Inviscid information-embedded machine learning for the airfoil inverse mapping

The mapping process within the airfoil inverse design is to derive airfoil geometry based on the prescribed surface aerodynamic distribution, typically the pressure coefficient (C_p) distribution. Recent studies have used neural networks (C_p,v-y models) to rapidly predict airfoil shapes according to the designed C_p distributions which consider viscosity (C_p,v). However, the complex relationship between C_p,v and airfoil geometry challenges surrogate models, often requiring extensive training data to achieve sufficient accuracy. This study employs inviscid C_p distribution (C_p,i) as an intermediate bridge between C_p,v and airfoil geometry. The proposed C_p,v-C_p,i-y model simplifies the mapping learned by neural network through converting C_p,v-y into C_p,v-C_p,i. And the C_p,i-y is achieved via parametric airfoil iteration based on potential flow theory (panel method). Results demonstrate that the new model reduces airfoil prediction errors by 25–40 % on average compared with two existing C_p,v-y models. Notably, 100–500 % reduction in maximum relative error, which often occurs at the critical parts in airfoil design such as the maximum thickness and shape of leading edge under C_p,v models, can be observed in the test samples. And the better generalization ability is further validated through the flatter minima and less non-convexity of the loss surface under C_p,v-C_p,i-y model compared with the one under C_p,v-y model. The idea of introducing C_p,i provides insights into addressing the issue of large prediction errors caused by strong nonlinear mappings in the traditional C_p,v-y models and has the potential to handle similar issues like cascade or three-dimensional inverse problems.