Fourier neural operator with boundary conditions for efficient prediction of steady airfoil flows

Abstract

An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator (FNO), which is a new framework of neural networks. Theoretical reasons and experimental results are provided to support the necessity and effectiveness of the improvements made to the FNO, which involve using an additional branch neural operator to approximate the contribution of boundary conditions to steady solutions. The proposed approach runs several orders of magnitude faster than the traditional numerical methods. The predictions for flows around airfoils and ellipses demonstrate the superior accuracy and impressive speed of this novel approach. Furthermore, the property of zero-shot super-resolution enables the proposed approach to overcome the limitations of predicting airfoil flows with Cartesian grids, thereby improving the accuracy in the near-wall region. There is no doubt that the unprecedented speed and accuracy in forecasting steady airfoil flows have massive benefits for airfoil design and optimization.