Enhanced PINNs with augmented Lagrangian method and transfer learning for hydrodynamic lubrication analysis

Purpose: By seamlessly integrating physical laws, physics-informed neural networks (PINNs) have flexibly solved a wide variety of partial differential equations (PDEs). However, encoding PDEs and constraints as soft penalties in the loss function can cause gradient imbalances, leading to training and accuracy issues. This study aims to introduce the augmented Lagrangian method (ALM) and transfer learning to address these challenges and enhance the effectiveness of PINNs for hydrodynamic lubrication analysis. Design/methodology/approach: The loss function was reformatted by ALM, adaptively adjusting the loss weights during training. Transfer learning was used to accelerate the convergence of PINNs under similar conditions. Additionally, the iterative process for load balancing was reframed as an inverse problem by extending film thickness as a trainable variable. Findings: ALM-PINNs significantly reduced the maximum absolute boundary error by almost 80%. Transfer learning accelerated PINNs for solving the Reynolds equation, reducing training epochs by an order of magnitude. The iterative process for load balancing was effectively eliminated by extending the thickness as a trainable parameter, achieving a maximum percentage error of 2.31%. These outcomes demonstrated strong agreement with FDM results, analytical solutions and experimental data. Originality/value: This study proposes a PINN-based approach for hydrodynamic lubrication analysis that significantly improves boundary accuracy and the training process. Additionally, it effectively replaces the load balancing procedure. This methodology demonstrates considerable potential for broader applications across various boundary value problems and iterative processes. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2024-0277/