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Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences

COMPARATIVE ANALYSIS OF PHYSICS-INFORMED NEURAL NETWORKS AND THE RUNGE-KUTTA METHOD FOR SOLVING ONE-DIMENSIONAL EULER EQUATIONS

Published December 2025

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S. Alpar+
International Information Technology University, Almaty
https://orcid.org/0000-0003-0579-4180
R. Faizulin+
International Information Technology University, Almaty
https://orcid.org/0009-0005-2824-9312
F. Tokmukhamedova+
International Information Technology University, Almaty
https://orcid.org/0000-0001-7980-8245
International Information Technology University, Almaty
International Information Technology University, Almaty
International Information Technology University, Almaty
Abstract

This study presents a model describing the physical process associated with gas flow through pipelines using a system of one-dimensional Euler equations. In this work the numerical solution of the system of Euler equations through physically informed neural networks is used, a method that combines modern approaches of deep learning models together with the physical conditions of the problem, which specify the differential equations, initial and boundary conditions. For the validation of the model, the analytical solution of the system of one-dimensional Euler equations will be used and compared with the numerical solution obtained by the deep learning model in the form of graph comparison and metrics calculation. Also, for the relative comparison of this model will be compared with the classical 4-th order Runge-Kutta (RK4) numerical method, where the deep learning method showed higher quality compared to the classical method. The obtained model is of high quality and can be used in gas flow modeling, and the quality of the deep learning model was significantly higher in relative comparison with the classical RK4 method, which emphasizes the effectiveness and novelty of using deep learning methods in comparison with classical methods.

Language

Русский

How to Cite

[1]
Alpar С., Faizulin Р. and Tokmukhamedova Ф. 2025. COMPARATIVE ANALYSIS OF PHYSICS-INFORMED NEURAL NETWORKS AND THE RUNGE-KUTTA METHOD FOR SOLVING ONE-DIMENSIONAL EULER EQUATIONS. Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences. 92, 4 (Dec. 2025). DOI:https://doi.org/10.51889/2959-5894.2025.92.4.003.