Preprint Technical Note Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 3 August 2021 / Approved: 4 August 2021 / Online: 4 August 2021 (09:45:41 CEST)

A peer-reviewed article of this Preprint also exists.

Almqvist, A. Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem. Lubricants 2021, 9, 82. Almqvist, A. Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem. Lubricants 2021, 9, 82.

Journal reference: Lubricants 2021, 9, 82
DOI: 10.3390/lubricants9080082

Abstract

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 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.

Keywords

PINN; Reynolds equation; Machine Learning

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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