GCN-based 3D aerodynamic optimization design based on discrete adjoint method

Gradient-based optimization algorithms, particularly the discrete adjoint method, are widely used in aerodynamic shape optimization due to their independence from design variable dimensionality. However, solving the adjoint equations incurs a computational cost comparable to that of flow field solutions, making it crucial to reduce this burden. In this paper, a three-dimensional aerodynamic shape optimization framework integrating the discrete adjoint method with a graph convolutional neural network (GCN) was proposed. A database of flow fields and optimization gradients for various wings was constructed, and a GCN-based gradient prediction model was developed to replace the traditional discrete adjoint solution. Benefiting from the model’s strong capability in topological aggregation and spatial feature extraction, its prediction accuracy reaches approximately ${10}^{-5}$. The proposed framework was applied to the aerodynamic shape optimization of the ONERA M6 wing under aerodynamic and geometric constraints. Compared with the traditional discrete adjoint method, the GCN-based framework reduces computational time by about 76.2%, significantly improving optimization efficiency. This method provides a new technical pathway for efficient and accurate aerodynamic shape optimization.