Learn to Simulate Finite Element Analysis via Mesh-based Graph Networks

Using Graph Neural Networks (GNNs) to simulate complex physical systems is currently a popular field. Finite Element Analysis (FEA) is a numerical analysis solution in physical simulation and involves dividing a physical structure into finite elements. A mesh-based graph network is formed by interconnecting the nodes of the finite elements. Mesh-based simulations are central to the modeling of physical systems, and GNNs are used to overcome the high cost of the simulation. However, most existing GNNs-based methods lack the ability to generalize when small changes in structure occur. The cantilever beam, which is a fundamental component of many physical structures, is a classic study case for FEA stress analysis. In this paper, we propose a Mesh-based Graph Transfer Learning (MGTL) method for beams, in which the knowledge learned on a mesh-based graph network of one beam structure via contrastive learning, and then is transferred to another. Furthermore, an augmentation approach is proposed for the mesh-based graph in contrastive learning. Our experiments demonstrate the effectiveness of transfer learning in the MGTL method, as well as its generalization ability across different mesh sizes and structure types.