Multiscale lubrication simulation based on fourier feature networks with trainable frequency

TL;DR

This paper introduces a multi-scale neural network with trainable Fourier features to improve rough surface lubrication simulation, overcoming spectral bias in traditional PINNs, and demonstrating high accuracy and efficiency compared to FEM.

Contribution

The work presents a novel neural network architecture with learnable frequency embeddings, enabling better analysis of rough surfaces in lubrication simulations.

Findings

Achieves high consistency with finite element method results.

Surpasses traditional Fourier feature networks in accuracy and efficiency.

Effectively analyzes various surface morphologies.

Abstract

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.