TY  - EJOU
AU  - Shen, Yida 
AU  - Dong, Bin 
AU  - Ma, Quan 
AU  - Dang, Chao 
AU  - Li, Congjian 
AU  - Ren, Guojian 
AU  - Wang, Shaozhan 
AU  - Sun, Xiaozhe 
AU  - Ding, Yong 

TI  - Study on Flow and Heat Characteristics of Compressible Gas in a Supersonic Nozzle Based on PINNs with Sparse Data
T2  - Frontiers in Heat and Mass Transfer

PY  - 2026
VL  - 24
IS  - 2
SN  - 2151-8629

AB  - 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.
KW  - Physics-informed neural networks; sparse data; supersonic flow; specific physical knowledge; shortcut connections

DO  - 10.32604/fhmt.2025.077096