A transformer-based convolutional method to model inverse cascade in forced two-dimensional turbulence

Abstract

The present work proposes a novel transformer-based convolutional neural network (TransCNN) method to effectively model the inverse energy cascade in two dimensional (2D) turbulence. The TransCNN structure combines large-scale features extracted by transformer with small-scale features from convolutional layers, thus is considered suitable for multi-scale modeling. The novel TransCNN method has been applied to model sub-grid scale (SGS) stress for large-eddy simulation (LES) of 2D turbulence, under the extremely challenging situation that the LES grid is too coarse to resolve the external forcing scale. The data-driven model trained by the novel TransCNN structure is compared to two deep CNN models with varying complexities. All models exhibit proficiency during a priori tests. Notably, TransCNN surpasses its counterparts in predictive accuracy and generalizability in a posteriori tests. An investigation into the receptive fields reveals that the TransCNN model can efficiently leverage global information with the transformer structure, which is key to its superior performance in representing the inverse energy cascade in the 2D turbulent simulations.