Monday, April 20 2020
2:30pm - 4:30pm
PhD Thesis Presentation
Thesis Proposal - Wenjuan Zhang

Chair: Joshua French
Members: Yaning Liu
Erin Austin
Tim Wildey
Advisor: Troy Butler

Title of the proposal: A Convergence and Numerical Analysis Framework for Data Consistent Inversion

Here is the abstract of my thesis proposal:

The field of uncertainty quantification (UQ) primarily focuses on the quantitative characterization and reduction of uncertainties in causal models. The models are often of computational or physical applications. Subsequently, the models are usually described explicitly (e.g., as algebraic or differential equations), implicitly (e.g., as a ``black box'' computational library, possibly containing legacy code spanning decades of development to simulate physical processes), or, in some cases, some coupling of various explicit and implicit models. We separate UQ problems into two types: forward and inverse UQ problems. Forward UQ problems involve the analysis of uncertainty in model output data given some prescribed uncertainty of parameters (i.e., model inputs) that are usually physical in nature in the sense that they describe physical processes and often have dimensional units assigned to them. Inverse UQ problems involve the analysis of uncertainty on parameters given some prescribed uncertainty on model outputs. Data-consistent inversion is a recently developed approach that utilizes push-forward measures (i.e., solutions to a forward UQ problem) to construct pullback measures (i.e., solutions to an inverse UQ problem). While the data-consistent approach is built upon rigorous measure theory, the solution is itself easy to describe and relatively straightforward to implement. However, there are several computational and practical bottlenecks impacting the accuracy of solutions. We propose the development and analysis of a framework for studying the convergence and numerical analysis of data-consistent solutions to inverse UQ problems.
Speaker:Wenjuan Zhang
Location:Zoom meeting

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