A data-driven approach to the modeling of turbulent and transitional flows is proposed in this work, with the goal of developing more robust and accurate closure models. The key idea is to (ⅰ) infer the functional form of deficiencies in known closure models by applying inverse problems to computational and experimental data, (ⅱ) use machine learning to reconstruct the improved functional forms, and (ⅲ) to inject the improved functional forms in simulations to obtain more accurate predictions. The inverse modeling step, on its own, can yield valuable insight to the modeler, essentially converting data to information. The machine learning step is a tool to convert information into modeling knowledge. Representative examples are used to describe the methodology and to demonstrate its viability. The first example investigates the modeling of a non-equilibrium turbulent boundary layer, and the second involves the modeling of bypass transition to turbulence. Evidence from these problems emphasizes the utility of the proposed approach in offering new routes to closure modeling in general computational physics disciplines.
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