Tessellation and lmprovement of Simplicial Meshes using Neural Networks

Modern mesh generation addresses the development of robust algorithms that construct a discrete representation of the geometry into polytopal elements conforming to divergent properties: (i) fidelity to complex geometrical features, (ii) support for high spatial resolution in areas of interest and sparsity elsewhere, and (iii) preservation of optimal element geometry (quality). The automation of the meshing process with respect to these properties is still considered a critical bottleneck as it is often tied to the development of complex algorithms. Although such algorithms produce meshes that satisfy desirable properties, they may entail a significant computational cost. To tackle the automation hurdles of current algorithms, this research work studies the adaption of Neural Networks (NNs) that have been proven efficient in automating complex problems, for the development of meshing algorithms. A machine learning meshing scheme for the generation of simplicial meshes is proposed based on the predictions of NNs. The scheme is applied to small contours with up to 16 edges. The data extracted from the meshed contours are utilized to train NNs that approximate the number of vertices to be inserted inside a contour cavity, their location, and the connectivity. Based on an element quality metric, the results show a maximum deviation of 27.3% on the minimum quality between the elements of the meshes generated by the scheme and the ones generated from a reference mesher. This level of deviation corresponds to produced meshes with element angles that lie between 28°