Equivariant Flow-Based Sampling for Lattice Gauge Theory

Kanwar, Gurtej; Albergo, Michael S.; Boyda, Denis; Cranmer, Kyle; Hackett, Daniel C.; Racanière, Sébastien; Rezende, Danilo Jimenez; Shanahan, Phiala E.

doi:10.1103/physrevlett.125.121601

Title: Equivariant Flow-Based Sampling for Lattice Gauge Theory

Abstract

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that, at small bare coupling, the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as hybrid Monte Carlo and heat bath.

Authors:

;

; Cranmer, Kyle;

; Racanière, Sébastien;

; Shanahan, Phiala E.

Publication Date:: Tue Sep 15 00:00:00 EDT 2020

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Argonne National Laboratory (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility (ALCF)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)

OSTI Identifier:: 1661702

Alternate Identifier(s):: OSTI ID: 1713189

Grant/Contract Number:: SC0011090; AC02-06CH11357; 1841699; ACI-1450310; OAC-1836650; OAC-1841471

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 125 Journal Issue: 12; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice QCD; gauge symmetries; lattice field theory; lattice gauge theory; lattice models in condensed matter

Citation Formats


                    Kanwar, Gurtej, Albergo, Michael S., Boyda, Denis, Cranmer, Kyle, Hackett, Daniel C., Racanière, Sébastien, Rezende, Danilo Jimenez, and Shanahan, Phiala E. Equivariant Flow-Based Sampling for Lattice Gauge Theory.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevlett.125.121601.

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                    Kanwar, Gurtej, Albergo, Michael S., Boyda, Denis, Cranmer, Kyle, Hackett, Daniel C., Racanière, Sébastien, Rezende, Danilo Jimenez, & Shanahan, Phiala E. Equivariant Flow-Based Sampling for Lattice Gauge Theory.  United States.  https://doi.org/10.1103/physrevlett.125.121601

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                    Kanwar, Gurtej, Albergo, Michael S., Boyda, Denis, Cranmer, Kyle, Hackett, Daniel C., Racanière, Sébastien, Rezende, Danilo Jimenez, and Shanahan, Phiala E. Tue .  
"Equivariant Flow-Based Sampling for Lattice Gauge Theory".  United States.  https://doi.org/10.1103/physrevlett.125.121601.

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@article{osti_1661702,

  title        = {Equivariant Flow-Based Sampling for Lattice Gauge Theory},

  author       = {Kanwar, Gurtej and Albergo, Michael S. and Boyda, Denis and Cranmer, Kyle and Hackett, Daniel C. and Racanière, Sébastien and Rezende, Danilo Jimenez and Shanahan, Phiala E.},

  abstractNote = {We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that, at small bare coupling, the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as hybrid Monte Carlo and heat bath.},

  doi          = {10.1103/physrevlett.125.121601},

  journal      = {Physical Review Letters},

  number       = 12,

  volume       = 125,

  place        = {United States},

  year         = {Tue Sep 15 00:00:00 EDT 2020},

  month        = {Tue Sep 15 00:00:00 EDT 2020}

}

Copy to clipboard

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Title: Equivariant Flow-Based Sampling for Lattice Gauge Theory

Abstract

Citation Formats

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Topological order, emergent gauge fields, and Fermi surface reconstruction journal, November 2018

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Neural Canonical Transformation with Symplectic Flows journal, April 2020

Kaon B -parameter from quenched domain-wall QCD journal, May 2006

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Meron-Cluster Simulation of the θ Vacuum in the 2D O(3) Model journal, December 1995

Worm Algorithms for Classical Statistical Models journal, September 2001

A Model of Leptons journal, November 1967

Testing the event-chain algorithm in asymptotically free models
journal, September 2018

Recent Developments of World-Line Monte Carlo Methods
journal, June 2004

Hybrid Monte Carlo
journal, September 1987

Diffusion of topological charge in lattice QCD simulations
journal, October 2014

Trivializing Maps, the Wilson Flow and the HMC Algorithm
journal, November 2009

Testing trivializing maps in the Hybrid Monte Carlo algorithm
journal, October 2011

Solving Statistical Mechanics Using Variational Autoregressive Networks
journal, February 2019

Topological properties of CPN − 1 models in the large-N limit
journal, January 2019

Fighting topological freezing in the two-dimensional $C P^{N - 1}$ model
journal, September 2017

Confinement and the Critical Dimensionality of Space-Time
journal, August 1979

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk
journal, January 1988

Spin and Unitary-Spin Independence in a Paraquark Model of Baryons and Mesons
journal, November 1964

New Monte Carlo technique for studying phase transitions
journal, December 1988

Gauge Invariance and Mass. II
journal, December 1962

Langevin simulations of configurations with static charges
journal, September 1985

Nonuniversal critical dynamics in Monte Carlo simulations
journal, January 1987

Weak and electromagnetic interactions
book, May 1994

Dual simulation of the two-dimensional lattice U(1) gauge-Higgs model with a topological term
journal, December 2015

Topological order, emergent gauge fields, and Fermi surface reconstruction
journal, November 2018

A new method for updating SU(N) matrices in computer simulations of gauge theories
journal, December 1982

Exploring cluster Monte Carlo updates with Boltzmann machines
journal, November 2017

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journal, August 1965

Regressive and generative neural networks for scalar field theory
journal, July 2019

Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning
journal, September 2019

Accelerated Monte Carlo simulations with restricted Boltzmann machines
journal, January 2017

Targeted Adversarial Learning Optimized Sampling
journal, September 2019

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Duality in field theory and statistical systems
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An introduction to lattice gauge theory and spin systems
journal, October 1979

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journal, October 1974

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A duality web in $2 + 1$ dimensions and condensed matter physics
journal, November 2016

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journal, December 2018

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journal, May 2020

Lattice Methods for Quantum Chromodynamics
book, September 2006

Collective Monte Carlo Updating for Spin Systems
journal, January 1989

Confinement and the Critical Dimensionality of Space-Time.
journal, September 1979

Neural Canonical Transformation with Symplectic Flows
journal, April 2020

Kaon $B$ -parameter from quenched domain-wall QCD
journal, May 2006

Simulations without critical slowing down
journal, April 1988

Critical slowing down
journal, September 1990

Geometric algorithm for abelian-gauge models
journal, August 2009

Cluster algorithm for two-dimensional U(1) lattice gauge theory
journal, March 1992

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conference, June 2010

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