Upcoming Event: PhD Dissertation Defense

Real-time inverse solutions for digital twins

Julie Pham, Ph.D. Candidate

Abstract

Digital twins require rapid data assimilation for digital state updating and downstream tasks, such as prediction and control. For many physical systems, the data assimilation task requires the solution of a partial differential equation (PDE)-constrained inverse problem, which is often computationally intractable in real time using traditional PDE solvers. This work develops computational methods to enable real-time, online inverse solutions for the digital twin setting. 

To achieve real-time performance, the methods developed in this thesis seek to exploit known structure in the PDE to enable rapid inversion for the unknown parameters. For linear settings, the structure of the inverse solution admits an offline-online decomposition, where offline precomputation of the high-dimensional matrix operations in the resulting inverse map enables rapid online evaluation of the unknown parameters. In the nonlinear case, scientific machine learning (SciML) methods are used to pre-train models that accelerate the inverse solutions online. Specifically, surrogate models are developed using optimal classification trees (OCTs) and neural matrix operators (NEMO). These methods combine physics-informed inverse structure with data-driven approaches to provide interpretable, rapid inverse solutions with quantifiable uncertainty. 

The methods are demonstrated on several engineering applications, including airborne contaminant initial condition identification, and aerodynamic pressure load estimation for hypersonics, with a focus on the latter. The numerical studies in this work demonstrate high quality inverse problem solutions, obtained with several orders of magnitude online speedup compared to traditional PDE methods for digital twin data assimilation in real time.

Biography

Julie Pham is a PhD student in aerospace engineering, advised by Dr. Karen Willcox. Her research interests include inverse problems, model reduction, and scientific machine learning.