Generation of gauge field configurations with equivariant neural networks

Abstract

In order to enhance the performance of neural networks in the context of lattice field theories, one can incorporate physical information directly into the network architecture. A key physical property of lattice gauge theories is gauge symmetry. Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) are neural networks consisting of gauge equivariant layers that preserve this symmetry. Their application has focused on regression tasks on physical observables, i.e. fitting gauge field configurations to gauge invariant observables.

In this talk we want to address the possibility of applying L-CNNs to generating or modifying gauge field configurations. We make use of neural ordinary differential equations (neural ODEs) to modify arbitrary gauge configurations in a gauge equivariant way to produce new configurations. We exemplify this approach with practical tests on toy models based on Wilson (gradient) flow.