Wavelet-enhanced attention fusion model for airfoil flow field prediction

Accurate prediction of complex flow fields around airfoils is crucial for aerodynamic performance. However, traditional numerical simulation methods cannot balance accuracy and efficiency, while existing deep learning approaches often exhibit limited accuracy and necessitate extensive high-fidelity training data. Here, we propose the wavelet-enhanced attention fusion networks (WAFNet), a novel multivariate prediction model designed for the efficient and accurate forecasting of steady-state pressure fields. WAFNet employs an encoder–decoder architecture. Its encoder integrates wavelet, convolutional operations, multi-layer perceptrons, and cross linear-attention mechanisms to enhance physical field data features and highlight critical flow details, particularly near airfoil edges. The decoder first predicts the global flow field structure using Fourier neural operators, and then enhances local features via a multi-scale fusion process. This allows for an accurate prediction of the physical field. A clever design is the wavelet component, which significantly improves the model's ability to capture subtle but important features in complex flow fields, and also greatly reduces the scale and computational cost of the model. Empirical results demonstrate that WAFNet achieves high-precision aerodynamic predictions for airfoil flow fields, even under limited sample conditions. Furthermore, it offers significant advantages in model compactness and computational efficiency compared to purely vision-based deep learning models. These findings suggest WAFNet provides a promising direction for developing efficient, data-driven tools for aerodynamic analysis.