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

This Article presents two optimized multi-GPU algorithms for Fock matrix construction, building on the work of Ufimtsev and Martinez [J. Chem. Theory Comput. 2009, 5, 1004–1015] and Barca et al. [J. Chem. Theory Comput. 2021, 17, 7486–7503]. 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-ζ 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-ζ basis sets of 1.4×, 8.4×, and 9.4× were observed compared to TeraChem, QUICK, and GPU4PySCF respectively. An increased average speedup of 2.1× over TeraChem is observed when using four A100 GPUs. 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× and 31×, respectively, enhancing power efficiency by up to 18×.本文提出了两种针对福克矩阵（Fock matrix）构建的优化多GPU（multi-GPU）算法，其研究基础为Ufimtsev与Martinez[《化学理论与计算杂志》（Journal of Chemical Theory and Computation）2009年，第5卷，1004–1015页]以及Barca等人[《化学理论与计算杂志》2021年，第17卷，7486–7503页]的工作。本文所提出的新型算法opt-UM与opt-Brc实现了多项重要改进，包括优化的积分筛选、稀疏性与对称性利用、线性标度交换矩阵组装算法，以及支持将哈特利-福克（Hartree–Fock）计算扩展至f型角动量函数的能力。opt-Brc在小型分子体系与高收缩三重ζ基组场景下表现更优，而opt-UM则更适用于大型分子体系。在NVIDIA A100 GPU上的性能基准测试结果显示，我们集成于超大规模电子结构系统（EXtreme-scale Electronic Structure System，简称EXESS）的两款算法联合使用时，其性能优于当前所有在TeraChem、QUICK、GPU4PySCF、LibIntX、ORCA及Q-Chem中部署的GPU与CPU版福克矩阵构建实现方案。本次基准测试覆盖了线型与球状分子体系，相较于TeraChem、QUICK与GPU4PySCF，两款算法分别实现了1.4倍、8.4倍与9.4倍的平均加速比。当使用4块A100 GPU时，相较于TeraChem的平均加速比提升至2.1倍。强缩放分析表明，opt-Brc在4块GPU上的并行效率超过91%，使其在多GPU执行场景下通常更快。与基于CPU的ORCA、Q-Chem等软件进行单计算节点对比时，本方案的最大加速比分别可达42倍与31倍，能效提升最高可达18倍。