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 augmentations from sparse data. The proposed approach, referred to as Learning and Inference assisted by Feature Engineering (LIFE), 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)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; (2) Explicit control over feature space to locally infer the augmentation without affecting other feature space regions, especially when limited data is available; (3) Maintaining consistency across the learning and prediction environments to make the augmentation case-agnostic; (4) Tightly-coupled inference and learning by constraining the augmentation to be learnable throughout the inference process to avoid significant loss of information (and hence accuracy). To demonstrate the viability of this approach, it is used in the modeling of bypass transition. The augmentation is developed on skin friction data from two flat plate cases from the ERCOFTAC dataset. 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.