Neural Network Field Transformation and Its Application in HMC

TL;DR

This paper introduces a neural network-based gauge field transformation for Hybrid Monte Carlo, improving sampling efficiency and topological tunneling in lattice gauge simulations, especially at higher couplings.

Contribution

It presents a novel gauge covariant neural network construction and applies it to enhance HMC sampling in lattice gauge theories.

Findings

Improved tunneling of topological charges in simulations.

Reduced force calculations at higher couplings.

Enhanced sampling efficiency in lattice gauge configurations.

Abstract

We propose a generic construction of Lie group agnostic and gauge covariant neural networks, and introduce constraints to make the neural networks continuous differentiable and invertible. We combine such neural networks and build gauge field transformations that is suitable for Hybrid Monte Carlo (HMC). We use HMC to sample lattice gauge configurations in the transformed space by the neural network parameterized gauge field transformations. Tested with 2D U(1) pure gauge systems at a range of couplings and lattice sizes, compared with direct HMC sampling, the neural network transformed HMC (NTHMC) generates Markov chains of gauge configurations with improved tunneling of topological charges, while allowing less force calculations as the lattice coupling increases.