Seminars

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 requiresthe solution of a partial differential equation (PDE)-constrained inverse problem, which is oftencomputationally intractable in real time using traditional PDE solvers. This work developscomputational 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 knownstructure 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 pre-computation of the high-dimensional matrix operations in the resulting inverse map enablesrapid online evaluation of the unknown parameters. In the nonlinear case, scientific machinelearning (SciML) methods are used to pre-train models that accelerate the inverse solutionsonline. Specifically, surrogate models are developed using optimal classification trees (OCTs)and neural matrix operators (NEMO). These methods combine physics-informed inversestructure with data-driven approaches to provide interpretable, rapid inverse solutions with quantifiable uncertainty.
The methods are demonstrated on several engineering applications, including airbornecontaminant initial condition identification, and aerodynamic pressure load estimation forhypersonics, with a focus on the latter. The numerical studies in this work demonstrate highquality inverse problem solutions, obtained with several orders of magnitude online speedupcompared to traditional PDE methods for digital twin data assimilation in real time.