Rapid Prediction of Surface Parameters on Bodies in External Flow Using Physics-Embedded Neural Networks

The flow field around hypersonic vehicles features high temperatures and pressures with sharp parameter variations, while available data are limited. As a result, deep learning models struggle to honor physical constraints and often yield predictions lacking physical consistency. To address this, we propose a physics‑embedding strategy that injects fluid‑mechanics and heat‑transfer priors into the model inputs, architecture, and loss. Building convolutional and graph neural networks (PE‑CNN and PE‑GNN), we markedly improve physical consistency and generalization under small‑sample regimes, enabling node‑level rapid prediction of wall pressure and heat‑flux density. Experiments show that, relative to CNNs/GNNs without physics embedding, our approach reduces the mean pressure error from 50% to 6%, and further to 2.85% with PE‑GNN; moreover, over 90% of predicted nodes have errors below 10%. In sum, the method achieves technical breakthroughs in hypersonic‑flow modeling, small‑sample learning, and physics‑embedding strategies, delivering high‑accuracy, rapid prediction of wall parameters from very limited training data, with predictions that are physically consistent and in close agreement with CFD.