ReF-nets: Physics-informed neural network for Reynolds equation of gas bearing

Based on the deep learning method, the physical information of Reynolds equation is introduced into the neural network, and a deep learning network frame (ReF-nets) is built to predict the flow fields and aerodynamic characteristics of gas bearing. The prediction results of neural network have high enough accuracy comparing with those from finite difference method (FDM). Furthermore, a comprehensive investigation of unsupervised learning, supervised learning and semi-supervised learning in PDE (partial differential equation) solution prediction is carried out, which is the first time these three learning strategies are fully compared in PDE solving field to our best knowledge. The advantages and disadvantages of the three learning methods are illustrated in detail from the perspectives of physics interpretability and prediction accuracy. It is found that the unsupervised learning method has the strongest physics interpretability in predicting the flow field. The supervised learning method has the highest prediction accuracy, but it has nearly no physics interpretability. While semi-supervised learning method can take into account the advantages of both methods, and perform well when there are some known flow field data.