Exploring Variational Methods in Hydro- and Hemodynamics Through Incompressible Velocity Distribution Sampling

Artificial neural networks are a robust tool for approximating spatial and temporal functions. This study introduces a novel method for hydro- and hemodynamics based on the minimization of a power loss. This loss function corresponds to the variational formulation of the boundary value problem, gene...

Full description

Saved in:
Bibliographic Details
Published in:IEEE access 2024, Vol.12, p.191109-191119
Main Authors: Stebakov, Ivan, Kornaev, Alexei, Kornaeva, Elena, Majorov, Sergey
Format: Article
Language:English
Subjects:
Approximation
Artificial neural networks
Boundary conditions
Boundary value problems
Calculus of variations
Fluid flow
Hemodynamics
Hydrodynamics
Incompressible flow
Kinematics
Mathematical analysis
Mathematical models
Numerical models
physics-based machine learning
Pressure distribution
Solid modeling
Stress
Tensors
Three dimensional flow
Three-dimensional displays
Two dimensional analysis
Two dimensional flow
Variational methods
Velocity distribution
viscous fluids
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Artificial neural networks are a robust tool for approximating spatial and temporal functions. This study introduces a novel method for hydro- and hemodynamics based on the minimization of a power loss. This loss function corresponds to the variational formulation of the boundary value problem, generalizing the Helmholtz variational principle to accommodate various mechanical boundary conditions. The method employs a global approximation of velocity distribution within the flow domain, parameterized by flow rate, allowing a single inference model to address multiple problems. The efficacy of the method was validated using 2D and 3D images, including 3D vessel images, with results compared against analytical and numerical solutions. Potential applications span a range of medical tasks, such as drug delivery, pressure distribution calculation, and vessel strength assessment.
ISSN:2169-3536
DOI:10.1109/ACCESS.2024.3517143