Abstract
Aerodynamic surrogate modeling mostly relies only on integrated loads data obtained from simulation or experiment,while neglecting and wasting the valuable distributed physical infor-mation on the surface.To make full use of both integrated and distributed loads,a modeling para-digm,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 appli-cable 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 mul-tiple feature extraction methods,and the well-performed generalization capabilities over different airfoils are verified through a transonic case.Compared with traditional direct modeling,the pro-posed 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 supe-rior performance offered by the proposed deep learning framework.
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