  Rough surface lubrication simulation is crucial for designing and optimizing
tribological performance. Despite the growing application of Physical
Information Neural Networks (PINNs) in hydrodynamic lubrication analysis, their
use has been primarily limited to smooth surfaces. This is due to traditional
PINN methods suffer from spectral bias, favoring to learn low-frequency
features and thus failing to analyze rough surfaces with high-frequency
signals. To date, no PINN methods have been reported for rough surface
lubrication. To overcome these limitations, this work introduces a novel
multi-scale lubrication neural network architecture that utilizes a trainable
Fourier feature network. By incorporating learnable feature embedding
frequencies, this architecture automatically adapts to various frequency
components, thereby enhancing the analysis of rough surface characteristics.
This method has been tested across multiple surface morphologies, and the
results have been compared with those obtained using the finite element method
(FEM). The comparative analysis demonstrates that this approach achieves a high
consistency with FEM results. Furthermore, this novel architecture surpasses
traditional Fourier feature networks with fixed feature embedding frequencies
in both accuracy and computational efficiency. Consequently, the multi-scale
lubrication neural network model offers a more efficient tool for rough surface
lubrication analysis.
