Physics-informed neural network for hydrodynamic lubrication with film thickness discontinuity

Recent advancements in physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs), including those in hydrodynamic lubrication. However, PINNs struggle with film thickness discontinuities because of their requirement for continuous differentiability. This paper introduces two novel PINNs models to address this challenge. Model I employs a hyperbolic tangent function to approximate discontinuous film thickness, ensuring differentiability and continuity. The traditional PINNs structure is maintained by adjusting only the film thickness definition in the Reynolds equation. Model II reframes the lubrication problem as an interface issue, introducing a jump equation and an augmented variable to handle discontinuities. It extends the Reynolds equation into a three-dimensional form and includes an interface loss function for accuracy. Numerical experiments demonstrate the effectiveness of both models in handling thickness discontinuities, with the model showing superior computational precision. The model parameters, including the number of sampling points and loss function weights, were optimized for enhanced accuracy. The models were also tested on various groove shapes, confirming their adaptability in resolving discontinuity issues.