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

Abstract

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