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Abstract.
This paper presents a study on the application of neural operators, specifically the Fourier Neural Operator (FNO), for modeling gas flow regimes in gas transportation systems (GTS). The research aims to accelerate the calculation of transient gas flow in extensive pipelines while maintaining accuracy and spatial-temporal invariance. The proposed method integrates classical numerical solutions of gas dynamics equations into the training of the neural operator. The first part of the study validates the accuracy of the FNO-based model in predicting gas pressure and flow rates, achieving errors below 0.05% in Mean Absolute Percentage Error (MAPE) and 0.5% in Maximum Absolute Percentage Error (max APE). The second part addresses scenarios involving flow direction reversals in pipelines by extending the training dataset to include cases with reverse pressure gradients and adjusted boundary conditions. Results demonstrate that the model effectively replicates numerical solutions for such cases. Further, the study explores the modeling of GTS with complex topologies, representing the system as a directed graph. The optimization-based approach minimizes flow imbalances at pipeline junctions using a gradient descent algorithm (Adam), leveraging the differentiable nature of the FNO. Computational experiments reveal acceptable computation times and scalability, with GPU acceleration significantly enhancing individual pipeline predictions. The proposed hybrid method combines neural network modeling, optimization, and graph theory to enable the simulation of large-scale GTS. The findings highlight the potential of neural operators in automating and optimizing real-world pipeline network operations, offering a robust framework for future advancements in engineering system modeling.
Keywords:
dynamic system, fluid dynamics, numerical methods, neural operators, optimization methods.
DOI 10.14357/20718632250305
EDN AZJACG
PP. 44-57.
References
1. Emelyanov S.V., Oleynik A.G., Popkov Y.S., Putilov V.A. Information Technologies of Regional Management. Moscow: Editorial URSS; 2004. 400 p. (In Russ). 2. Gelovani V.A., Yurchenko V.V. Problems of Computer Modeling. Moscow: MNIIPU; 1990. 238 p. (In Russ). 3. Gelovani V.A., Britkov V.B., Dubovsky S.V. USSR and Russia in the Global System (1985–2030): Results of Global Modeling. Moscow: URSS; 2025. 320 p. (In Russ). 4. Makarov V.L., Okrepilov V.V., Bakhtizin A.R. Scientific Solutions to Complex Economic and Social Problems Using Supercomputers. Moscow: LENAND; 2023. 416 p. (In Russ). 5. Buch G. Object-Oriented Design with Applications. Moscow: Concord; 1992. 519 p. (In Russ). 6. Gladkov L.A., Kureichik V.V., Kureichik V.M. Genetic Algorithms. 2nd ed. Moscow: Fizmatlit; 2006. 320 p. (In Russ). 7. Yeremeyev A.P., Kurilenko I.E. Temporal Models Based on Branching Time Logic in Intelligent Systems. Artificial Intelligence and Decision Making. 2011;(1):14-26 (In Russ). 8. Pospelov D.A. Multi-Agent Systems – Present and Future. Information Technologies and Computing Systems. 1998;(1):14-21 (In Russ). 9. Gorodetsky V.I., Skobelev P.O. Multi-Agent Technologies for Industrial Applications: Reality and Perspective. Proceedings of SPIIRAS. 2017;(6):11-45 (In Russ). 10. Smirnov A.V., Sheremetov L.B. Models of Coalition Formation of Cooperative Agents: State and Research Perspectives. Artificial Intelligence and Decision Making. 2011;(1):36-48 (In Russ). 11. Sokhova Z.B., Redko V.G. Modeling the Search for Investment Decisions by Autonomous Agents in a Transparent Competitive Economy. Artificial Intelligence and Decision Making. 2019;(2):98-108 (In Russ). 12. Novikov D., Bakhtadze N., Elpashev D., Suleykin A. Integrated Resource Management in the Digital Ecosystem of the Enterprise Based on Intelligent Consorts. IFACPapersOnLine. 2022;55(10):2330-2335. doi:10.1016/j.ifacol.2022.10.056. 13. Kislenko N.A., Belinsky A.V., Kazak A.S., Belinskaya O.I. On the Justification of Using, the Current State, and Some Prospects for the Development of Neural Network Models of the Unified Gas Supply System of Russia. Automation and Informatization of the Fuel and Energy Complex. 2022;5(586):6-17 (In Russ). doi:10.33285/2782-604X-2022-5(586)-6-17. 14. Li Z, Kovachki N.B., Azizzadenesheli K., Liu B., Bhattacharya K., Stuart A.M., et al. Fourier neural operator for parametric partial differential equations. arXiv preprint. 2020. Available from: https://arxiv.org/abs/2010.08895 [Accessed 1 April 2025]. 15. Belinsky A.V., Gorlov D.V., Pyatyshev I.A., Titov A.E. A New Method for Digital Modeling of Unsteady Gas Flow Regimes in Trunk Gas Pipelines Using Neural Operators. Gazovaya Promyshlennost. 2024;5(865):54-66 (In Russ). 16. Chentsov A.G., Chentsov P.A. Routing under constraints: Problem of visit to megalopolises. Autom Remote Control. 2016;77: 1957-1974. doi:10.1134/S0005117916110060 17. Malinetsky G.G. Mathematical Foundations of Synergetics: Chaos, Structures, Computational Experiment. 6th ed. Moscow: URSS; 2017. 312 p. (In Russ). 18. Zhuravlev Y.I. Correct Algebras on Sets of Incorrect (Heuristic) Algorithms. Selected Scientific Works. Moscow: Magistr; 1998. p. 324-377 (In Russ). 19. Roizenson G.V. Synergetic Effect in Decision Making. In: System Studies. Methodological Problems. Yearbook. Ed. by Popkov Y.S., Sadovsky V.N., Tishchenko V.I. No. 36. Moscow: URSS; 2012. p. 248-272 (In Russ). 20. Korshunov S.A., Chionov A.M., Kazak K.A. A Calculation Method for Unsteady Gas Transport Regimes in Linear Sections of Gas Pipelines in Case of Leakage. Gazovaya Promyshlennost. 2012;4(675):44-47 (In Russ). 21. Ermolaeva N.N. Unsteady Models of Heat Exchange and Gas Transportation Through Offshore Gas Pipelines. Proc Karelian Res Cent Russ Acad Sci. 2016;(8):3–10 (In Russ). 22. Bazarov A.A., Danilushkin A.I. Modeling of Thermal and Hydraulic Processes in a Trunk Gas Pipeline. Izvestiya Tomsk Polytechnic University. Geo Assets Engineering. 2017;328(6):81–90 (In Russ). 23. Ali A.H., et al. A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model. Complexity. 2022;2022(1):9367638. doi:10.1155/2022/9367638. 24. Evstigneev N.M. Analysis of Block Stokes-Algebraic Multigrid Preconditioners on GPU Implementations. Communications in Computer and Information Science. 2022. doi:10.1007/978-3-031-11623-0_9. 25. Alpar S., et al. Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines. Symmetry. 2024;16(5):538. doi:10.3390/sym16050538. 26. Zhou W., Miwa S., Okamoto K. Advancing Fluid Dynamics Simulations: A Comprehensive Approach to Optimizing Physics-Informed Neural Networks. Physics of Fluids. 2024;36(1):013615. doi:10.1063/5.0180770. 27. Belinsky A.V. Differentiable Physics – the Basis of Digital Twins in the Oil and Gas Industry. Automation and Informatization of the Fuel and Energy Complex. 2024;12(617):38–50 (In Russ). 28. Sergeyev Y.D., Nasso M.C., Lera D. Numerical Methods Using Two Different Approximations of Space-Filling Curves for Black-Box Global Optimization. Journal of Global Optimization. 2024;88(3):707–722. doi:10.1007/s10898-023-01394-w. 29. Averkin A.N. Explainable Artificial Intelligence in Large Language Models. Speech Technologies. 2024;(1):3–13 (In Russ). 30. Chereshkin D.S., Roizenson G.V., Britkov V.B. Application of Artificial Intelligence Methods for Risk Analysis in Socio-Economic Systems. Information Society. 2020;(3):14–24 (In Russ). 31. Yi K., et al. FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective. Adv Neural Inf Process Syst. 2023;36:69638–69660. 32. Xu M., et al. Equivariant Graph Neural Operator for Modeling 3D Dynamics. arXiv preprint arXiv:2401.11037. 2024. Available from: https://arxiv.org/abs/2401.11037 [Accessed 1 April 2025]. 33. Larichev O.I. Verbal Analysis of Decisions. Moscow: Nauka; 2006. 181 p. (In Russ).
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