计算流体力学（CFD）代码所需的计算成本和内存需求对于工程设计（如空气动力学形状优化）可能变得非常高。基于深度学习的亚声速流场重构已经非常成功。相比亚声速流场，跨声速流场数据梯度更大，几何敏感度高。因此，基于传统的编码器-解码器架构的模型精度有限。建立基于U-Net架构的深度卷积神经网络（CNN）来快速预测跨声速流场。不同几何翼型的高保真度求解流场被用作训练数据。神经网络将表示翼型几何的符号距离函数（SDF）作为输入，将翼型外围压力场和速度场作为输出。与基准编码器-解码器架构相比，新的U-Net架构的误差降低了约24%。梯度锐化增强了流场的可视化效果，同时进一步将误差减小了约10%。最终，深度学习模型在速度场和压力场的误差保持在1.013%和4.625%。
The computational cost and memory requirements for Computational Fluid Dynamics (CFD) codes can be demanding for engineering design. Reconstruction of subsonic aerodynamic flow fields based on deep learning has been highly successful. Compared with the subsonic flow field, the transonic flow field has a larger gradient and higher geometric sensitivity, resulting in limited accuracy of the model based on the traditional encoder-decoder architecture. A deep Convolutional Neural Network (CNN) based on the U-Net architecture is therefore established to quickly predict the transonic flow field. High-fidelity CFD solutions to different geometric airfoils are used as the training dataset, while the neural network takes the Signed Distance Function (SDF) representing the airfoil geometry as input, outputting the airfoil peripheral pressure field and velocity field. The CNN model based on the U-Net architecture automatically detects multi-scale low-dimensional features and reflects them in the output results. Compared with the benchmark encoder-decoder architecture, the error of the new U-Net architecture is reduced by about 24%. Gradient sharpening enhances the visualization of the flow field while further reducing the error by approximately 10%. The effectiveness of the neural network in predicting unseen airfoil flow fields is explored, and the error of our model on the velocity field and pressure field is maintained at 1.013% and 4.625%, respectively.
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