Accelerated Monte Carlo simulations with restricted Boltzmann machines

By Li Huang, Lei Wang. 2016

206 citations recorded by the source corpus.

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.

Subfields: Computer Vision and Pattern Recognition, Condensed Matter Physics, Statistical and Nonlinear Physics, Probabilistic & Bayesian Methods, AI for Physical Sciences

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Citations in the corpus

Monge-Ampère Flow for Generative Modeling (2018, methodology): “Therefore, it can be used to accelerate Monte Carlo simulations, by either recommending the updates as a generative model Huang & Wang (2017); Liu et al. (2017) or performing hybrid Monte Carlo in the latent space Li & Wang (2018).”
Neural Network Renormalization Group (2018, background): “(5) can be more efficient compared to the conventional maximum likelihood density estimation [42, 55] and the supervised learning approach [57, 58] since one di-”
Neural-Network Quantum States, String-Bond States, and Chiral Topological States (2017, background): “In the last few years we are experiencing interesting developments also for some central problems in condensed matter, such as quantum phase classification/recognition[7–10], improvement of dynamical mean field theory[11], enhancement of Quantum Monte Carlo methods [12, 13] or approximations of ther”
Ising machines as hardware solvers of combinatorial optimization problems (2022, methodology): “Such an approach was used in the context of dynamic portfolio optimization, which can be encoded as an Ising problem 186 .”
All-optical neural network with nonlinear activation functions (2019, background): “They may be used to solve some problems which are intractable in conventional appraches [13–20].”