A solution for finite journal bearings by using physics-informed neural networks with both soft and hard constrains

Purpose The purpose of this study is to solve the Reynolds equation for finite journal bearings by using the physics-informed neural networks (PINNs) method. As a meshless method, it is unnecessary to use big data to train the neural networks, but to satisfy the Reynolds equation and the corresponding boundary conditions by using the known physics information. Design/methodology/approach Here, the boundary conditions are enforced through the loss function firstly, i.e. the soft constrain method. After this, an equation was constructed to build a surrogate model for satisfying the corresponding boundary conditions naturally, i.e. the hard constrain method. Findings For the soft one, in brief, the pressure results agree well with existing results, apart from the ones on the boundaries. While for the hard one, it can be noted that the discrepancies on the boundaries are reduced significantly. Originality/value The PINNs method is used to solve the Reynolds equation for finite journal bearings, and the error values on the boundaries for the results of the soft constrain method are improved by using the hard constrain method. Therefore, the hard constraint maybe also a good option when the pressure results on the boundaries are emphasized. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2023-0045/