Thesis Proposal for River Bond

Date: Friday October 7, 2022
Time: 1:00 pm – 2:30 pm
Room: ACAD-4113

Committee: Erin Austin, Troy Butler, Yaning Liu, Emily Speakman

Title: UTILIZING KOOPMAN OPERATORS AND DATA-CONSISTENT INVERSION FOR FORWARD AND INVERSE PROPAGATION OF UNCERTAINTIES IN DYNAMICAL SYSTEMS

Abstract: Over the last two decades, the Koopman operator has become a powerful tool in the area of Data Science. This operator is part of a new paradigm of data-driven approaches that extract meaningful insights from clouds of data. The Koopman operator is an infinite dimensional linear operator that moves the dynamics forward in time. This research proposes to connect the insights of the Koopman operator to Data-Consistent Inversion (DCI) and the Learning Uncertain Quantities (LUQ) algorithms. This research will also investigate the adjoint of the Koopman operator, the Perron-Frobenius operator that evolves a distribution forward in time. This will allow us to explore the propagation of the updated density (i.e., the solution to DCI). This research will result in, among other things, a new Python package that will unify several of the current algorithms and paradigms for propagating uncertainties in dynamical systems.