skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

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 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. Here 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 CPUs and GPUs.

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [2];  [1]; ORCiD logo [2]
  1. Univ. of Tennessee, Knoxville, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory, Oak Ridge Leadership Computing Facility (OLCF); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1407773
Alternate Identifier(s):
OSTI ID: 1407834
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 17; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

McDaniel, Tyler, D’Azevedo, Ed F., Li, Ying Wai, Wong, Kwai, and Kent, Paul R. C. Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo. United States: N. p., 2017. Web. doi:10.1063/1.4998616.
McDaniel, Tyler, D’Azevedo, Ed F., Li, Ying Wai, Wong, Kwai, & Kent, Paul R. C. Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo. United States. doi:10.1063/1.4998616.
McDaniel, Tyler, D’Azevedo, Ed F., Li, Ying Wai, Wong, Kwai, and Kent, Paul R. C. Tue . "Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo". United States. doi:10.1063/1.4998616. https://www.osti.gov/servlets/purl/1407773.
@article{osti_1407773,
title = {Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo},
author = {McDaniel, Tyler and D’Azevedo, Ed F. and Li, Ying Wai and Wong, Kwai and Kent, Paul R. C.},
abstractNote = {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 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. Here 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 CPUs and GPUs.},
doi = {10.1063/1.4998616},
journal = {Journal of Chemical Physics},
number = 17,
volume = 147,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Communication: Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule
journal, April 2016

  • Caffarel, Michel; Applencourt, Thomas; Giner, Emmanuel
  • The Journal of Chemical Physics, Vol. 144, Issue 15
  • DOI: 10.1063/1.4947093

Towards a systematic assessment of errors in diffusion Monte Carlo calculations of semiconductors: Case study of zinc selenide and zinc oxide
journal, December 2015

  • Yu, Jaehyung; Wagner, Lucas K.; Ertekin, Elif
  • The Journal of Chemical Physics, Vol. 143, Issue 22
  • DOI: 10.1063/1.4937421

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm
journal, December 2011

  • Clark, Bryan K.; Morales, Miguel A.; McMinis, Jeremy
  • The Journal of Chemical Physics, Vol. 135, Issue 24
  • DOI: 10.1063/1.3665391

Accelerating Quantum Monte Carlo Simulations of Real Materials on GPU Clusters
journal, January 2012

  • Esler, Kenneth; Kim, Jeongnim; Ceperley, David
  • Computing in Science & Engineering, Vol. 14, Issue 1
  • DOI: 10.1109/mcse.2010.122

Diffusion quantum Monte Carlo study of the equation of state and point defects in aluminum
journal, April 2012


Many-body ab initio diffusion quantum Monte Carlo applied to the strongly correlated oxide NiO
journal, October 2015

  • Mitra, Chandrima; Krogel, Jaron T.; Santana, Juan A.
  • The Journal of Chemical Physics, Vol. 143, Issue 16
  • DOI: 10.1063/1.4934262

Monte Carlo simulation of a many-fermion study
journal, October 1977


Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite TiO 2 polymorphs
journal, March 2017


Cohesive energy and structural parameters of binary oxides of groups IIA and IIIB from diffusion quantum Monte Carlo
journal, May 2016

  • Santana, Juan A.; Krogel, Jaron T.; Kent, Paul R. C.
  • The Journal of Chemical Physics, Vol. 144, Issue 17
  • DOI: 10.1063/1.4947569

Ground- and Excited-State Geometry Optimization of Small Organic Molecules with Quantum Monte Carlo
journal, November 2013

  • Guareschi, Riccardo; Filippi, Claudia
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 12
  • DOI: 10.1021/ct400876y

Phase stability of TiO 2 polymorphs from diffusion Quantum Monte Carlo
journal, November 2016


Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo
journal, May 2016

  • Filippi, Claudia; Assaraf, Roland; Moroni, Saverio
  • The Journal of Chemical Physics, Vol. 144, Issue 19
  • DOI: 10.1063/1.4948778

Discovering correlated fermions using quantum Monte Carlo
journal, August 2016


A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations
journal, May 2009

  • Nukala, Phani K. V. V.; Kent, P. R. C.
  • The Journal of Chemical Physics, Vol. 130, Issue 20
  • DOI: 10.1063/1.3142703