Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
This addresses efficiency issues in computational physics simulations, though it is an incremental application of existing machine learning techniques to a specific domain.
The paper tackled slow mixing times in Monte Carlo simulations for statistical physics by using a restricted Boltzmann machine (RBM) to fit the model's probability distribution, resulting in improved acceptance ratio and autocorrelation time near phase transitions.
Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feedforward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine for efficient Monte Carlo updates and to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate improved acceptance ratio and autocorrelation time near the phase transition point.