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arXiv · 1810.11503

Machine learning determination of dynamical parameters: The Ising model case

Guido Cossu·Luigi Del Debbio·Tommaso Giani·Ava Khamseh·Michael Wilson
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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.

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Guido Cossu, Luigi Del Debbio, Tommaso Giani, Ava Khamseh, Michael Wilson. 2018-10-26. Machine learning determination of dynamical parameters: The Ising model case. https://doi.org/10.1103/physrevb.100.064304

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