Comprehensive Exam of CMSE Sunia Tanweer
Department of Computational Mathematics, Science & Engineering
Michigan State University
Comprehensive Exam Notice
November 22, 2024, 9:00 AM, CMSE Conference Room 1502
Investigating Dynamical Systems with Stochastic Theory and Topological Data Analysis
Sunia Tanweer
Abstract:
Topological Data Analysis (TDA) provides an extremely useful framework for insight extraction from complex datasets such as time series of dynamical systems. However, the vast majority of TDA studies have focused on signals from deterministic systems. In contrast, in this work I aim to advance TDA tools to the analysis of time series of stochastic dynamical systems. The contributions of my thesis include: a) leveraging recent stochastic theories to elucidate whether a time series was generated by a deterministic or a stochastic system, b) defining and coining “homological bifurcation plots” for identifying phenomenological bifurcations in stochastic systems for both reliable and unreliable density estimates, and c) demonstrating the effectiveness of the developed tools using applications in engineering, epidemiology, and neuroscience.
Specifically, I will show how homological plots automate and enable P-bifurcation detection in dynamic stall flutter in airfoils and allow unprecedented studies on disease spread in stochastic compartmental models with different noise types. I will also present current results and ongoing work on using TDA for classifying epilepsy seizure EEG data into preictal, interictal, and postictal regions. Finally, I will also present preliminary results and planned work for using stochastic tools, graph theory, and TDA for delineating the basins of attraction in the state space of deterministic nonlinear dynamical systems.
Committee:
Firas A. Khasawneh (chair)
Elizabeth Munch
Daniel Segalman
Wei-Che Tai
Hamidreza Modare
