# Flow-based generative models for Markov chain Monte Carlo in lattice field theory

## TL;DR

This paper introduces a flow-based generative model for Markov chain Monte Carlo in lattice field theory, improving sampling efficiency and reducing critical slowing down without requiring prior samples.

## Contribution

It presents a novel flow-based generative approach for MCMC that enhances autocorrelation times and can be trained without existing samples, outperforming traditional methods.

## Key findings

- Reduces autocorrelation times in lattice simulations.
- Performs comparably or better than HMC and Metropolis methods.
- Effective even in critical slowing down regions.

## Abstract

A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution approximating the desired Boltzmann distribution determined by the lattice action of the theory being studied. Training the model systematically improves autocorrelation times in the Markov chain, even in regions of parameter space where standard Markov chain Monte Carlo algorithms exhibit critical slowing down in producing decorrelated updates. Moreover, the model may be trained without existing samples from the desired distribution. The algorithm is compared with HMC and local Metropolis sampling for $\phi^4$ theory in two dimensions.