Hypersonic flow field and heat flux prediction model based on physics-informed neural networks with positional encoding

The calculation of flow fields and aerodynamic heat under hypersonic flow conditions faces challenges such as low computational efficiency and stringent grid requirements. In contrast, the physics-informed neural network (PINN) model exhibits advantages such as adhering to physical laws, being mesh-free, and having high computational efficiency. Given that neural network models tend to smooth out the data distribution at locations with large gradients and strong discontinuities in hypersonic flow fields, this paper develops a PINN model with high-frequency positional encoding (PE-PINN). This model maps coordinate information to a high-dimensional space, enhancing the network's capability to capture high-gradient features. Furthermore, in the process of modeling two-dimensional flow fields, the PE-PINN model incorporates a shock wave attention module to capture shock wave positions and weighted enhancement of features in shock wave regions, allowing the network to better capture areas with large gradient data distributions in hypersonic flow fields. Compared with the traditional PINN model, the PE-PINN maintains the same prediction efficiency while improving the accuracy of shock wave position characterization from 91.2% to 99%. It successfully simulates the large gradient temperature distribution near the wall, achieving aerothermal prediction with 65.96% and 72.34% efficiency improvements compared to traditional numerical simulations using the PINN and PE-PINN models. This provides an effective method for rapid iterative calculations of fluid–structure interaction in the thermal protection systems of hypersonic vehicles.