A Priori Assessment of Rotational Invariance in Multiscale Convolutional Neural Network-Based Subgrid-Scale Model for Wall-Bounded Turbulent Flows

Abstract

This study proposes a rotationally invariant data-driven subgrid-scale (SGS) model for large-eddy simulation (LES) of wall-bounded turbulent flows. Building upon the multiscale convolutional neural network subgrid-scale model, which outputs SGS stress tensors ($\tau_{ij}$) as the baseline, the deep neural network (DNN) architecture is modified to satisfy the principle of material objectivity by removing the bias terms and batch normalization layers while incorporating a spatial transformer network (STN) algorithm. The model was trained on a turbulent channel flow at $\mathrm{Re}_\tau = 180$ and evaluated using both non-rotated and rotated inputs. The results show that the model performs well in predicting $\tau_{ij}$ and key turbulence statistics, including dissipation, backscatter, and SGS transport. These quantities reflect the ability of the model to reproduce the energy transfer between the resolved scale and SGS. Moreover, it effectively generalizes to unseen rotated inputs, accurately predicting $\tau_{ij}$ despite the input configurations not being encountered during the training. These findings highlight that modifying the DNN architecture and integrating the STN-based algorithm improves the ability to recognize and correctly respond to rotated inputs. The proposed data-driven SGS model addresses the key limitations of common data-driven SGS approaches, particularly their sensitivity to rotated input conditions. It also marks an important advancement in data-driven SGS modeling for LES, particularly in flow configurations where rotational effects are non-negligible.