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We introduce a novel approach to automatic unstructured mesh generation usingmachine learning to predict an optimal finite element mesh for a previouslyunseen problem. The framework that we have developed is based around trainingan artificial neural network (ANN) to guide standard mesh generation software,based upon a prediction of the required local mesh density throughout thedomain. We describe the training regime that is proposed, based upon the use of\emph{a posteriori} error estimation, and discuss the topologies of the ANNsthat we have considered. We then illustrate performance using two standard testproblems, a single elliptic partial differential equation (PDE) and a system ofPDEs associated with linear elasticity. We demonstrate the effective generationof high quality meshes for arbitrary polygonal geometries and a range ofmaterial parameters, using a variety of user-selected error norms.

MeshingNet: A New Mesh Generation Method based on Deep Learning