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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Jaesung Lee, Wm Michael Barnes Department of Industrial & Systems Engineering
Statistical Modeling of Random Shifting and Shapes in Functional Data and Uncertainty Quantification via Landmark-Embedded Hierarchical Gaussian Processes


This presentation focuses on a statistical model designed to characterize complex random variations - specifically, random shifting and shape - in functional data, as well as a method for inferring an underlying physical variable based on this observed functional data. The primary goal of this research is to employ data collected from graphene field-effect transistor nanosensors to infer the concentration levels of lead contaminants in water. At varying levels of contamination, the nanosensors tend to generate different sensor signals, manifesting as functional data types. However, nanosensors inherently exhibit substantial variability in their internal components, thereby creating significant variations in the output signals. Therefore, it is crucial not only to provide the point estimate but also to quantify the associated uncertainty in the contaminant estimation. To accomplish this objective, we have proposed a hierarchical Gaussian process model incorporating prior knowledge about the random shape and location attributes of the functional data. Building upon this model, a Bayesian statistical calibration technique is proposed to infer the underlying physical variable from the observed functional data and quantify the associated uncertainty. Additionally, this presentation will discuss other research topics centered on uncertainty-aware, data-driven methodologies.