Evaluation of physics-informed neural networks (PINN) in the solution of the Reynolds equation

Using neural networks to solve engineering problems has become increasingly common and relevant because of their versatility and efficiency. Although this tool can handle complex identification and prediction problems, a large amount of data are often required for training the neural network, making its application prohibitive for problems where the data are unavailable and it is not viable to obtain. Physics-informed neural networks (PINN) attempt to circumvent this problem and eliminate the need for large databases for neural network training since it uses only the partial differential equation that governs the physical problem and its boundary conditions as information for the supervised training. This work explores the capability and appropriateness of using PINN in the solution of the Reynolds equation, which models the hydrodynamic pressure in journal bearings. For this, a neural network was trained for both the static and the dynamic cases of the Reynolds equation. The results for the hydrodynamic pressure field and rotor orbit were compared with those obtained by finite volume method (FVM). The results obtained in this paper show that the PINN can be successfully applied to solve static and dynamic cases of hydrodynamic lubrication in journal bearings.