Skip navigation
Please use this identifier to cite or link to this item:
Title: Making Sense of a Complex World: A Data-Driven Approach
Authors: Thiem, Thomas Noel
Advisors: Kevrekidis, Yannis G
Contributors: Chemical and Biological Engineering Department
Subjects: Applied mathematics
Artificial intelligence
Chemical engineering
Issue Date: 2022
Publisher: Princeton, NJ : Princeton University
Abstract: In this dissertation we develop a suite of data-driven modeling techniques for dynamical systems by leveraging manifold learning, dimensionality reduction, and deep learning methodologies. We apply these techniques to a variety of systems including coupled oscillators, agent-based systems, and optimization and root-finding algorithms. With each system we demonstrate a different facet of the techniques. Beginning with coupled oscillator systems in chapter 1, we describe how manifold learning can be used to tackle the challenge of finding coarse descriptions of collective dynamics. We then present a specialized neural network architecture that allows us to learn the dynamics of coarse variables directly from time series. Finally, we leverage manifold learning once again to find reduced sets of parameters, the "effective" parameters, for multi-parameter coupled oscillator models. Moving on to heterogeneous agent-based models in chapter 2, we present techniques for deriving data-driven surrogate models in the presence of low-dimensional dynamics. We present a global approach, that constructs a basis from spatiotemporal data and learns a system of ODEs in the basis coordinates, and a local approach, that learns a PDE in heterogeneity space. We discuss the implications of an agent-based PDE and illustrate a subsampling approach. In chapter 3 we utilize manifold learning to extend our agent-based PDE approach to cases in which the heterogeneities are unknown. We present examples of this modification for both one and two-dimensional data-driven spaces. We conclude by examining algorithms from the Koopman point of view in chapter 4. We discuss how employing the Koopman framework proves beneficial for the analysis and acceleration of algorithms and showcase the approach with examples including both the gradient descent and Nesterov optimization algorithms and the Newton-Raphson root-finding algorithm. As the world continues to become ever more saturated in data new analysis techniques will be required to extract meaningful information. We believe that our data-driven modeling techniques offer a step toward making sense of a data-driven future.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Chemical and Biological Engineering

Files in This Item:
File Description SizeFormat 
Thiem_princeton_0181D_13946.pdf22.96 MBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.