A new method to solve the Reynolds equation including mass-conserving cavitation by physics informed neural networks (PINNs) with both soft and hard constraints

Abstract

In this work, a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks (PINNs) is proposed. The complementarity relationship between the pressure and the void fraction is used. There are several difficulties in problem solving, and the solutions are provided. Firstly, the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error. While the void fraction inequality constraint is considered by using the hard constraint with the max-min function. Secondly, to avoid the fluctuation of the boundary value problems, the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided. Lastly, for avoiding the trivial solution the limitation for the mean value of the void fraction is applied. The results are validated against existing data, and both the incompressible and compressible lubricant are considered. Good agreement can be found for both the domain and domain boundaries.

Extrapolation of Hydrodynamic Pressure in Lubricated Contacts: A Novel Multi-Case Physics-Informed Neural Network Framework

“…Their approach utilized three different multi-task learning strategies to effectively balance the loss components associated with the models [8]. Most recently, Xi et al investigated the stationary Reynolds equation with cavitation, introducing both soft and hard constraints within the loss function to enhance the precision of the solution [9]. Additionally, Rimon et al explored the feasibility of applying PINNs to EHL simulations, employing a simplified Reynolds equation and describing the seal's deformation through the Lamé equation [44].…”

“…In subsequent work, PINNs were applied to 2D problems [4][5][6]. The newest achievements consider the computation of pressure and cavitation in tribological systems [7][8][9]. The conducted research displays the potential of PINNs to combine the strengths of distributed simulation models with the computational efficiency of classical neural networks.…”