Doctoral Defense - Max Chumley

About the Event

The Department of Mechanical Engineering

Michigan State University

Ph.D. Dissertation Defense

Tuesday, March 25, 2025 at 3:00 PM EDT

Engineering Building Room 1502 and via Zoom

Contact Department or Advisor for Zoom Information

ABSTRACT

LEVERAGING DIFFERENTIATION OF PERSISTENCE DIAGRAMS FOR PARAMETER SPACE OPTIMIZATION AND DATA ASSIMILATION

By: Max Chumley

Advisor: Dr. Firas Khasawneh

Persistent homology, the flagship tool from Topological Data Analysis (TDA), has been successfully utilized across many different domains despite the absence of a differentiation framework. Only recently has a differential calculus been defined on the space of persistence diagrams, thus unlocking new possibilities for combining persistence with powerful solvers and optimizers. This work explores harnessing persistence differentiation for topologically driven data assimilation and for optimally navigating parameter spaces of dynamical systems.  In this defense, I provide an overview and present background on TDA and persistence optimization. I then introduce a new topological data assimilation framework using the Wasserstein distance to minimize topological differences between incoming measurements and model predictions, and I demonstrate the capabilities of this new method by applying it to high-fidelity Hall Effect Thruster (HET) simulation data from the Air Force Research Laboratory (AFRL). I also show how persistence-based cost functions can be constructed and used to optimally traverse the parameter space of a dynamical system with an optimization pipeline to promote specified dynamic states for the system. The cost functions are designed by specifying criteria that correspond to the structure of a desirable target persistence diagram while penalizing undesirable persistence features. This approach enables a more efficient method for exploring high-dimensional parameter spaces by obtaining paths between parameters to drive a system to a desired response.

Persons with disabilities have the right to request and receive reasonable accommodation. Please call the Department of Mechanical Engineering at 355-5131 at least one day prior to the seminar; requests received after this date will be met when possible.