A Data-Driven Approach for Simultaneous Mesh Untangling and Smoothing Using Pointer Networks

Poorly-shaped and/or inverted elements negatively affect numerical simulation accuracy and efficiency. Most current approaches consider mesh quality improvement and mesh untangling problems as numerical optimization problems and solve them using nonlinear optimization. However, these optimization-based approaches require users to set and solve complex numerical optimization problems with no guarantee that the output meshes are valid meshes with good element qualities. Therefore, this paper proposes a data-driven approach for simultaneous mesh untangling and smoothing using a Pointer network. The proposed approach generates various triangular meshes and employs a novel sequence generation algorithm to train the Pointer network and predicts competitive approximate solutions using the trained network. The strength of the proposed framework lies in its simplicity to predict the best free vertex candidate, providing high-quality output meshes, since it does not require solving complex numerical optimization for prediction. Experimental results show that the proposed framework successfully eliminates inverted elements on the meshes and improved average and worst element quality up to 85.9% and 97.8%, respectively, compared to current optimization-based methods.