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. We perform both interpolation and extrapolation to 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.

AdvNF: Reducing mode collapse in conditional normalising flows using adversarial learning

“…external parameter-dependent distributions are commonly referred to as conditional distributions, where the set of external parameters is generally used to represent the condition. Many conditional generative models, such as conditional VAEs [21,22], conditional GANs [23][24][25][26] and conditional NFs [27,28] have been developed over time for sampling from such conditional distributions. Both approaches-repeated training and conditional modelling-have been the subject of substantial investigation over time.…”