Heterogeneous data-driven aerodynamic modeling based on physical feature embedding

Aerodynamic surrogate modeling mostly relies only on integrated loads data obtained from simulation or experiment, while neglecting and wasting the valuable distributed physical information on the surface. To make full use of both integrated and distributed loads, a modeling paradigm, called the heterogeneous data-driven aerodynamic modeling, is presented. The essential concept is to incorporate the physical information of distributed loads as additional constraints within the end-to-end aerodynamic modeling. Towards heterogenous data, a novel and easily applicable physical feature embedding modeling framework is designed. This framework extracts low-dimensional physical features from pressure distribution and then effectively enhances the modeling of the integrated loads via feature embedding. The proposed framework can be coupled with multiple feature extraction methods, and the well-performed generalization capabilities over different airfoils are verified through a transonic case. Compared with traditional direct modeling, the proposed framework can reduce testing errors by almost 50%. Given the same prediction accuracy, it can save more than half of the training samples. Furthermore, the visualization analysis has revealed a significant correlation between the discovered low-dimensional physical features and the heterogeneous aerodynamic loads, which shows the interpretability and credibility of the superior performance offered by the proposed deep learning framework.