Flow-based generative models for Markov chain Monte Carlo in lattice field theory
This addresses sampling inefficiencies in computational physics, particularly for lattice field theories, by introducing a machine learning approach that can be trained without existing samples, though it is incremental as it builds on existing MCMC methods.
The authors tackled the problem of critical slowing down in Markov chain Monte Carlo (MCMC) sampling for lattice field theories by proposing a flow-based generative model to approximate the Boltzmann distribution, resulting in systematically improved autocorrelation times compared to standard algorithms like HMC and Metropolis sampling in 2D φ⁴ theory.
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 $φ^4$ theory in two dimensions.