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A methodology for non-intrusive, projection-based non-linear model reductionoriginally presented by Renganathan et. al.(2018)~\cite{renganathan2018koopman} is further extended towards parametricsystems with focus on application to aerospace design. Specifically, we extendthe method for static systems with parametric geometry (that deforms the mesh),in addition to parametric boundary conditions. The main idea is to firstperform a transformation on the governing equations such that it is lifted to ahigher dimensional but linear under-determined system. This enables one toextract the system matrices easily compared to that of the original non-linearsystem. The under-determined system is closed with a set of model-dependentnon-linear constraints upon which the model reduction is finally performed. Themethodology is validated on the subsonic and transonic inviscid flow past theNACA0012 and the RAE2822 airfoils. We further demonstrate the utility of theapproach by applying it to two common problems in aerospace design namely,derivative-free global optimization and parametric uncertainty quantificationwith Monte Carlo sampling. Overall, the methodology is shown to achieveaccuracy upto 5\% and computational speed-up of 2-3 orders of magnitude as thatof the full-order model. Comparison against another non-intrusive modelreduction method revealed that the proposed approach is more robust, accurateand retains the consistency between the state variables.

Koopman-Based Approach to Non-intrusive Projection-Based Reduced-Order Modeling with Black-Box High-Fidelity Models. Part II: Application