论文标题
无网格的方法通过机器学习评估
Meshless method stencil evaluation with machine learning
论文作者
论文摘要
无网格方法是数值分析的活跃而现代的分支，具有许多有趣的好处。与本地无网格方法相关的主要开放研究问题之一是如何选择最佳的模板 - 相邻节点的集合 - 以基于计算。在本文中，我们描述了生成标记的模具数据集的过程，并使用PointNet的变体（基于点云的深度学习网络）来创建用于模板质量的分类器。我们利用PointNet的功能来实现一个模型，该模型可用于对不同尺寸的模板进行分类，并将其与专用于单个模板尺寸的模型进行比较。该模型尤其擅长检测最佳和最差的模板，其曲线下方具有可观的区域（AUC）度量约为0.90。在无网状域中有很多进一步改进和直接应用的潜力。
Meshless methods are an active and modern branch of numerical analysis with many intriguing benefits. One of the main open research questions related to local meshless methods is how to select the best possible stencil - a collection of neighbouring nodes - to base the calculation on. In this paper, we describe the procedure for generating a labelled stencil dataset and use a variation of pointNet - a deep learning network based on point clouds - to create a classifier for the quality of the stencil. We exploit features of pointNet to implement a model that can be used to classify differently sized stencils and compare it against models dedicated to a single stencil size. The model is particularly good at detecting the best and the worst stencils with a respectable area under the curve (AUC) metric of around 0.90. There is much potential for further improvement and direct application in the meshless domain.
