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 journalArticlepeer-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 languageEnglish
Number of pages31
JournalPhysical Review B
DOIs
Publication statusPublished - 7 Aug 2019

Keywords

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

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