Machine learning determination of dynamical parameters:: The Ising model case

Guido Cossu; Luigi Del Debbio; Tommaso Giani; Ava Khamseh; Michael Wilson

doi:10.1103/PhysRevB.100.064304

Machine learning determination of dynamical parameters: The Ising model case

Guido Cossu, Luigi Del Debbio, Tommaso Giani, Ava Khamseh, Michael Wilson

Research output: Contribution to journal › Article › peer-review

Abstract

We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several estimators, including measurements of
the log-likelihood, with the corresponding partition functions estimated using annealed importance
sampling. The effects of various choices of hyper-parameters on training the RBM are discussed
in detail, with a generic prescription provided. Finally, we present a closed form expression for
extracting the values of couplings, for every n-point interaction between the visible nodes of an
RBM, in a binary system such as the Ising model. We aim at using this study as the foundation for
further investigations of less well-known systems.

Original language	English
Number of pages	31
Journal	Physical Review B
DOIs	https://doi.org/10.1103/PhysRevB.100.064304
Publication status	Published - 7 Aug 2019

Keywords

physics.comp-ph
cond-mat.stat-mech
hep-lat

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rbm_paper_PRB_submitted_finalAccepted author manuscript, 2.42 MB

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.064304

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Particle Theory at the Higgs Centre
Ball, R., Boyle, P., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., O'Connell, D., Smillie, J. & Zwicky, R.
STFC
1/10/17 → 30/09/21
Project: Research
High-performance computing at the high-energy frontier: results for the LHC
Del Debbio, L.
UK-based charities
1/01/15 → 31/12/19
Project: Research

Ava Khamseh
- ava.khamseh@ed.ac.uk
- MRC Human Genetics Unit
- School of Informatics - Lecturer in Biomedical Artificial Intelligence
- Institute for Adaptive and Neural Computation
Person: Academic: Research Active , Academic: Research Active (Research Assistant)

Cite this

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title = "Machine learning determination of dynamical parameters:: The Ising model case",

abstract = "We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several estimators, including measurements ofthe log-likelihood, with the corresponding partition functions estimated using annealed importancesampling. The effects of various choices of hyper-parameters on training the RBM are discussedin detail, with a generic prescription provided. Finally, we present a closed form expression forextracting the values of couplings, for every n-point interaction between the visible nodes of anRBM, in a binary system such as the Ising model. We aim at using this study as the foundation forfurther investigations of less well-known systems.",

keywords = "physics.comp-ph, cond-mat.stat-mech, hep-lat",

author = "Guido Cossu and Debbio, {Luigi Del} and Tommaso Giani and Ava Khamseh and Michael Wilson",

note = "31 pages",

year = "2019",

month = aug,

day = "7",

doi = "10.1103/PhysRevB.100.064304",

language = "English",

journal = "Physical review B: Condensed matter and materials physics",

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publisher = "American Physical Society",

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T1 - Machine learning determination of dynamical parameters:

T2 - The Ising model case

AU - Cossu, Guido

AU - Debbio, Luigi Del

AU - Giani, Tommaso

AU - Khamseh, Ava

AU - Wilson, Michael

N1 - 31 pages

PY - 2019/8/7

Y1 - 2019/8/7

N2 - We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several estimators, including measurements ofthe log-likelihood, with the corresponding partition functions estimated using annealed importancesampling. The effects of various choices of hyper-parameters on training the RBM are discussedin detail, with a generic prescription provided. Finally, we present a closed form expression forextracting the values of couplings, for every n-point interaction between the visible nodes of anRBM, in a binary system such as the Ising model. We aim at using this study as the foundation forfurther investigations of less well-known systems.

AB - We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several estimators, including measurements ofthe log-likelihood, with the corresponding partition functions estimated using annealed importancesampling. The effects of various choices of hyper-parameters on training the RBM are discussedin detail, with a generic prescription provided. Finally, we present a closed form expression forextracting the values of couplings, for every n-point interaction between the visible nodes of anRBM, in a binary system such as the Ising model. We aim at using this study as the foundation forfurther investigations of less well-known systems.

KW - physics.comp-ph

KW - cond-mat.stat-mech

KW - hep-lat

U2 - 10.1103/PhysRevB.100.064304

DO - 10.1103/PhysRevB.100.064304

M3 - Article

JO - Physical review B: Condensed matter and materials physics

JF - Physical review B: Condensed matter and materials physics

SN - 1098-0121

ER -

Machine learning determination of dynamical parameters: The Ising model case

Abstract

Keywords

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Particle Theory at the Higgs Centre

High-performance computing at the high-energy frontier: results for the LHC

Ava Khamseh

Cite this