Symmetry-preserving neural networks in lattice field theories

TL;DR

This thesis explores neural networks that preserve symmetries in lattice field theories, demonstrating their advantages in accurately modeling physical observables and introducing neural gradient flow for configuration generation.

Contribution

It introduces gauge-equivariant neural networks tailored for lattice gauge theories and proposes neural gradient flow as a novel method for generating lattice configurations.

Findings

Gauge-equivariant networks outperform traditional models in predicting Wilson loops.

Neural gradient flow offers a new approach to generate lattice gauge configurations.

Equivariance is crucial for preserving symmetries in neural network models.

Abstract

This thesis deals with neural networks that respect symmetries and presents the advantages in applying them to lattice field theory problems. The concept of equivariance is explained, together with the reason why such a property is crucial for the network to preserve the desired symmetry. The benefits of choosing equivariant networks are first illustrated for translational symmetry on a complex scalar field toy model. The discussion is then extended to gauge theories, for which Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs) are specifically designed ad hoc. Regressions of physical observables such as Wilson loops are successfully solved by L-CNNs, whereas traditional architectures which are not gauge symmetric perform significantly worse. Finally, we introduce the technique of neural gradient flow, which is an ordinary differential equation solved by neural networks, and propose it as a method to generate lattice gauge configurations.