# Meshless method stencil evaluation with machine learning

arXiv: https://arxiv.org/abs/2204.12940 · HTML: https://mlsanity.com/paper/2204.12940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 25 Apr 2022.

## Builds on (most cited first, 3 of 3)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [On generation of node distributions for meshless PDE discretizations](https://mlsanity.com/paper/1812.03160/) (2018)

## Abstract (arXiv)

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.