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

Swansea University Author: DIMITRIOS BACHTIS

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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...

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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
first_indexed 2022-07-20T12:06:26Z
last_indexed 2023-01-13T19:20:46Z
id cronfa60555
recordtype RisThesis
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spelling 2022-07-20T13:18:03.2018405 v2 60555 2022-07-20 Quantum field-theoretic machine learning and the renormalization group e447edf75f7a470c683d5e9c5251a883 DIMITRIOS BACHTIS DIMITRIOS BACHTIS true false 2022-07-20 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. E-Thesis Swansea Quantum Field Theory, Statistical Mechanics, Machine Learning 6 7 2022 2022-07-06 10.23889/SUthesis.60555 COLLEGE NANME COLLEGE CODE Swansea University Aarts, Gert ; Lucini, Biagio Doctoral Ph.D Marie-Skłowdoska Curie ITN Fellowship 2022-07-20T13:18:03.2018405 2022-07-20T13:03:04.5642883 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics DIMITRIOS BACHTIS 1 60555__24674__12db263e6f764d879fce4f4fd95fa800.pdf Bachtis_Dimitrios_PhD_Thesis_Final_Redacted_Signature.pdf 2022-07-20T13:16:22.1382431 Output 5476141 application/pdf E-Thesis – open access true 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. true eng https://creativecommons.org/licenses/by/4.0/
title Quantum field-theoretic machine learning and the renormalization group
spellingShingle Quantum field-theoretic machine learning and the renormalization group
DIMITRIOS BACHTIS
title_short Quantum field-theoretic machine learning and the renormalization group
title_full Quantum field-theoretic machine learning and the renormalization group
title_fullStr Quantum field-theoretic machine learning and the renormalization group
title_full_unstemmed Quantum field-theoretic machine learning and the renormalization group
title_sort Quantum field-theoretic machine learning and the renormalization group
author_id_str_mv e447edf75f7a470c683d5e9c5251a883
author_id_fullname_str_mv e447edf75f7a470c683d5e9c5251a883_***_DIMITRIOS BACHTIS
author DIMITRIOS BACHTIS
author2 DIMITRIOS BACHTIS
format E-Thesis
publishDate 2022
institution Swansea University
doi_str_mv 10.23889/SUthesis.60555
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2022-07-06T02:29:14Z
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score 11.047674

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