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Enabling new capabilities for QMC using HPC without sacrificing developer productivity.

Luke Shulenburger

Published Jul 24, 2020• 0 citations
OpenAlex

Abstract

SAND2019-7114CThis paper describes objective technical results and analysis.Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.How do we currently address scaling?Current parallelization strategy relies on distributing walkers among processing elements Highly scalable algorithm, as demonstrated on Sequoia at LLNL Nearly perfect parallel efficiency in moving walkers to over 1.5M cores It appears possible to achieve performance portability within a single code base Can use the same framework to achieve parallel algorithms that are suitable for both GPUs and CPUs Work of this nature can allow codes to take advantage of new classes of hardware without requiring developers to learn new frameworks each time

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SAND2019-7114CThis paper describes objective technical results and analysis.Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.How do we currently address scaling?Current parallelization strategy relies on distributing walkers among processing elements Highly scalable algorithm, as demonstrated on Sequoia at LLNL Nearly perfect parallel efficiency in moving walkers to over 1.5M cores It appears possible to achieve performance portability within a single code base Can use the same framework to achieve parallel algorithms that are suitable for both GPUs and CPUs Work of this nature can allow codes to take advantage of new classes of hardware without requiring developers to learn new frameworks each time
High-Performance Computing (HPC) has historically served as the primary engine for scientific advancement, enabling complex simulations ranging from meteorological prediction to protein folding or drug discovery. For decades, the exponential growth in computational power was sustained by the empirical axioms of Moore’s Law and Dennard scaling. However, in the last decade, these principles have begun to exhibit unambiguous signs of saturation. The fundamental physical, thermodynamic, and quantum limitations of silicon transistors have compelled the industry to abandon frequency scaling in favor of massive parallelism and architectural heterogeneity. Consequently, contemporary top-tier supercomputers are no longer homogeneous machines, but complex clusters that integrate multicore Central Processing Units (CPU) with specialized accelerators such as Graphics Processing Units (GPU) or FPGAs.
In the Monte Carlo second-order many-body perturbation (MC-MP2) method, the long sum-of-product matrix expression of the MP2 energy, whose literal evaluation may be poorly scalable, is recast into a single high-dimensional integral of functions of electron pair coordinates, which is evaluated by the scalable method of Monte Carlo integration. The sampling efficiency is further accelerated by the redundant-walker algorithm, which allows a maximal reuse of electron pairs. Here, a multitude of graphical processing units (GPUs) offers a uniquely ideal platform to expose multilevel parallelism: fine-grain data-parallelism for the redundant-walker algorithm in which millions of threads compute and share orbital amplitudes on each GPU; coarse-grain instruction-parallelism for near-independent Monte Carlo integrations on many GPUs with few and infrequent interprocessor communications. While the efficiency boost by the redundant-walker algorithm on central processing units (CPUs) grows linearly with the number of electron pairs and tends to saturate when the latter exceeds the number of orbitals, on a GPU it grows quadratically before it increases linearly and then eventually saturates at a much larger number of pairs. This is because the orbital constructions are nearly perfectly parallelized on a GPU and thus completed in a near-constant time regardless of the number of pairs. In consequence, an MC-MP2/cc-pVDZ calculation of a benzene dimer is 2700 times faster on 256 GPUs (using 2048 electron pairs) than on two CPUs, each with 8 cores (which can use only up to 256 pairs effectively). We also numerically determine that the cost to achieve a given relative statistical uncertainty in an MC-MP2 energy increases as O ( n 3 ) or better with system size n, which may be compared with the O ( n 5 ) scaling of the conventional implementation of deterministic MP2. We thus establish the scalability of MC-MP2 with both system and computer sizes.