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.

翻译：粗糙表面润滑模拟对于设计和优化摩擦学性能至关重要。尽管物理信息神经网络（PINNs）在流体动压润滑分析中的应用日益广泛，但其使用目前主要局限于光滑表面。这是因为传统PINN方法存在频谱偏差，倾向于学习低频特征，因而无法分析具有高频信号的粗糙表面。迄今为止，尚未有PINN方法被报道用于粗糙表面润滑。为克服这些局限，本研究引入了一种新颖的多尺度润滑神经网络架构，该架构采用可训练的傅里叶特征网络。通过融入可学习的特征嵌入频率，该架构能自动适应不同频率分量，从而增强对粗糙表面特性的分析能力。该方法已在多种表面形貌上进行了测试，并将结果与有限元法（FEM）获得的结果进行了对比。对比分析表明，该方法与有限元结果具有高度一致性。此外，这一新颖架构在精度和计算效率上均超越了具有固定特征嵌入频率的传统傅里叶特征网络。因此，多尺度润滑神经网络模型为粗糙表面润滑分析提供了一种更高效的工具。