Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines

Abstract

This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flows in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the PINN utilizing the continuous symmetry data inherent in PDEs, which is called the symmetry-enhanced Physics-Informed Neural Network. This innovative approach combines artificial neural networks (ANNs) integrating physical equations, which provide enhanced efficiency and accuracy when modeling various complex processes related to physics with a symmetric and asymmetric nature. The presented mathematical model, based on the system of Euler equations, has been carefully implemented using Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In this research, a comparative and comprehensive analysis was carried out comparing the outcomes obtained using the symmetry-enhanced PINN method and those from conventional computational fluid dynamics (CFD) approaches. The analysis highlighted the advantages of the symmetry-enhanced PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing the computation time, demonstrating its capacity as a revolutionary modeling tool. The estimated results derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulations has the potential to improve the integrity of our energy infrastructure and utilization of gas resources, contributing to advancing our understanding of symmetry principles in nature. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations. The numerical data covered the physics of the process related to the modeling of high-pressure gas flows in pipelines with regard to density, velocity and pressure, where the PINN model was able to outperform the classical CFD method for velocity by 170% and for pressure by 360%, based on L∞ values.