ED-ResNet: Euler Equation Embedding Double-Series Residual Neural Network for Aerothermal Modeling

The data-driven aerothermal modeling method provides strong support for the hypersonic aircraft design. To reduce the training samples and improve the global geometric generalization ability, the Euler equation embedding double-series residual neural network (ED-ResNet) is presented. Firstly, the wall inviscid solution is approximated to the information of the boundary layer outer edge by solving the Euler equation. Then, based on the principle of feature construction, the physical features of the boundary layer outer edge can be constructed. Finally, the double-series residual neural network (D-ResNet) is employed to establish the aerothermal model by using physical features of the boundary layer outer edge as input data. The physical features of the boundary layer outer edge are the bridge between the Euler equation and D-ResNet; it has a prior ability to distinguish the quality of generalization. The performance of the proposed ED-ResNet is validated using hypersonic double-ellipsoid, hypersonic ellipsoid, and blunt cone. The results indicate that with only four training samples, ED-ResNet can obtain high-precision aerothermal extrapolation prediction results with an error of less than 7% relative to Reynolds-averaged Navier–Stokes calculation results. Meanwhile, the ED-ResNet can successfully predict aerothermal loads for unknown geometric shapes, with a global geometric generalization error less than 13%.