Advanced Techniques for High-Performance Fock Matrix Construction on GPU Clusters

TL;DR

This paper introduces two optimized multi-GPU algorithms, opt-UM and opt-Brc, for efficient Fock matrix construction in electronic structure calculations, achieving significant speedups and scalability improvements over existing methods.

Contribution

The paper presents novel multi-GPU algorithms that enhance Fock matrix construction by exploiting sparsity, symmetry, and linear scaling, extending capabilities to higher angular momentum functions.

Findings

Algorithms outperform existing GPU and CPU implementations in speed.

Achieve up to 8.5× speedup on benchmark systems.

Maintain over 91% parallel efficiency on four GPUs.

Abstract

This Article presents two optimized multi-GPU algorithms for Fock matrix construction, building on the work of Ufimtsev et al. and Barca et al. The novel algorithms, opt-UM and opt-Brc, introduce significant enhancements, including improved integral screening, exploitation of sparsity and symmetry, a linear scaling exchange matrix assembly algorithm, and extended capabilities for Hartree-Fock caculations up to $f$-type angular momentum functions. Opt-Brc excels for smaller systems and for highly contracted triple-$\zeta$ basis sets, while opt-UM is advantageous for large molecular systems. Performance benchmarks on NVIDIA A100 GPUs show that our algorithms in the EXtreme-scale Electronic Structure System (EXESS), when combined, outperform all current GPU and CPU Fock build implementations in TeraChem, QUICK, GPU4PySCF, LibIntX, ORCA, and Q-Chem. The implementations were benchmarked on linear and globular systems and average speed ups across three double-$\zeta$ basis sets of 1.5$\times$, 5.2$\times$, and 8.5$\times$ were observed compared to TeraChem, GPU4PySCF, and QUICK respectively. Strong scaling analysis reveals over 91% parallel efficiency on four GPUs for opt-Brc, making it typically faster for multi-GPU execution. Single-compute-node comparisons with CPU-based software like ORCA and Q-Chem show speedups of up to 42$\times$ and 31$\times$, respectively, enhancing power efficiency by up to 18$\times$.