Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics
Artificial neural networks are a powerful tool for spatial and temporal functions approximation. This study introduces a novel approach for modeling non-Newtonian fluid flows by minimizing a proposed power loss metric, which aligns with the variational formulation of boundary value problems in hydro...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10752927/ |
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| _version_ | 1846160811848892416 |
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| author | Ivan Stebakov Alexei Kornaev Elena Kornaeva Nikita Litvinenko Yuri Kazakov Oleg Ivanov Bulat Ibragimov |
| author_facet | Ivan Stebakov Alexei Kornaev Elena Kornaeva Nikita Litvinenko Yuri Kazakov Oleg Ivanov Bulat Ibragimov |
| author_sort | Ivan Stebakov |
| collection | DOAJ |
| description | Artificial neural networks are a powerful tool for spatial and temporal functions approximation. This study introduces a novel approach for modeling non-Newtonian fluid flows by minimizing a proposed power loss metric, which aligns with the variational formulation of boundary value problems in hydrodynamics and extends the classical Lagrange variational principle. The method is distinguished by its data-free nature, enabling problem-solving through 2D or 3D images of the flow domain. Validation was performed using both multi-layer perceptrons and U-Net architectures, with results compared against analytical and numerical benchmarks. The method demonstrated good results with a relative error of 1.41% in comparison with the analytical solution for non-Newtonian fluids. The power loss formulation offers a clear advantage by simplifying the modeling process and enhancing interpretability. Notably, the proposed method demonstrates improvements over existing techniques by providing algorithmic simplicity and universality, with applications ranging from blood flow modeling in vessels and tissues to broader hydrodynamic scenarios. |
| format | Article |
| id | doaj-art-fd1bc629cefc41bcad6c844f069d0af1 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-fd1bc629cefc41bcad6c844f069d0af12024-11-22T00:00:47ZengIEEEIEEE Access2169-35362024-01-011216994516995410.1109/ACCESS.2024.349843710752927Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in HydrodynamicsIvan Stebakov0https://orcid.org/0000-0003-1897-683XAlexei Kornaev1Elena Kornaeva2https://orcid.org/0000-0003-0123-4004Nikita Litvinenko3https://orcid.org/0009-0003-2983-8608Yuri Kazakov4https://orcid.org/0000-0002-9655-4520Oleg Ivanov5https://orcid.org/0009-0006-1508-8430Bulat Ibragimov6https://orcid.org/0000-0001-7739-7788Research Center for Artificial Intelligence, Innopolis University, Innopolis, RussiaResearch Center for Artificial Intelligence, Innopolis University, Innopolis, RussiaDepartment of Information Systems and Digital Technologies, Orel State University, Oryol, RussiaResearch Center for Artificial Intelligence, Innopolis University, Innopolis, RussiaDepartment of Mechatronics, Mechanics, and Robotics, Orel State University, Oryol, RussiaResearch Center for Artificial Intelligence, Innopolis University, Innopolis, RussiaDepartment of Computer Science, University of Copenhagen, Copenhagen, DenmarkArtificial neural networks are a powerful tool for spatial and temporal functions approximation. This study introduces a novel approach for modeling non-Newtonian fluid flows by minimizing a proposed power loss metric, which aligns with the variational formulation of boundary value problems in hydrodynamics and extends the classical Lagrange variational principle. The method is distinguished by its data-free nature, enabling problem-solving through 2D or 3D images of the flow domain. Validation was performed using both multi-layer perceptrons and U-Net architectures, with results compared against analytical and numerical benchmarks. The method demonstrated good results with a relative error of 1.41% in comparison with the analytical solution for non-Newtonian fluids. The power loss formulation offers a clear advantage by simplifying the modeling process and enhancing interpretability. Notably, the proposed method demonstrates improvements over existing techniques by providing algorithmic simplicity and universality, with applications ranging from blood flow modeling in vessels and tissues to broader hydrodynamic scenarios.https://ieeexplore.ieee.org/document/10752927/Physics-based machine learningcalculus of variationshydrodynamicsnon-Newtonian fluids |
| spellingShingle | Ivan Stebakov Alexei Kornaev Elena Kornaeva Nikita Litvinenko Yuri Kazakov Oleg Ivanov Bulat Ibragimov Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics IEEE Access Physics-based machine learning calculus of variations hydrodynamics non-Newtonian fluids |
| title | Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics |
| title_full | Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics |
| title_fullStr | Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics |
| title_full_unstemmed | Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics |
| title_short | Artificial Neural Networks as a Natural Tool in Solution of Variational Problems in Hydrodynamics |
| title_sort | artificial neural networks as a natural tool in solution of variational problems in hydrodynamics |
| topic | Physics-based machine learning calculus of variations hydrodynamics non-Newtonian fluids |
| url | https://ieeexplore.ieee.org/document/10752927/ |
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