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Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and

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A new machine learning K-means algorithm accelerates density functional perturbation theory (DFPT) calculations. This method improves convergence and reduces computational cost for lattice dynamics simulations.

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Area of Science:

  • Computational materials science
  • Condensed matter physics
  • Quantum chemistry

Background:

  • Density functional perturbation theory (DFPT) is essential for lattice dynamics.
  • The adaptively compressed polarizability (ACP) method optimizes DFPT, reducing complexity.
  • Current methods like QR factorization with column pivoting (QRCP) for interpolative separable density fitting (ISDF) are computationally expensive (O(N^3)) and can have convergence issues.

Purpose of the Study:

  • To develop a more efficient and accurate method for selecting interpolation points in ISDF for ACP-based DFPT.
  • To reduce the computational cost and improve convergence in DFPT calculations.

Main Methods:

  • Implemented a machine learning K-means clustering algorithm for ISDF point selection.
  • Integrated the K-means-ISDF algorithm into the KSSOLV MATLAB toolbox for plane-wave DFPT.
  • Compared the K-means approach with the conventional QRCP algorithm.

Main Results:

  • The K-means algorithm achieves quadratic scaling (O(N^2)), significantly outperforming QRCP's cubic scaling (O(N^3)).
  • K-means demonstrated comparable accuracy to QRCP in ISDF.
  • The K-means approach led to improved convergence in ACP-based DFPT calculations.
  • Computational cost for interpolation point selection was reduced by nearly two orders of magnitude.

Conclusions:

  • The K-means clustering algorithm offers a computationally efficient and accurate alternative for ISDF in DFPT.
  • This method enhances the performance of ACP-based DFPT, particularly for complex systems.
  • The K-means approach represents a significant advancement in accelerating materials simulations.