Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines

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.

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• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Quantum phase recognition via unsupervised machine learning
• Deep Learning on the 2-Dimensional Ising Model to Extract the Crossover Region with a Variational Autoencoder
• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Towards reduction of autocorrelation in HMC by machine learning
• Barriers and Dynamical Paths in Alternating Gibbs Sampling of Restricted Boltzmann Machines
• Towards meaningful physics from generative models
• Generation of ice states through deep reinforcement learning
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• Neural networks in quantum many-body physics: a hands-on tutorial
• Machine-learning approach to finite-size effects in systems with strongly interacting fermions
• Universal crossover from ground state to excited-state quantum criticality
• Probing Criticality in Quantum Spin Chains with Neural Networks
• Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows
• Thermodynamics of the Ising model encoded in restricted Boltzmann machines
• A Probability Density Theory for Spin-Glass Systems
• Effective classical correspondence of the Mott transition
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Machine learning dynamics of phase separation in correlated electron magnets
• Weakly-supervised learning on Schrodinger equation