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

被引:30
作者
Almqvist, Andreas [1 ]
机构
[1] Lulea Univ Technol, Div Machine Elements, SE-97187 Lulea, Sweden
基金
瑞典研究理事会;
关键词
PINN; machine learning; reynolds equation;
D O I
10.3390/lubricants9080082
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
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.
引用
收藏
页数:9
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