使用机器学习评估无网格法模板
Meshless method stencil evaluation with machine learning
AI总结：
针对局部无网格法中模板选择难题，本文构建带标注模板数据集，并利用 PointNet 变体实现可兼容不同尺寸模板的质量分类器，AUC约达0.90。
摘要：
无网格法是数值分析中一个活跃且现代的分支，具有许多引人注目的优势。与局部无网格法相关的主要开放性研究问题之一是，如何选择尽可能最佳的模板（即一组相邻节点）作为计算基础。在本文中，我们描述了生成带标注模板数据集的流程，并使用 PointNet（一种基于点云的深度学习网络）的变体来创建一个模板质量分类器。我们利用 PointNet 的特性实现了一个可用于分类不同尺寸模板的模型，并将其与专用于单一模板尺寸的模型进行比较。该模型在检测最佳和最差模板方面表现尤为出色，其曲线下面积（AUC）指标约为0.90，表现可观。该方法在无网格领域具有进一步改进和直接应用的巨大潜力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
