U-Net-based hybrid framework for accelerating deterministic rough-surface mixed lubrication simulations

Despite significant advances in deterministic mixed lubrication modelling, the computational complexity of these simulations remains prohibitive, limiting their practical use in rapid analysis and design optimisation. This study addresses this bottleneck by developing a hybrid machine learning framework that integrates artificial neural networks (ANNs) and convolutional neural networks (CNNs), specifically U-Nets, into a classical finite volume mixed lubrication solver to accelerate rough surface simulations without sacrificing fidelity. The approach uses ANNs to predict smooth pressure, film thickness, and temperature fields from operating conditions, while U-Nets reconstruct rough fields from smooth solutions and rough surface topographies. The ANNs achieve high accuracy for smooth fields, with mean  values of 0.998 for pressure, 0.999 for film thickness, and 0.925 for temperature. The U-Nets generalise well to rough surfaces, achieving  values of 0.990, 0.996, and 0.938 for pressure, film thickness, and temperature respectively. Six hybrid configurations are assessed, all of which reduce computational cost relative to the classical solver (average simulation time: 10.36 minutes). The most efficient framework delivers a 74.39% reduction in computation time across all testing samples. Overall, the results demonstrate that hybrid machine learning-physics frameworks can substantially accelerate deterministic mixed lubrication simulations while preserving high predictive accuracy.