Comprehensive Exam of CMSE Maxwell Chumley
Department of Computational Mathematics, Science & Engineering
Michigan State University
Comprehensive Exam Notice
April 11th, 2024, 12:00 PM, EGR 1502
Zoom link: https://msu.zoom.us/j/97365184740
Passcode: 374278
Leveraging differentiation of persistence diagrams for parameter space optimization and data assimilation
By: Maxwell Chumley
Abstract:
Persistent homology, the flagship tool from Topological Data Analysis (TDA) has been successfully utilized in many different domains despite the absence of a differentiation framework. Only recently a differential calculus has been defined on the space of persistence diagrams thus unlocking new possibilities for combining persistence with powerful solvers and optimizers. This talk explores harnessing persistence differentiation for navigating the parameter space of dynamical systems, and for topological data assimilation. Specifically, I will show preliminary work on how persistence-based cost functions can be constructed and used to optimally traverse the parameter space of a dynamical 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. I will also explore possibilities for topological data assimilation and discuss some promising future applications in time series analysis.
Committee:
- Firas Khasawneh
- Elizabeth Munch
- Hamidreza Modares
- Brian Feeny
- Mengsen Zhang
