Deep structured neural networks for turbulence closure modeling

Despite well-known limitations of Reynolds-averaged Navier–Stokes (RANS) simulations, this methodology remains the most widely used tool for predicting many turbulent flows due to computational efficiency. Machine learning is a promising approach improve accuracy RANS simulations. One major area improvement using machine models represent complex relationship between mean flow field gradients and Reynolds stress tensor. In present work, modifications stability previous optimal eddy viscosity approaches simulations are presented evaluated. The reformulated with non-negativity constraint, which promotes numerical stability. We demonstrate that new formulation improves conditioning equations periodic hills test case. To suitability proportional/orthogonal tensor decomposition use in physics-informed data-driven turbulence closure, we two neural networks (structured on specific decomposition, incorporated as an inductive bias into network design) predict newly linear non-linear parts Injecting these model predictions stresses simulation velocity field, even when compared sophisticated (state art) physics-based closure model. Finally, apply shapley additive explanations values obtain insights from learned representation inner workings input feature data.