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On Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models

Kim A. Nicoli
Christopher J. Anders
Lena Funcke
Tobias Hartung
Karl Jansen
Pan Kessel
Shinichi Nakajima
Paolo Stornati

January 19, 2021

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. 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 ϕ4 theory and compare it to MCMC-based methods in detailed numerical experiments.