Machine Learning K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Accurate and Efficient...

Area of Science:

• Computational Chemistry and Materials Science
• Quantum Mechanical Simulations
• Electronic Structure Theory

Background:

• The exact-exchange plus random-phase approximation (EXX+RPA) method is vital for electronic structure characterization in molecules and solids.
• Conventional EXX+RPA implementations face computational challenges, particularly with plane wave basis sets and interpolative separable density fitting (ISDF) algorithms.
• The QRCP algorithm, used in ISDF, has a high prefactor for interpolation point selection, limiting computational efficiency.

Purpose of the Study:

• To develop an accurate and efficient implementation of EXX+RPA calculations using plane waves.
• To mitigate computational bottlenecks in ISDF by introducing an enhanced machine learning K-means method for interpolation point selection.
• To improve the overall computational scaling and accelerate EXX+RPA calculations, including GPU optimization.

Main Methods:

• Implemented EXX+RPA calculations with a cubic scaling approach within a plane wave basis set.
• Integrated the interpolative separable density fitting (ISDF) algorithm.
• Introduced a machine learning K-means method with a novel 'SSM+' weight function for improved interpolation point selection, replacing the cubic-scaling QRCP algorithm with a quasiquadratic scaling alternative.
• Optimized GPU acceleration using MATLAB's integrated GPU toolkit.

Main Results:

• Reduced computational scaling of the dielectric function (χ0) from 3.80 to 2.13 and overall EXX scaling from 2.74 to 2.10.
• Achieved up to 35× GPU acceleration speedup.
• Demonstrated significant CPU time reductions: K-means reduced computation time for Si128 from 22 h (standard) to 800 s (100× improvement), and QRCP interpolative point calculation time from 1 h to 1 min (55× speed increase).
• Successfully computed the H2 dissociation curve and C18 polyynic geometry.

Conclusions:

• The developed machine learning-enhanced EXX+RPA method offers a computationally efficient and accurate approach for electronic structure calculations.
• The quasiquadratic scaling and GPU acceleration provide substantial speedups, making complex calculations more feasible.
• This improved methodology enables the study of larger and more complex molecular and solid systems.