

Main Results:

• The new weight function yields smoother interpolation points, leading to more stable energy potentials and longer simulation time steps.
• Achieved more accurate oxygen-oxygen radial distribution functions in liquid water and improved power spectrum in silicon dioxide.
• Demonstrated scalability for simulations with thousands of atoms on supercomputers.

Conclusions:

• The improved K-means clustering method effectively handles complex-valued orbitals in hybrid AIMD.
• This advancement accelerates large-scale electronic structure calculations with enhanced accuracy.
• The parallel implementation facilitates simulations of complex systems previously out of reach.