Exploration of robust machine learning strategy for subgrid scale stress modeling

Abstract

Various aspects of machine learning (ML) are explored to resolve limitations appearing in current ML-based subgrid scale (SGS) stress modeling. Graph neural network (GNN), applied in the present study, allows flexible and rigorous use of spatial convolution regardless of the proximity to physical boundaries and mesh uniformity. Along with GNN, the proposed feature scaling method relies only on the local quantities and can be applied for a range of flow configurations. A data augmentation method is also proposed to consider the rotational invariant. All these techniques are implemented in the present model, and the model is compared with versions of corresponding ML-based models including a typical multilayer perceptron (MLP) for various flow configurations. The results showed that both GNN and MLP models yield reasonable prediction overall. However, GNN shows superior performance near-wall due to spatial convolution. Although the present method implements the rotational invariant discretely, the augmentation method is found to produce consistent performance for any rotated coordinates. The minimal flow configuration, which can train a model to predict a range of flow configurations, is also explored. It is found that a model trained based on turbulent channel flows alone yields a close level of prediction robustness to the ones trained with multiple flow configurations. The developed GNN model is implemented in OpenFOAM, and large eddy simulation (LES) results are compared with corresponding direct numerical simulation data. With these proposed techniques, ML-based SGS models can be improved in terms of robustness and usability for a range of LES applications.