An Optimized Deep Learning Framework for Turbulence Modeling

The recent rise of machine learning in computer engineering, serving purposes such as prediction, image processing, classification, and clustering, has extended into various scientific fields. Recently, neural networks have been developed to be integrated with Reynolds-averaged Navier–Stokes (RANS) modeling to improve the prediction of turbulent flow. In this study, a multilayer perceptron network (MLP) and a cascade MLP network will be trained to predict the turbulent eddy viscosity ( $${\nu _t}$$ ) and the Reynolds stress ( $${R_{ij}}$$ ). To predict the eddy viscosity, input variables are selected from high-fidelity data at $${\mathop {{\text{Re}}}\nolimits_\tau } = 180$$ . First, they are grouped based on feature importance to determine input categories for the MLP network, and then the performance of each group is evaluated. All studied groups demonstrated acceptable performance; among them, the model closest to the direct numerical simulation (DNS) solution was identified. In the spectrum of input variables, the wall distance emerged as the paramount parameter, boasting the highest feature importance value among the variables considered. To assess the accuracy of the neural network, the prediction of turbulent viscosity is carried out at $${\mathop {{\text{Re}}}\nolimits_\tau } = 381$$ . The output of the MLP network and the strain-rate tensor are considered as the input of the cascade MLP network to investigate the effect of these inputs on Reynolds stress prediction. The cascade MLP and MLP networks demonstrated acceptable accuracy in predicting Reynolds stress and eddy viscosity, with their results indicating a strong correlation between the outputs of the two neural networks.