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

TL;DR

This paper introduces a Conditional GAN approach to generate lattice configurations in the Gross-Neveu model, effectively reducing critical slowing down and computational costs in lattice field theory simulations.

Contribution

The paper presents a novel use of C-GANs trained on non-critical data to generate independent samples in the critical region, addressing critical slowing down.

Findings

C-GAN generated samples match HMC distributions

Reduced computational cost near critical points

Circumvented critical slowing down problem

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.