How to teach neural networks to mesh: Application on 2-D simplicial contours.

A machine learning meshing scheme for the generation of 2-D simplicial meshes is proposed based on the predictions of neural networks. The data extracted from meshed contours are utilized to train neural networks which are used to approximate the number of vertices to be inserted inside the contour cavity, their location, and connectivity. The accuracy of the scheme is evaluated by comparing the quality of the mesh generated by the neural networks with that generated by a reference mesher. Based on an element quality metric, after conducting tests on contours for a various number of edges, the results show a maximum average deviation of 15.2% on the mean quality and 27.3% on the minimum quality between the elements of the meshes generated by the scheme and the ones generated from the reference mesher; the scheme is able to produce good quality meshes that are suitable for meshing purposes. The meshing scheme is also applied to generate larger scale meshes with a recursive implementation. The findings encourage the adaption of the scheme for 3-D mesh generation.