Physics-informed neural networks for the Reynolds equation with cavitation modeling

The Reynolds equation with cavitation modeling describes the pressure and liquid ratio in thin viscous flows and is widely used in the field of hydrodynamic lubrication. This work presents a method solving it with physics-informed neural networks (PINNs). A strategy for the efficient training of the PINNs, involving adaptation and loss balancing, is proposed. By extending its inputs by parameters such as the relative eccentricity of a journal bearing, the PINN solves several problems simultaneously and generalizes well making it reusable. Accurate pressure and liquid ratio predictions for further values of the relative eccentricity are then obtained by just evaluating the PINN taking less than a second. Solutions for a journal bearing test case are compared with finite difference solutions.

Automated summary

This study proposes a method for solving the Reynolds equation with cavitation modeling using physics-informed neural networks (PINNs). The PINN solves multiple problems simultaneously and generalizes well by extending its inputs with parameters such as the relative eccentricity. Accurate pressure and liquid ratio predictions for further values of the relative eccentricity can be obtained by just evaluating the PINN, taking less than a second. Solutions for a journal bearing test case are compared with finite difference solutions.