No Cover Image

E-Thesis 457 views 234 downloads

Quantum field-theoretic machine learning and the renormalization group / DIMITRIOS BACHTIS

Swansea University Author: DIMITRIOS BACHTIS

  • Bachtis_Dimitrios_PhD_Thesis_Final_Redacted_Signature.pdf

    PDF | E-Thesis – open access

    Copyright: The author, Dimitrios S. Bachtis, 2022. This thesis is licensed under the terms of a Creative Commons Attribution 4.0 International (CC BY 4.0) License. Third party content is excluded for use under the license terms.

    Download (5.22MB)

DOI (Published version): 10.23889/SUthesis.60555

Abstract

Within the past decade, machine learning algorithms have been proposed as a po-tential solution to a variety of research problems which emerge within physics. As this cross-fertilization matures, one is able to investigate if the efficiency of machine learning algorithms can be increased by interpreti...

Full description

Published: Swansea 2022
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: Aarts, Gert ; Lucini, Biagio
URI: https://cronfa.swan.ac.uk/Record/cronfa60555
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: Within the past decade, machine learning algorithms have been proposed as a po-tential solution to a variety of research problems which emerge within physics. As this cross-fertilization matures, one is able to investigate if the efficiency of machine learning algorithms can be increased by interpreting them physically and if there exist fundamental connections that can be established between the two research fields. In this thesis, we pursue research directions intimately related to the above questions.First, we investigate the practical implications of interpreting machine learning functions as statistical-mechanical observables. Through this perspective, we explore if we can extend the classification capabilities of machine learning algorithms and if we are able to include neural networks within Hamiltonians to induce phase transitions in systems. A related direction concerns the use of machine learning to construct inverse renormalization group transformations to arbitrarily increase the size of a system. These techniques are then utilized to study the infinite volume limit of discrete spin systems and of quantum field theories, in order to investigate if machine learning is a powerful tool to study phase transitions.In another research direction we explore the derivation of machine learning algo-rithms from quantum field theories. We investigate if the φ4 scalar field theory satisfies the Hammersley-Clifford theorem and if it can be recast as a Markov random field. We then explore if φ4 neural networks can be derived that generalize a certain class of standard neural network architectures, and we present relevant numerical appli-cations. Finally, we discuss how this research direction opens up the opportunity to investigate machine learning within quantum field theory and how it solidifies a rig-orous connection between the research fields of machine learning, probability theory, statistical mechanics, lattice and constructive quantum field theory.
Keywords: Quantum Field Theory, Statistical Mechanics, Machine Learning
College: Faculty of Science and Engineering