Generalizable physics-constrained modeling using learning and inference assisted by feature-space engineering

This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable model augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to as "learning and inference assisted by feature-space engineering", is based on the hypothesis that robustness and generalizability demand a meticulously designed feature space that is informed by the underlying physics and a carefully constructed features-to-augmentation map. The critical components of this approach are: (1) maintaining consistency across the learning and prediction environments to make the augmentation case-agnostic; (2) tightly coupled inference and learning by constraining the augmentation to be learnable throughout the inference process to avoid loss of inferred information (and hence accuracy); (3) identification of relevant physics-informed features in appropriate functional forms to enable significant overlap in feature space for a wide variety of cases to promote generalizability; (4) localized learning, i.e., maintaining explicit control over feature space to change the augmentation function behavior only in the vicinity of available data points. To demonstrate the viability of this approach, it is used in the modeling of bypass transition. The augmentation-in the form of model coefficient functions-is developed using skin friction data from two flat plate cases from the ERCOFTAC dataset. Piecewise linear interpolation on a structured grid in feature space is used as a sample functional form for the augmentation to demonstrate the capability of localized learning. The impact of using a different function class (neural network) is also assessed. The augmented model is then applied to a variety of flat plate cases which are characterized by different freestream turbulence intensities, pressure gradients, and Reynolds numbers. The predictive capability of the augmented model is also tested on single-stage high-pressure-turbine cascade cases, and the model performance is analyzed from the perspective of information contained in the feature space. The results show consistent improvements across these cases, as long as the physical phenomena in question are well-represented in the training.