Self-learning Monte Carlo method

Liu, Junwei; Qi, Yang; Meng, Zi Yang; Fu, Liang

doi:10.1103/PhysRevB.95.041101

Title: Self-learning Monte Carlo method

Abstract

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. Lastly, we demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10–20 times speedup.

Authors:

Liu, Junwei ^[1]; Qi, Yang ^[1]; Meng, Zi Yang ^[2]; Fu, Liang ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
Chinese Academy of Sciences, Beijing (China). Institute of Physics

Publication Date:: 2017-01-04

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

OSTI Identifier:: 1424928

Alternate Identifier(s):: OSTI ID: 1338104

Grant/Contract Number:: SC0010526

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 95; Journal Issue: 4; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Ising model; Machine learning; Markoavian processes; Monte Carlo methods; Stochastic analysis

Citation Formats


                    Liu, Junwei, Qi, Yang, Meng, Zi Yang, and Fu, Liang. Self-learning Monte Carlo method.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevB.95.041101.

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                    Liu, Junwei, Qi, Yang, Meng, Zi Yang, & Fu, Liang. Self-learning Monte Carlo method.  United States.  https://doi.org/10.1103/PhysRevB.95.041101

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                    Liu, Junwei, Qi, Yang, Meng, Zi Yang, and Fu, Liang. Wed .  
"Self-learning Monte Carlo method".  United States.  https://doi.org/10.1103/PhysRevB.95.041101.  https://www.osti.gov/servlets/purl/1424928.

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@article{osti_1424928,

  title        = {Self-learning Monte Carlo method},

  author       = {Liu, Junwei and Qi, Yang and Meng, Zi Yang and Fu, Liang},

  abstractNote = {Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. Lastly, we demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10–20 times speedup.},

  doi          = {10.1103/PhysRevB.95.041101},

  journal      = {Physical Review B},

  number       = 4,

  volume       = 95,

  place        = {United States},

  year         = {2017},

  month        = {1}

}

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Cited by: 23 works

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Figures / Tables:

FIG. 1: Schematic illustration of the learning process (top panel) and simulating process (bottom panel) in self-learning Monte Carlo.

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