Spatiotemporal wall pressure forecast of a rectangular cylinder with physics-aware DeepU-Fourier neural network

The wall pressure is of great importance in understanding the forces and structural responses induced by fluid. Recent works have investigated the potential of deep learning techniques in predicting mean pressure coefficients and fluctuating pressure coefficients, but most of existing deep learning frameworks are limited to predicting a single snapshot using full spatial information. To forecast spatiotemporal wall pressure of flow past a rectangular cylinder, this study develops a physics-aware DeepU-Fourier neural Network (DeepUFNet) deep learning model. DeepUFNet comprises the UNet structure and the Fourier neural network, with physical high-frequency loss control embedded in the model training stage to optimize model performance. Wind tunnel testing was performed to collect wall pressures on two-dimensional rectangular cylinders using high-frequency pressure scanning, thereby constructing a database for DeepUFNet training and testing. The DeepUFNet model is found capable of forecasting spatiotemporal wall pressure information with high accuracy on the rectangular cylinder with side ratio 1.5. The comparison between forecast results and experimental data presents agreement in statistical information and physical interpretation. It is also found that embedding a physical high-frequency loss control coefficient b in the DeepUFNet model can significantly improve model performance in forecasting spatiotemporal wall pressure information, particularly, high-order frequency fluctuation and wall pressure variance. Furthermore, the DeepUFNet extrapolation capability is tested with sparse spatial information input, and the model presents a satisfactory extrapolation ability. Last, the DeepUFNet is tested for generalization in unseen cases, rectangular cylinders with side ratio 4 and 3.75, and the model presents satisfactory generalization ability.