A Neural Network-Based Feature Recognition Method in Adaptive Refinement for Efficient Reynolds Equation Solving

This study proposes an adaptive refinement method based on feature recognition to rapidly obtain solutions of the Reynolds equation. Leveraging an isogeometric analysis (IGA) solution framework supporting local refinement, three natural refinement features tailored to solving the Reynolds equation in fluid lubrication, including two physical features, a pressure value, a pressure gradient, and an element size feature for discretization, are introduced first to identify mesh elements. Then a neural network model is trained on feature data to predict element classifications effectively. Finally, this model is integrated into the adaptive refinement solution framework and validated through simulations. Comparative validation was conducted on two distinct Reynolds equation instances, with the results demonstrating that the proposed algorithm can effectively evaluate refinement regions globally, avoiding issues such as mesh non-conformity often caused by conventional independent element marking algorithms. The distribution of degrees of freedom is more rational, and the parallel prediction model enhances the speed of the refinement solution.