Predicting the Near-Optimal Mesh Spacing for a Simulation Using Machine Learning

This paper presents a novel approach, based on neural networks, to predict the mesh spacing for a simulation by making use of the large amount of simulations that are currently available to industry. The main idea is to compute a spacing function suitable to capture every solution available. The spacing function is then interpolated into a background mesh. A conservative interpolation strategy is proposed to ensure that the mesh spacing function in the coarse mesh does not under-resolve the spacing on the available fine mesh. This steps allows to homogenise the data in such a way that a neural network can be employed to predict the spacing at the background mesh. Once the neural network is trained, it can be used to predict the spacing at the nodes of the background mesh, so that near-optimal meshes can be produced for new cases. Numerical examples are use to show the potential of the proposed approach. In addition, a detailed comparison is presented with respect to a recently proposed NN approach in which the location, strength and radius of influence of a set of point sources is predicted.