Unsupervised Machine Learning for Improved Delaunay Triangulation

Abstract

Physical oceanography models rely heavily on grid discretization. It is known that unstructured grids perform well in dealing with boundary fitting problems in complex nearshore regions. However, it is time-consuming to find a set of unstructured grids in specific ocean areas, particularly in the case of land areas that are frequently changed by human construction. In this work, an attempt was made to use machine learning for the optimization of the unstructured triangular meshes formed with Delaunay triangulation in the global ocean field, so that the triangles in the triangular mesh were closer to equilateral triangles, the long, narrow triangles in the triangular mesh were reduced, and the mesh quality was improved. Specifically, we used Delaunay triangulation to generate the unstructured grid, and then developed a K-means clustering-based algorithm to optimize the unstructured grid. With the proposed method, unstructured meshes were generated and optimized for global oceans, small sea areas, and the South China Sea estuary to carry out data experiments. The results suggested that the proportion of triangles with a triangle shape factor greater than 0.7 amounted to 77.80%, 79.78%, and 79.78%, respectively, in the unstructured mesh. Meanwhile, the proportion of long, narrow triangles in the unstructured mesh was decreased to 8.99%, 3.46%, and 4.12%, respectively.

Neural-Network-Assisted Finite Difference Discretization for Numerical Solution of Partial Differential Equations

“…Generating a suitable mesh for this purpose is still a challenging problem. At this step, one can also make use of ANN-based procedures; see, e.g., [10][11][12].…”

Prediction of significant wave height based on EEMD and deep learning

“…Unstructured meshes are meshes without regular topological relationships. An unstructured grid is one in which the interior points within the grid region do not have the same adjacent cells (Song et al, 2021).That is, there are different numbers of grids connected to different interior points within the grid section area. The unstructured grid has strong flexibility in modeling and can be good for shoreline boundary fitting.…”