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...

Full description

Saved in:
Bibliographic Details
Published in:IEEE access 2024, Vol.12, p.169945-169954
Main Authors: Stebakov, Ivan, Kornaev, Alexei, Kornaeva, Elena, Litvinenko, Nikita, Kazakov, Yuri, Ivanov, Oleg, Ibragimov, Bulat
Format: Article
Language:English
Subjects:
Artificial neural networks
Blood flow
Boundary value problems
calculus of variations
Error analysis
Exact solutions
Fluid flow
Fluid mechanics
Fluids
Hydrodynamics
Image enhancement
Image resolution
Machine learning
Machine learning algorithms
Mathematical analysis
Multilayer perceptrons
Multilayers
Neural networks
Newtonian fluids
Non Newtonian fluids
Numerical models
Physics-based machine learning
Problem solving
Three dimensional flow
Three-dimensional displays
Two dimensional analysis
Two dimensional flow
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2024.3498437