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 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.

arXiv comment31 pages

References in corpus (4)

• A nonequilibrium equality for free energy differences
• A high-bias, low-variance introduction to Machine Learning for physicists
• Learning Thermodynamics with Boltzmann Machines
• Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow

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