Multiple spatio-temporal attention network: A deep convolutional network for spatio-temporal evolution prediction of flow fields

Abstract

The recent rapid development of machine learning has promoted its application in turbulence research. This paper presents a Multiple Spatio-Temporal Attention (MSTA) Network to predict the spatio-temporal evolution of multi-variable, multi-timestep turbulent flow fields. The model adopts a complete convolutional architecture instead of a recurrent structure typical of traditional time series models. Nonetheless, the model shows the ability to capture the temporal features of turbulence and form complex nonlinear relationships, thereby predicting the spatio-temporal evolution of turbulent flow fields both accurately and quickly. To improve the model’s prediction accuracy, we propose a novel channel attention mechanism, called Multiple Fusion Attention (MFA), which is designed to capture and fuse channel features at different positions more effectively. Additionally, a Spatial Transform Gradient Sharpening (STGS) method is proposed to constrain the spatial gradient in non-uniform curvilinear grids accurately. Based on the direct numerical simulations (DNS) results of a Mach 6, 34° compression ramp flow, two datasets of different sizes are established and related experiments are designed to validate the effectiveness of the proposed MSTA Network. The experimental comparison and analysis demonstrated the best performance in terms of accuracy and efficiency in the present comparison with other machine-learning models. Besides, a series of experiments considering different sample numbers, dataset sizes, prediction lengths, etc., also confirmed the robustness in various application scenarios. Finally, an extended experiment of the model was conducted on the HyTRV dataset from AeroFlowData under flow conditions of Mach 6 and 0° angle of attack, further demonstrating the model’s universality in diverse conditions.