@article{Shen2026, 
author = {Yida Shen and Bin Dong and Quan Ma and Chao Dang and Congjian Li and Guojian Ren and Shaozhan Wang and Xiaozhe Sun and Yong Ding},
title = {Study on Flow and Heat Characteristics of Compressible Gas in a Supersonic Nozzle Based on PINNs with Sparse Data},
year = {2026},
journal = {Frontiers in Heat and Mass Transfer},
volume = {24},
number = {2},
pages = {7},
keywords = {Physics-informed neural networks, sparse data, supersonic flow, specific physical knowledge, shortcut connections},
url = {https://www.sciopen.com/article/10.32604/fhmt.2025.077096},
doi = {10.32604/fhmt.2025.077096},
abstract = {This article explores the application of Physics-Informed Neural Networks (PINNs) in solving supersonic flow problems within a Laval nozzle, proposing innovative methods by integrating physical constraints and neural network optimization techniques. The main innovations of this study include the construction of a novel neural network architecture with shortcut connections to enhance the prediction of overall flow trends and local fluctuations, thereby improving convergence speed, reducing computational costs, and increasing the accuracy of flow field reconstruction. Additionally, this study designs a PINNs framework that incorporates specific physical knowledge (SPK) to improve model stability, generalization, and accuracy, even with sparse training data. A dynamic loss weighting strategy is employed to optimize training convergence, and velocity components are reformulated as magnitude and angle to simplify boundary conditions and reduce the dimensionality of the solution space. The results demonstrate that the proposed methods achieve satisfactory accuracy and robustness in solving supersonic problems, highlighting their potential application value.}
}