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Generalizability of machine-learning (ML) based turbulence closures toaccurately predict unseen practical flows remains an important challenge. Atthe Reynolds-averaged Navier-Stokes (RANS) level, NN-based turbulence closuremodeling is rendered difficult due to two important reasons: inherentcomplexity of the constitutive relation arising from flow-dependentnon-linearity and bifurcations; and, inordinate difficulty in obtaininghigh-fidelity data covering the entire parameter space of interest. In thiscontext, the objective of the work is to investigate the approximationcapabilities of standard moderate-sized fully-connected NNs. We seek tosystematically investigate the effects of: (i) intrinsic complexity of thesolution manifold; (ii) sampling procedure (interpolation vs. extrapolation)and (iii) optimization procedure. To overcome the data acquisition challenges,three proxy-physics turbulence surrogates of different degrees of complexity(yet significantly simpler than turbulence physics) are employed to generatethe parameter-to-solution maps. Even for this simple proxy-physics system, itis demonstrated that feed-forward NNs require more degrees of freedom than theoriginal proxy-physics model to accurately approximate the true model even whentrained with data over the entire parameter space (interpolation).Additionally, if deep fully-connected NNs are trained with data only from partof the parameter space (extrapolation), their approximation capability reducesconsiderably and it is not straightforward to find an optimal architecture.Overall, the findings provide a realistic perspective on the utility of MLturbulence closures for practical applications and identify areas forimprovement.

Turbulence closure modeling with data-driven techniques: Investigation of generalizable deep neural networks