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This work presents a review and perspectives on recent developments in theuse of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS)and Large Eddy Simulation (LES) models of turbulent flows. Different approachesof applying supervised learning to represent unclosed terms, modeldiscrepancies and sub-filter scales are discussed in the context of RANS andLES modeling. Particular emphasis is placed on the impact of the trainingprocedure on the consistency of ML augmentations with the underlying physicalmodel. Techniques to promote model-consistent training, and to avoid therequirement of full fields of direct numerical simulation data are detailed.This is followed by a discussion of physics-informed and mathematicalconsiderations on the choice of the feature space, and imposition ofconstraints on the ML model. With a view towards developing generalizableML-augmented RANS and LES models, outstanding challenges are discussed, andperspectives are provided. While the promise of ML-augmented turbulencemodeling is clear, and successes have been demonstrated in isolated scenarios,a general consensus of this paper is that truly generalizable models requiremodel-consistent training with careful characterization of underlyingassumptions and imposition of physically and mathematically informed priors andconstraints to account for the inevitable shortage of data relevant topredictions of interest. Thus, machine learning should be viewed as one tool inthe turbulence modeler's toolkit. This modeling endeavor requiresmulti-disciplinary advances, and thus the target audience for this paper is thefluid mechanics community, as well as the computational science and machinelearning communities.

Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence