Learning mesh-based numerical analysis using graph neural networks

Abstract

Mesh-structured data is an important data structure to perform numerical analyses such as the finite element method and the finite volume method. It is known that graph neural networks (GNNs) can deal with mesh-structured data since meshes can be regarded as graphs. In this work, we demonstrate GNNs are useful in learning finite element analysis results. The proposed method efficiently leverages spatial information; that is, the input feature does not change under any rotation and translation. We show that our model generalizes to much larger meshes than these in the training dataset. Moreover, our model can perform inference for meshes, which have up to one million nodes.