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 hyperparameters 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.