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Quantifying the agreement between computational models and experimental data under uncertainty


Bound-to-bound data collaboration (abbreviated B2BDC) is a deterministic optimization-based approach for uncertainty quantification. The framework combines models and data from multiple sources by formulating inequality constraints over a parameter space. This dissertation explores the following question: how can agreement between computational models and experimental data be quantified while necessarily accounting for uncertainty in both model parameters and observations? In a typical B2BDC application, this is performed by constructing a dataset -- a collection of constraints over an uncertain parameter space involving surrogate models, experimental data, and prior knowledge -- and then assessing its consistency. Our first contribution is a formalization of this procedure within an iterative context. This new strategy effectively extends the applicability of the B2BDC technique and can be viewed as a natural extension of previous work. Oftentimes, demonstrating model-data disagreement is just as important as verifying agreement. In B2BDC, this is manifested through dataset inconsistency. Our second contribution is a new tool for analyzing inconsistency called the vector consistency measure. This measure provides a more thorough diagnosis of an inconsistent dataset by computing minimal constraint corrections that lead to consistency. The inclusion of weights facilitates domain expert knowledge and opinions to be incorporated in the process of resolving an inconsistency. The primary developments in this thesis are methodological. Their application is illustrated on various examples, ranging from the small-scale instances drawn from the literature to larger-scale realistic gas combustion datasets.

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