MeshingNet: A New Mesh Generation Method based on Deep Learning

• URL: http://arxiv.org/abs/2004.07016v1
• Date: Wed, 15 Apr 2020 11:29:00 GMT
• Title: MeshingNet: A New Mesh Generation Method based on Deep Learning
• Authors: Zheyan Zhang, Yongxing Wang, Peter K. Jimack, and He Wang
• Abstract summary: We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an artificial neural network (ANN) to guide standard mesh generation software.
• Score: 4.230005855201131
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an artificial neural network (ANN) to guide standard mesh generation software, based upon a prediction of the required local mesh density throughout the domain. We describe the training regime that is proposed, based upon the use of \emph{a posteriori} error estimation, and discuss the topologies of the ANNs that we have considered. We then illustrate performance using two standard test problems, a single elliptic partial differential equation (PDE) and a system of PDEs associated with linear elasticity. We demonstrate the effective generation of high quality meshes for arbitrary polygonal geometries and a range of material parameters, using a variety of user-selected error norms.

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