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Mathematical models are used extensively for diverse tasks includinganalysis, optimization, and decision making. Frequently, those models areprincipled but imperfect representations of reality. This is either due toincomplete physical description of the underlying phenomenon (simplifiedgoverning equations, defective boundary conditions, etc.), or due to numericalapproximations (discretization, linearization, round-off error, etc.). Modelmisspecification can lead to erroneous model predictions, and respectivelysuboptimal decisions associated with the intended end-goal task. To mitigatethis effect, one can amend the available model using limited data produced byexperiments or higher fidelity models. A large body of research has focused onestimating explicit model parameters. This work takes a different perspectiveand targets the construction of a correction model operator with implicitattributes. We investigate the case where the end-goal is inversion andillustrate how appropriate choices of properties imposed upon the correctionand corrected operator lead to improved end-goal insights.

Should You Derive, Or Let the Data Drive? An Optimization Framework for Hybrid First-Principles Data-Driven Modeling