Flow-based generative models for Markov chain Monte Carlo in lattice field theory
Abstract
A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution approximating the desired Boltzmann distribution determined by the lattice action of the theory being studied. Training the model systematically improves autocorrelation times in the Markov chain, even in regions of parameter space where standard Markov chain Monte Carlo algorithms exhibit critical slowing down in producing decorrelated updates. Moreover, the model may be trained without existing samples from the desired distribution. The algorithm is compared with HMC and local Metropolis sampling for Φ4 theory in two dimensions.
- Authors:
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)
- OSTI Identifier:
- 1558693
- Alternate Identifier(s):
- OSTI ID: 1611585; OSTI ID: 1635370
- Grant/Contract Number:
- SC0011090; AC02-06CH11357; SC0018121; PHY-1748958
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Astronomy & Astrophysics; Physics; lattice QCD; lattice field theory; machine learning; Monte Carlo methods
Citation Formats
Albergo, M. S., Kanwar, G., and Shanahan, P. E. Flow-based generative models for Markov chain Monte Carlo in lattice field theory. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.034515.
Albergo, M. S., Kanwar, G., & Shanahan, P. E. Flow-based generative models for Markov chain Monte Carlo in lattice field theory. United States. https://doi.org/10.1103/PhysRevD.100.034515
Albergo, M. S., Kanwar, G., and Shanahan, P. E. Thu .
"Flow-based generative models for Markov chain Monte Carlo in lattice field theory". United States. https://doi.org/10.1103/PhysRevD.100.034515.
@article{osti_1558693,
title = {Flow-based generative models for Markov chain Monte Carlo in lattice field theory},
author = {Albergo, M. S. and Kanwar, G. and Shanahan, P. E.},
abstractNote = {A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution approximating the desired Boltzmann distribution determined by the lattice action of the theory being studied. Training the model systematically improves autocorrelation times in the Markov chain, even in regions of parameter space where standard Markov chain Monte Carlo algorithms exhibit critical slowing down in producing decorrelated updates. Moreover, the model may be trained without existing samples from the desired distribution. The algorithm is compared with HMC and local Metropolis sampling for Φ4 theory in two dimensions.},
doi = {10.1103/PhysRevD.100.034515},
journal = {Physical Review D},
number = 3,
volume = 100,
place = {United States},
year = {Thu Aug 22 00:00:00 EDT 2019},
month = {Thu Aug 22 00:00:00 EDT 2019}
}
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https://doi.org/10.1103/PhysRevD.100.034515
https://doi.org/10.1103/PhysRevD.100.034515
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Cited by: 62 works
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Figures / Tables:
FIG. 1: In (a), a normalizing flow is shown transforming samples z from a prior distribution r(z) to samples ϕ distributed according to p̃$\mathcal{f}$(ϕ). The mapping $\mathcal{f}$−1(z) is constructed by composing inverse coupling layers $g^{−1}_{i}$ as defined in Eq. (10) in terms of neural networks si and ti and shownmore »
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