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.