Graph neural network accelerated generalizable stress field prediction for mesh-based finite element simulations

Finite element (FE) simulation is an important numerical method for structural analysis. However, one persistent issue is that the computational cost grows rapidly as the studied geometry becomes more complex. It offers great value if one can forward predict accurate FE results such as the stress distribution of a component without running expensive simulations. Deep learning techniques have been widely used for such prediction tasks. However, traditional frameworks such as the convolutional neural network (CNN) are not well suited for this problem. This is because CNN is based on grid-like, predefined filters, while the mesh in the FE simulations is highly irregular and variable. Graph neural network (GNN), a novel deep learning structure that operates on graph objects, can make predictions based on the learned relationships between vertices and edges. This is particularly suitable for our task because the components of GNN show a strong resemblance to nodes and element edges in the mesh-based FE simulation. In our study, we develop GNN models to predict stress and strain distributions in a body subject to external loads. Our GNN model achieves high prediction accuracies for 2D and 3D solid mechanics problems. In addition, the approach is highly generalizable because the way GNN learns does not depend on the shape of the structure, but on the intrinsic physics of the FE methodology. Our method may shed light on the fast prediction of stress and strain fields for complex useful engineering structures.