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

Generalizability of machine-learning (ML) based turbulence closures to accurately predict unseen practical flows remains an important challenge. At the Reynolds-averaged Navier-Stokes (RANS) level, NN-based closure modeling is rendered difficult due two reasons: inherent complexity constitutive relation arising from flow-dependent non-linearity and bifurcations; and, inordinate difficulty in obtaining high-fidelity data covering entire parameter space interest. In this context, objective work investigate approximation capabilities standard moderate-sized fully-connected NNs. We seek systematically effects of: (i) intrinsic solution manifold; (ii) sampling procedure (interpolation vs. extrapolation) (iii) optimization procedure. To overcome acquisition challenges, three proxy-physics surrogates different degrees (yet significantly simpler than physics) are employed generate parameter-to-solution maps. Even for simple system, it demonstrated that feed-forward NNs require more freedom original model approximate true even when trained with over (interpolation). Additionally, if deep only part (extrapolation), their capability reduces considerably not straightforward find optimal architecture. Overall, findings provide a realistic perspective on utility ML applications identify areas improvement.