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Self-learning Monte Carlo method

Journal Article · · Physical Review B
 [1];  [2];  [3];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics; Massachusetts Institute of Technology
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
  3. Chinese Academy of Sciences, Beijing (China). Institute of Physics
+ Show Author Affiliations
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.
Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
Grant/Contract Number:
SC0010526
OSTI ID:
1424928
Alternate ID(s):
OSTI ID: 1338104
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 4 Vol. 95; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (22)

The Elements of Statistical Learning book January 2001
The Elements of Statistical Learning book January 2009
The Elements of Statistical Learning book January 2009
“Worm” algorithm in quantum Monte Carlo simulations journal February 1998
A Guide to Monte Carlo Simulations in Statistical Physics book January 2009
Optimization of probiotic therapeutics using machine learning in an artificial human gastrointestinal tract journal January 2021
Equation of State Calculations by Fast Computing Machines journal June 1953
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions journal August 2015
The loop algorithm journal January 2003
Monte Carlo sampling methods using Markov chains and their applications journal April 1970
Learning thermodynamics with Boltzmann machines journal October 2016
Discovering phase transitions with unsupervised learning journal November 2016
Accelerated Monte Carlo simulations with restricted Boltzmann machines journal January 2017
Quantum Monte Carlo with directed loops journal October 2002
Generalized directed loop method for quantum Monte Carlo simulations journal March 2005
Nonuniversal critical dynamics in Monte Carlo simulations journal January 1987
Collective Monte Carlo Updating for Spin Systems journal January 1989
Cluster algorithm for vertex models journal February 1993
Accelerating diffusive nonequilibrium processes in discrete spin systems journal September 1993
Equation of state calculations by fast computing machines report March 1953
Discovering Phase Transitions with Unsupervised Learning text January 2016
Generalized Directed Loop Method for Quantum Monte Carlo Simulations text January 2003

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Neural Network Renormalization Group journal December 2018
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Self-Learning Monte Carlo Method: Continuous-Time Algorithm text January 2017
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Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks text January 2017
Neural-Network Quantum States, String-Bond States, and Chiral Topological States text January 2017
Machine learning out-of-equilibrium phases of matter text January 2017
Self-learning Monte Carlo with Deep Neural Networks text January 2018
Matrix Product Operators for Sequence to Sequence Learning text January 2018
Machine learning of phase transitions in the percolation and XY models text January 2018
Identifying topological order through unsupervised machine learning text January 2018
Deep Learning Topological Invariants of Band Insulators text January 2018
Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system text January 2018
A machine-learning solver for modified diffusion equations text January 2018
Multi-faceted machine learning of competing orders in disordered interacting systems text January 2019
All Optical Neural Network with Nonlinear Activation Functions text January 2019
Flow-based generative models for Markov chain Monte Carlo in lattice field theory text January 2019
Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines text January 2019
Machine learning dynamical phase transitions in complex networks text January 2019
Learning epidemic threshold in complex networks by Convolutional Neural Network text January 2019

Figures / Tables (5)

FIG. 1(p. 3)figure FIG. 1
TABLE I(p. 3)table TABLE I
FIG. 2(p. 4)figure FIG. 2
FIG. 3(p. 4)figure FIG. 3
FIG. 4(p. 4)figure FIG. 4

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Related Subjects

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