Graph Neural Network enhanced Finite Element modelling

Abstract

In this study, we introduce a Graph network‐enhanced Finite Element approach to accelerate Finite Element simulations. We utilize the discretized geometry from a Finite Element pre‐processor to establish the graph and use the Graph Neural Network to solve the boundary value problem of the discretized domain. The advantage of graph neural networks is that they have a similar structure as compared to a discretized domain with nodes and elements. The underlying dynamics of the system are computed via a learned message‐passing. The goal here is to enhance and accelerate the FEM simulations using the proposed GNN network by incorporating the underlying mechanics knowledge into the network to enhance the generalizing ability of the network on various loading and boundary conditions. All the proposed studies in the literature where graph networks are applied to Finite Element Methods use images as input and output. The advantage of the proposed model is that it takes inputs such as the nodal information, their corresponding edges, nodal coordinates and the boundary conditions for each particular node from a Finite Element pre‐processor and computes the von‐Mises stress at each node along with their edge connections as output that can be read by a Finite Element post‐processor.