Upcoming Event: PhD Dissertation Defense

Mathematical and Computational Foundations for Predictive Digital Twins

Graham Pash, CSEM Ph.D. Candidate

Abstract

Predictive digital twins combine mathematical models with system-specific data to create co-evolving constructs capable of supporting complex decisions. The bidirectional exchange between physical and virtual systems distinguishes this paradigm from traditional modeling and simulation, and demands techniques scalable to high-dimensional, nonlinear, multi-physics settings in science, engineering, and medicine. This dissertation advances mathematical and computational methods for uncertainty quantification and optimization in this context. As a concrete demonstration, proposed approaches are applied to precision oncology, with a particular focus on the modeling and treatment of high-grade gliomas. 

This thesis explores the development and application of methods to (i) overcome computational barriers in high-dimensional uncertainty quantification, and (ii) close the loop from modeling to action with uncertainty-aware decision frameworks. Three principal contributions are presented. First, we contribute theory for the analysis of a quasi-Monte Carlo method for a class of semilinear parabolic partial dierential equations, and apply the method to accelerate the propagation of uncertainty through a model of tumor growth. Second, we propose a formulation, method, and scalable algorithm for the solution of a statistical inverse problem to assimilate longitudinal imaging data with mathematical models. Third, we demonstrate the end-to-end application of a digital twin formulation by posing a multiobjective optimization problem minimizing statistical risk and applying it to patient-specific therapy adaptation. Throughout, the methods blend approximation theory, numerical optimization, and high-performance computing to lay a foundation for the realization of predictive digital twins that integrate models, data, and decisions to deliver robust, actionable insights under uncertainty.

Biography

Graham Pash is a PhD candidate in the Computational Science, Engineering, and Mathematics program, advised by Dr. Karen Willcox. He received his MS in 2022. His BS in Applied Mathematics and BS in Mechanical Engineering are from North Carolina State University in 2019. His research interests are in the intersection of computational science, inverse problems, and optimization.