Simulation of lubrication on rough surfaces with multiscale lubrication neural networks

The simulation of lubrication on rough surfaces is essential for the design and optimization of tribological performance. Although the application of physics-informed neural networks (PINNs) in analyzing hydrodynamic lubrication has been increasing, their implementation has predominantly been restricted to smooth surfaces. This limitation arises from the inherent spectral bias of conventional PINN methodologies, which tend to prioritize the learning of low-frequency features, thereby hindering their ability to analyze rough surfaces characterized by high-frequency signals effectively. To date, there have been no reported instances of PINN methodologies being applied to rough surface lubrication. In response to these challenges, this paper presents an innovative multiscale lubrication neural network (MLNN) architecture that incorporates a trainable Fourier feature embedding. By integrating learnable feature embedding frequencies, this architecture is capable of automatically adjusting to various frequency components, thus improving the analysis of rough surface characteristics. The proposed method has been evaluated across a range of surface topographies, with results compared to those derived from the finite element method (FEM). The comparative analysis indicates a high degree of consistency between the MLNN results and those obtained through FEM. Moreover, this novel architecture demonstrates superior performance in terms of both accuracy and computational efficiency when compared to traditional Fourier feature networks that utilize fixed feature embedding frequencies. As a result, the MLNN model represents a more effective tool for the analysis of lubrication on rough surfaces.