Super-Resolving Normalising Flows for Lattice Field Theories

TL;DR

This paper introduces a renormalisation group inspired normalising flow that leverages coarse lattice samples to efficiently generate fine lattice field theory configurations, combining MCMC benefits with super-resolution techniques.

Contribution

It presents a novel architecture that learns stochastic maps from coarse to fine lattice theories, enabling scalable and systematic super-resolution sampling in lattice field theories.

Findings

Effective sampling on large lattices up to 128x128.

Combines MCMC advantages with normalising flows for super-resolution.

Allows structural improvements by optimizing the base distribution.

Abstract

We propose a renormalisation group inspired normalising flow that combines benefits from traditional Markov chain Monte Carlo methods and standard normalising flows to sample lattice field theories. Specifically, we use samples from a coarse lattice field theory and learn a stochastic map to the targeted fine theory. The devised architecture allows for systematic improvements and efficient sampling on lattices as large as $128 \times 128$ in all phases when only having sampling access on a $4\times 4$ lattice. This paves the way for reaping the benefits of traditional MCMC methods on coarse lattices while using normalising flows to learn transformations towards finer grids, aligning nicely with the intuition of super-resolution tasks. Moreover, by optimising the base distribution, this approach allows for further structural improvements besides increasing the expressivity of the model.