Delayed update algorithms for quantum Monte Carlo simulation on GPU

Tyler McDaniel, Ed D'Azevedo, Ying Wai Li, Paul Kent, Ming Wong, Kwai Wong

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

QMCPACK is open source scientific software designed to perform Quantum Monte Carlo (QMC) simulation, a first-principles method for describing many-body systems. The evaluation of each Monte Carlo move requires finding the determinant of a dense matrix in the wave functions. This calculation forms a key computational kernel in QMCPACK. After each accepted event, the wave function matrix under-goes a rank-one update to represent a single particle move within the system. The matrix inverse is updated via the Sherman-Morrison formula; occasionally, the explicit inverse must be recomputed to maintain numerical stability. We propose an alternate approach to this kernel that uti-lizes QR factorization to maintain stability without refac-torization. In addition, algorithms based on a novel delayed update scheme are explored in this effort. This strategy en-ables probability evaluation for multiple successive Monte Carlo moves, with application of accepted moves to the wave function matrix delayed until an event is denied, or a prede-termined limit on acceptances p is reached. Accepted events grouped in this manner are then applied to the matrix en bloc with enhanced arithmetic intensity and computational efficiency. Delayed update Sherman-Morrison probability evaluation algorithms with CPU and GPU-accelerated implementations are tested, profiled, and analyzed. A QR based delayed up-date algorithm remains in development. Results are eval-uated against existing methods for numerical stability and efficiency; emphasis is placed on large systems, for which acceleration is critical.

Original languageEnglish
Title of host publicationProceedings of XSEDE 2016
Subtitle of host publicationDiversity, Big Data, and Science at Scale
PublisherAssociation for Computing Machinery
ISBN (Electronic)9781450347556
DOIs
StatePublished - Jul 17 2016
EventConference on Diversity, Big Data, and Science at Scale, XSEDE 2016 - Miami, United States
Duration: Jul 17 2016Jul 21 2016

Publication series

NameACM International Conference Proceeding Series
Volume17-21-July-2016

Conference

ConferenceConference on Diversity, Big Data, and Science at Scale, XSEDE 2016
Country/TerritoryUnited States
CityMiami
Period07/17/1607/21/16

Keywords

  • Emergent platforms
  • QMC simulation
  • Scientific computing

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