Physics-informed neural network-based solution of the Reynolds equation

This study addresses the inherent limitations of conventional numerical methods, particularly their slow convergence rates and pronounced dependency on mesh quality when solving complex partial differential equations with irregular boundary constraints. An innovative optimization approach based on physics-informed neural networks is developed for solving the Reynolds equation, wherein the governing physical laws are embedded directly within the neural network's loss function to establish a mesh-independent computational framework. Comparative analysis reveals that the proposed method outperforms traditional finite difference techniques, yielding a 42 percent enhancement in computational efficiency and a 31 percent improvement in accuracy within regions characterized by steep pressure gradients. The practical utility of the methodology is experimentally verified in the context of complex lubrication problems, confirming its potential for application in industrial equipment simulation and performance optimization. These findings underscore the considerable capability and broad deployment potential exhibited by physics-informed neural networks when addressing partial differential equations.