Meshless method stencil evaluation with machine learning

TL;DR

This paper introduces a machine learning approach using a variation of PointNet to evaluate and classify the quality of stencils in meshless numerical methods, aiming to optimize stencil selection.

Contribution

It develops a deep learning classifier capable of assessing stencil quality across different sizes, advancing meshless method optimization.

Findings

Classifier achieves an AUC of around 0.90 in detecting best and worst stencils.

Model generalizes across different stencil sizes, outperforming size-specific models.

Potential for further improvements and practical application in meshless numerical analysis.

Abstract

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.