Unsupervised Machine Learning for Improved Delaunay Triangulation

Tao Song,Runsheng Han,Wei Wei,Fan Meng,Jiarong Wang,Ying Li,Danya Xu,Pengfei Xie

doi:10.3390/jmse9121398

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.

Highlights

Abc In Equation (2), α = 1 for a positive triangle, and the larger α is, the closer the triangle is to the square triangle, and the better the mesh quality is. α does not depend on the size of triangle ABC, but only on its shape
This algorithm proposes a novel evaluation criterion for mesh quality, namely the ratio of long, narrow triangles. This refers to the proportion of long, narrow triangles whose interior angle is smaller than 30 degrees among the total triangles in the triangular mesh
The triangles with a triangle shape factor of greater than 0.7 amounted to 77.80%. This indicates that the triangles in the unstructured mesh after optimization were closer to equilateral triangles compared with those in the unstructured mesh before optimization; the number of long, narrow triangles was significantly reduced; the mesh quality was significantly improved

Summary

Introduction

In marine science and engineering, a physical oceanographic model generally consists of a set of partial differential equations, with its performance largely dependent on a mesh discretization scheme [1,2,3,4]. There are two kinds of mesh discretization schemes widely adopted in physical oceanographic models: structured mesh and unstructured mesh. Unstructured mesh is often used for the numerical simulation of coastal oceans, because it has no regular topological relation and well fits the complex coastal boundaries [5,6,7,8,9,10]. The automatic generation of high-quality unstructured meshes is of critical importance in ocean scientific calculations

Methods

Results

Conclusion