Computational and physical considerations for the development of machine learning augmented turbulence models

Despite the potential of data-driven methods for turbulence modeling, a critical gap exists between reported theoretical frameworks and practical implementation in engineering applications. Current literature often fails to provide comprehensive guidance on model development and computational considerations and leaves critical methodological decisions ambiguous, leading to fragmented approaches, limited reproducibility, models that do not generalize beyond their training domains, and generally a lack of trust in data-driven approaches among practitioners of turbulence modeling. This work reviews recent developments and presents a systematic, end-to-end demonstration of developing physically and computationally-informed machine learning augmentations for turbulence modeling. We use heat transfer predictions in hypersonic shock-boundary layer interactions as an exemplar case. We describe the rationale behind our choice of augmentation term and perform studies to determine the optimal mathematical augmentation form. We also investigate feature design and feature-space representation in an idealized learning problem, demonstrating how parsimonious representations, rather than neural networks, with properly designed features may be better suited for turbulence modeling. This knowledge is used to develop and train a predictive model that successfully extrapolates to a different geometry and shock mechanism. The main contributions of this work are to elucidate the process of developing machine learning augmentations, and provide a viable pathway towards developing generalizable turbulence models. • Systematic, end-to-end demonstration of the process of developing machine learning augmentations for turbulence modeling. • Rigorous feature-design principles that maintain model interpretability while enhancing data reconstruction and generalizability. • Illustration of effect of design decisions on model performance via an idealized learning problem. • Application of the methodology on a hypersonic wall heat transfer problem.