A paradigm for data-driven predictive modeling using field inversion and machine learning

We propose a modeling paradigm, termed field inversion and machine learning (FIML), that seeks to comprehensively harness data from sources such as high-fidelity simulations and experiments to aid the creation of improved closure models for computational physics applications. In contrast to inferring model parameters, this work uses inverse modeling to obtain corrective, spatially distributed functional terms, offering a route to directly address model-form errors. Once the inference has been performed over a number of problems that are representative of the deficient physics in the closure model, machine learning techniques are used to reconstruct the model corrections in terms of variables that appear in the closure model. These reconstructed functional forms are then used to augment the closure model in a predictive computational setting. As a first demonstrative example, a scalar ordinary differential equation is considered, wherein the model equation has missing and deficient terms. Following this, the methodology is extended to the prediction of turbulent channel flow. In both of these applications, the approach is demonstrated to be able to successfully reconstruct functional corrections and yield accurate predictive solutions while providing a measure of model form uncertainties.