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Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
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A Mixed-Precision Approach to a Preconditioned Eigensolver for Efficient Density Functional Calculations on

Jeheon Woo1, Sunghwan Choi2

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This summary is machine-generated.

This study introduces a mixed precision approach for density functional theory (DFT) calculations, enabling faster simulations on AI-focused GPUs. The method preserves accuracy while significantly boosting computational speed and system size capacity.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • High-Performance Computing

Background:

  • Graphics Processing Units (GPUs) have advanced computational chemistry.
  • AI-focused GPUs are inefficient with double-precision (FP64) quantum chemistry operations.
  • Limited GPU memory requires algorithmic adaptations for Density Functional Theory (DFT).

Purpose of the Study:

  • To develop a mixed precision strategy for iterative matrix diagonalization in real-space DFT.
  • To maintain numerical accuracy while improving computational efficiency on GPUs.
  • To enable larger-scale electronic structure simulations and broaden GPU applicability.

Main Methods:

  • Implemented a systematic mixed precision strategy for matrix diagonalization.
  • Utilized single-precision (FP32) and Brain Floating Point (BF16) arithmetic.
  • Developed and validated a mixed precision eigensolver across diverse material systems.

Main Results:

  • Achieved up to 10x speedup in diagonalization compared to FP64.
  • Extended feasible system size by approximately 50%.
  • Demonstrated comparable performance of AI-focused GPUs to HPC-focused GPUs.

Conclusions:

  • Mixed precision strategy preserves numerical accuracy in DFT calculations.
  • AI-focused GPUs can be effectively utilized for large-scale electronic structure simulations.
  • The developed method enhances accessibility to advanced computational chemistry tools.