A fast transonic airfoil flow field prediction model based on a modified Fourier neural operator

Traditional aerodynamic optimization coupled with computational fluid dynamics is associated with a high computational cost. Surrogate models based on deep learning methods can rapidly predict flow fields from the grid input but often suffer from poor accuracy and generalizability. This study introduces a modified Fourier neural operator for flow field prediction. Unlike most convolution-based models, the Fourier neural operator learns the solution operator directly in the function space, enhancing predictive accuracy and generalizability. The proposed model incorporates a shallow feature extractor, a boundary variable fine-tuner, and several physical priors, including the initial flow field and boundary conditions. The model is trained on uniformly parameterized algebraic grids to accelerate grid generation in aerodynamic optimization. The prediction error for the flow field and force coefficients on the validation and test sets is reduced by 70% to 90% compared with that of the previous convolutional model. The proposed model can make precise predictions for supercritical airfoils under typical working conditions, with a drag coefficient error of approximately 1 drag count on the validation set, and generalizes better than previous convolution-based methods do on extrapolative inflow conditions and airfoils.