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Journal of Chemical Theory and Computation

Performance of Coupled-Cluster Singles and Doubles on Modern Stream Processing Architectures

B. Scott Fales, Ethan R. Curtis, Katherine Grace Johnson, Dean Lahana, Stefan Seritan, Yuanheng Wang, Hayley Weir, Todd J. Martı́nez, Edward G. Hohenstein

Published Jun 20, 2020• 30 citations
Publisher

Abstract

We develop a new implementation of coupled-cluster singles and doubles (CCSD) optimized for the most recent graphical processing unit (GPU) hardware. We find that a single node with 8 NVIDIA V100 GPUs is capable of performing CCSD computations on roughly 100 atoms and 1300 basis functions in less than 1 day. Comparisons against massively parallel implementations of CCSD suggest that more than 64 CPU-based nodes (each with 16 cores) are required to match this performance.

DOI
10.1021/acs.jctc.0c00336

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We develop a new implementation of coupled-cluster singles and doubles (CCSD) optimized for the most recent graphical processing unit (GPU) hardware. We find that a single node with 8 NVIDIA V100 GPUs is capable of performing CCSD computations on roughly 100 atoms and 1300 basis functions in less than 1 day. Comparisons against massively parallel implementations of CCSD suggest that more than 64 CPU-based nodes (each with 16 cores) are required to match this performance.
A new coupled cluster singles and doubles with triples correction, CCSD(T), algorithm is presented. The new algorithm is implemented in object oriented C++, has a low memory footprint, fast execution time, low I/O overhead, and a flexible storage backend with the ability to use either distributed memory or a file system for storage. The algorithm is demonstrated to work well on single workstations, a small cluster, and a high-end Cray computer. With the new implementation, a CCSD(T) calculation with several hundred basis functions and a few dozen occupied orbitals can run in under a day on a single workstation. The algorithm has also been implemented for graphical processing unit (GPU) architecture, giving a modest improvement. Benchmarks are provided for both CPU and GPU hardware.
Abstract A high‐performance implementation of the coupled‐cluster singles, doubles, and perturbative triples [CCSD(T)] is developed in the Massively Parallel Quantum Chemistry program. Novel features include: (1) reduced memory requirements via a density‐fitting (DF) CCSD implementation utilizing distributed lazy evaluation for tensors with more than two unoccupied indices and (2) the ability to utilize efficiently many‐core nodes (Intel Xeon Phi) and heterogeneous nodes with multiple NVIDIA GPUs on each node. All data that are greater than quadratic in the system size are distributed among processes. Excellent strong scaling is observed on distributed‐memory computers equipped with conventional CPUs, Intel Xeon Phi processors, and heterogeneous nodes with multiple NVIDIA GPUs Canonical CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even larger computations possible on leadership‐class computing resources.
An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as O ( N O 2 N V 4 ), O ( N O 3 N V 3 ), and O ( N O 4 N V 2 ) (where N O and N V denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU–GPU data transfers. The performance of the hybrid CPU–GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world’s first exascale supercomputer named “Frontier”, the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4–8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16–66 carbon atoms demonstrate that the acceleration of the hybrid CPU–GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C 66 H 20 ). The GPU-offloaded code enables the computation of the perturbative triples correction for the C 60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.
We adapt an algorithm for singles and doubles coupled cluster (CCSD) that uses density fitting or Cholesky decomposition (CD) in the construction and contraction of all electron repulsion integrals (ERIs) for use on heterogeneous compute nodes consisting of a multicore central processing unit (CPU) and at least one graphics processing unit (GPU). The use of approximate three-index ERIs ameliorates two of the major difficulties in designing scientific algorithms for GPUs: (1) the extremely limited global memory on the devices and (2) the overhead associated with data motion across the bus. For the benzene trimer described by an aug-cc-pVDZ basis set, the use of a single NVIDIA Tesla C2070 (Fermi) GPU accelerates a CD-CCSD computation by a factor of 2.1, relative to the multicore CPU-only algorithm that uses six highly efficient Intel Core i7-3930K CPU cores. The use of two Fermi GPUs provides an acceleration of 2.89, which is comparable to that observed when using a single NVIDIA Kepler K20c GPU (2.73).
Coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) often provides ground state correlation energies within ″chemical accuracy", but it suffers from high computational cost and steep scaling with system size. We present a GPU-accelerated implementation of CCSD(T) in the TeraChem software package. The new implementation achieves state-of-the-art performance, enabling the calculation of the (T) correction for a system with 63 atoms and more than 1000 basis functions in a little under 8 h on a single node. Additionally, we demonstrate the utility of our optimized implementation for the rapid calculation of full CCSD(T)/CBS stacking energies for all ten unique DNA base pair stacked tetramers. We expect that the TeraChem CCSD(T) implementation will enable the rapid calculation of high-level data that was not previously accessible in a reasonable time frame.
We have developed a graphical processing unit (GPU) accelerated implementation of our recently introduced rank-reduced coupled-cluster singles and doubles (RR-CCSD) method. RR-CCSD introduces a low-rank approximation of the doubles amplitudes. This is combined with a low-rank approximation of the electron repulsion integrals via Cholesky decomposition. The result of these two low-rank approximations is the replacement of the usual fourth-order CCSD tensors with products of second- and third-order tensors. In our implementation, only a single fourth-order tensor must be constructed as an intermediate during the solution of the amplitude equations. Owing in large part to the compression of the doubles amplitudes, the GPU-accelerated implementation shows excellent parallel efficiency (95% on eight GPUs). Our implementation can solve the RR-CCSD equations for up to 400 electrons and 1550 basis functions—roughly 50% larger than the largest canonical CCSD computations that have been performed on any hardware. In addition to increased scalability, the RR-CCSD computations are faster than the corresponding CCSD computations for all but the smallest molecules. We test the accuracy of RR-CCSD for a variety of chemical systems including up to 1000 basis functions and determine that accuracy to better than 0.1% error in the correlation energy can be achieved with roughly 95% compression of the ov space for the largest systems considered. We also demonstrate that conformational energies can be predicted to be within 0.1 kcal mol−1 with efficient compression applied to the wavefunction. Finally, we find that low-rank approximations of the CCSD doubles amplitudes used in the similarity transformation of the Hamiltonian prior to a conventional equation-of-motion CCSD computation will not introduce significant errors (on the order of a few hundredths of an electronvolt) into the resulting excitation energies.