Study on Flow and Heat Characteristics of Compressible Gas in a Supersonic Nozzle Based on PINNs with Sparse Data

Yida Shen¹, Bin Dong², Quan Ma¹, Chao Dang^1,*, Congjian Li^2,*, Guojian Ren³, Shaozhan Wang^1,2, Xiaozhe Sun¹, Yong Ding⁴
1 Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and Small Scale, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China
2 High Speed Aerodynamics Institution, China Aerodynamics Research and Development Center, Mianyang, 621000, China
3 School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, 100044, China
4 School of Aerospace Engineering, Guizhou Institute of Technology, Guiyang, 550025, China
* Corresponding Author: Chao Dang. Email: email ; Congjian Li. Email: email
(This article belongs to the Special Issue: Advances in Microscale Fluid Flow, Heat Transfer, and Phase Change)

Frontiers in Heat and Mass Transfer https://doi.org/10.32604/fhmt.2025.077096

Received 02 December 2025; Accepted 26 December 2025; Published online 26 January 2026

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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.

Keywords

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

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Study on Flow and Heat Characteristics of Compressible Gas in a Supersonic Nozzle Based on PINNs with Sparse Data

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