Author: Sam Foreman

Submitted in partial fufillment of the requirements for the Doctor of Philosophy degree in Physics in the Graduate College of The University of Iowa

August 2019

Thesis Supervisor: Yannick Meurice

In this work we explore how lattice gauge theory stands to benefit from new developments in machine learning, and look at two specific examples that illustrate this point. % We begin with a brief overview of selected topics in machine learning for those who may be unfamiliar, and provide a simple example that helps to show how these ideas are carried out in practice.

After providing the relevant background information, we then introduce an example of renormalization group (RG) transformations, inspired by the tensor RG, that can be used for arbitrary image sets, and look at applying this idea to equilibrium configurations of the two-dimensional Ising model.

The second main idea presented in this thesis involves using machine learning to improve the efficiency of Markov Chain Monte Carlo (MCMC) methods. % Explicitly, we describe a new technique for performing Hamiltonian Monte Carlo (HMC) simulations using an alternative leapfrog integrator that is parameterized by weights in a neural network. % This work is based on the L2HMC `Learning to Hamiltonian Monte Carlo' algorithm.