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.

minor corrections, version published in the journal

References in corpus (7)

• Conditional Generative Adversarial Nets
• Critical slowing down and error analysis in lattice QCD simulations
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Flow-based sampling for fermionic lattice field theories
• Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
• Gross-Neveu model with Borici-Creutz fermion

Cited by in corpus (3)

• Exploring QCD matter in extreme conditions with Machine Learning
• Sampling U(1) gauge theory using a re-trainable conditional flow-based model
• AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning