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

This paper presents a complete derivation and design of physics-informed neural network (PINN) applicable to solve initial boundary value problems described by linear ordinary differential equations. The objective with this technical note is not develop numerical solution procedure which more accurate efficient than standard finite element- or difference-based methods, but give fully explicit mathematical description PINN present an application example in the context hydrodynamic lubrication. It is, however, worth noticing that developed herein, contrary FEM FDM, meshless method training does require big data typical machine learning.