MeshingNet: A New Mesh Generation Method based on Deep Learning
This work addresses mesh generation for computational simulations, offering a novel approach that could improve efficiency in engineering and scientific domains, though it appears incremental as it builds upon existing mesh generation software.
The authors tackled the problem of automatic unstructured mesh generation for finite element analysis by introducing a deep learning method that predicts optimal local mesh density, demonstrating effective generation of high-quality meshes for arbitrary polygonal geometries and various material parameters in standard test problems.
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.