Generative learning for the problem of critical slowing down in lattice Gross Neveu model

Abstract

In lattice field theory, Monte Carlo simulation algorithms get highly affected by critical slowing down in the critical region, where autocorrelation time increases rapidly. Hence the cost of generation of lattice configurations near the critical region increases sharply. In this paper, we use a Conditional Generative Adversarial Network (C-GAN) for sampling lattice configurations. We train the C-GAN on the dataset consisting of Hybrid Monte Carlo (HMC) samples in regions away from the critical region, i.e., in the regions where the HMC simulation cost is not so high. Then we use the trained C-GAN model to generate independent samples in the critical region. Thus, the overall computational cost is reduced. We test our approach for Gross-Neveu model in 1+1 dimension. We find that the observable distributions obtained from the proposed C-GAN model match with those obtained from HMC simulations, while circumventing the problem of critical slowing down.

Stochastic normalizing flows as non-equilibrium transformations

“…This also includes applications in lattice field theory: as examples of recent works in this area of research, we mention refs. [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81], but this list is likely to grow much longer in the next few years, as the lattice community is developing approaches that are expected to make machine-learning techniques part of the standard lattice-QCD toolbox [82]. A class of deep generative models called normalizing flows [83][84][85] represents one of the most active and interesting developments in this area of research [86][87][88][89][90][91][92][93][94][95].…”