You are here

FAU Collections » FAU Research Repository » FAU Theses and Dissertations

DATA-DRIVEN ATTRACTOR IDENTIFICATION VIA COMPUTATIONAL HOMOLOGY AND MACHINE LEARNING

Download pdf | Full Screen View

Date Issued:
2024
Abstract/Description:
Dynamical systems play a pivotal role across various scientific domains, encompassing disciplines from physics to biology and engineering. The long-term behavior of these systems hinges on the structure of their attractors, with many exhibiting multistability characterized by multiple minimal attractors. Understanding the structure of these attractors and their corresponding basins is a central theme in dynamical systems theory. In recent years, machine learning algorithms have emerged as potent tools for clustering, prediction, and modeling complex data. By harnessing the capabilities of neural networks along with techniques from topological data analysis, in particular persistence homology, we can construct surrogate models of system asymptotics. This approach also allows for the decomposition of phase space into polygonal regions and the identification of plausible attracting neighborhoods, facilitating homological Conley index computation at reduced computational expense compared to current methods. Through various illustrative examples, we demonstrate that sufficiently low training loss yields constructed neighborhoods whose homological Conley indices aligns with a priori knowledge of the dynamics.
Title: DATA-DRIVEN ATTRACTOR IDENTIFICATION VIA COMPUTATIONAL HOMOLOGY AND MACHINE LEARNING.
27 views
10 downloads
Name(s): Tatasciore, Paul , author
Wille, Luc T. , Thesis advisor
Florida Atlantic University, Degree grantor
Department of Physics
Charles E. Schmidt College of Science
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2024
Date Issued: 2024
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 113 p.
Language(s): English
Abstract/Description: Dynamical systems play a pivotal role across various scientific domains, encompassing disciplines from physics to biology and engineering. The long-term behavior of these systems hinges on the structure of their attractors, with many exhibiting multistability characterized by multiple minimal attractors. Understanding the structure of these attractors and their corresponding basins is a central theme in dynamical systems theory. In recent years, machine learning algorithms have emerged as potent tools for clustering, prediction, and modeling complex data. By harnessing the capabilities of neural networks along with techniques from topological data analysis, in particular persistence homology, we can construct surrogate models of system asymptotics. This approach also allows for the decomposition of phase space into polygonal regions and the identification of plausible attracting neighborhoods, facilitating homological Conley index computation at reduced computational expense compared to current methods. Through various illustrative examples, we demonstrate that sufficiently low training loss yields constructed neighborhoods whose homological Conley indices aligns with a priori knowledge of the dynamics.
Identifier: FA00014475 (IID)
Degree granted: Dissertation (PhD)--Florida Atlantic University, 2024.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Dynamical systems
Computational physics
Machine learning
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00014475
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU