HL-nets: Physics-informed neural networks for hydrodynamic lubrication with cavitation

Recently, physics-informed neural networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs). In this study, we establish a deep learning computational framework, HL-nets, for computing the flow field of hydrodynamic lubrication involving cavitation effects. Two classical cavitation conditions, i.e., the Swift-Stieber (SS) condition and the Jakobsson-Floberg-Olsson (JFO) condition, are implemented in the PINNs to solve the Reynolds equation. For the non-negativity constraint of the SS cavitation condition, a penalizing scheme with a residual of the non-negativity and an imposing scheme with a continuous differentiable non-negative function are proposed. For the complementarity constraint of the JFO cavitation condition, the pressure and cavitation fraction are taken as the neural network outputs, and the residual of the Fischer-Burmeister (FB) equation constrains their complementary relationships. Multi-task learning (MTL) methods are applied to balance the newly introduced loss terms described above. To estimate the accuracy of HL-nets, we present a numerical solution of the Reynolds equation for oil-lubricated bearings involving cavitation. The results indicate that the proposed HL-nets can highly accurately simulate hydrodynamic lubrication involving cavitation phenomena. The imposing scheme can effectively improve the accuracy of the training results of PINNs, and it is expected to have great potential to be applied to different fields where the non-negativity constraint is needed.