Decimation map in 2D for accelerating HMC

Abstract

To accelerate the HMC with field transformation, we consider a variant of the trivializing map, the decimation map, which can be regarded as a coarse-graining transformation. Using the 2D 𝑈 (1) pure gauge model, combined with the guided Monte Carlo algorithm, we show that the integrated autocorrelation time of the topological charge can be exponentially improved in the wall clock time. Our study indicates that incorporating renormalization group picture is a powerful and essential ingredient to accelerate the HMC at large 𝛽.

Flow-based sampling for fermionic lattice field theories

“…This can be considered an application of "in-painting" which has been studied thoroughly in the image generation community, including through the use of normalizing flows [12]. This approach has been explored in only a few lattice field theory examples so far [75,76].…”

“…Flows can also be incorporated into more standard Markov Chain sampling approaches. On one hand, both the trivializing map and more general flows have been applied to transform to a more easily sampled distribution on which standard HMC methods can be applied for faster mixing [7,8,38,39,57,75]. On the other hand, several recent works have explored flow-based HMC, in which HMC trajectories are themselves defined by learned flow transformations [77,78].…”