Abstract
In this Letter, we demonstrate that applying deep generative machine learning models for lattice field theory is a promising route for solving problems where Markov chain MonteCarlo (MCMC) methods are problematic. More specifically, we show that generative models can be used to estimate the absolute value of the free energy, which is in contrast to existing MCMC-based methods, which are limited to only estimate free energy differences. We demonstrate the effectiveness of the proposed method for two-dimensional ϕ^{4} theory and compare it to MCMC-based methods in detailed numerical experiments.
Highlights
In this Letter, we demonstrate that applying deep generative machine learning models for lattice field theory is a promising route for solving problems where Markov chain Monte Carlo (MCMC) methods are problematic
We show that generative models can be used to estimate the absolute value of the free energy, which is in contrast to existing MCMC-based methods, which are limited to only estimate free energy differences
Introduction.—The free energy of a physical system is of great importance since it can be related to several thermodynamical observables
Summary
In recent works [16,17,18], deep generative models have been used in the context of lattice quantum field theories (see [19,20]). Using the explicit expression for the probability of the flow (3), we can rewrite the variational free energy as βFq. ln ddgzθ ðzÞ þ ln qZðzÞ : In training, the expectation value is approximated by its Monte Carlo estimate. Ln ddgzθ ðzÞ þ ln qZðzÞ : In training, the expectation value is approximated by its Monte Carlo estimate In machine learning, this approach of learning a model from an unnormalized target distribution is very well established [31,32,33,34]. In the Supplemental Material [27], we show that
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
