Abstract
Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.
Original language | English |
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Article number | 174107 |
Journal | Journal of Chemical Physics |
Volume | 147 |
Issue number | 17 |
DOIs | |
State | Published - Nov 7 2017 |
Funding
Y.W.L. and computing resources were supported by the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC05-00OR22725. T.M. was sponsored by the National Science Foundation through the Research Experience for Undergraduates (REU) Award No. 1262937, with additional support from the National Institute of Computational Sciences at the University of Tennessee Knoxville. In addition, this work used allocations from the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation Grant No. ACI-1053575. P.R.C.K. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences Program and Center for Predictive Simulation of Functional Materials. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/ downloads/doe-public-access-plan). E.F.D. was supported by the U.S. Department of Energy Office of Science, Advanced Scientific Computing Research (ASCR).
Funders | Funder number |
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National Institute of Computational Sciences | |
National Science Foundation | |
U.S. Department of Energy | |
Directorate for Computer and Information Science and Engineering | 1262937, 1053575 |
Office of Science | DE-AC05-00OR22725 |
Basic Energy Sciences | |
Advanced Scientific Computing Research | |
Division of Materials Sciences and Engineering | |
University of Tennessee, Knoxville | ACI-1053575 |