Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines

TL;DR

This paper introduces a novel approach that leverages restricted Boltzmann machines, trained as neural networks, to enhance Monte Carlo simulations in statistical physics, significantly reducing mixing times and improving efficiency.

Contribution

The authors propose a method to use restricted Boltzmann machines as efficient proposal distributions for Monte Carlo updates in physical models.

Findings

Improved acceptance ratio near phase transition.

Reduced autocorrelation time in simulations.

Enhanced sampling efficiency in the Falicov-Kimball model.

Abstract

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.