Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem

This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial and boundary value problems described by linear ordinary differential equations. The objective with this technical note is not to develop a numerical solution procedure which...

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Bibliographic Details
Published in:Lubricants Vol. 9; no. 8; p. 82
Main Author: Almqvist, Andreas
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2021
Subjects:
Bias
Boundary value problems
Differential equations
Finite difference method
Finite element method
Fluid mechanics
Machine Elements
Machine learning
Maskinelement
Meshless methods
Neural networks
Ordinary differential equations
Partial differential equations
Physics
PINN
reynolds equation
ISSN:2075-4442, 2075-4442
Online Access:Get full text
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Summary:This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial and boundary value problems described by linear ordinary differential equations. The objective with this technical note is not to develop a numerical solution procedure which is more accurate and efficient than standard finite element- or finite difference-based methods, but to give a fully explicit mathematical description of a PINN and to present an application example in the context of hydrodynamic lubrication. It is, however, worth noticing that the PINN developed herein, contrary to FEM and FDM, is a meshless method and that training does not require big data which is typical in machine learning.
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ISSN:2075-4442
2075-4442
DOI:10.3390/lubricants9080082