3D Lattice Deformation Prediction with Hierarchical Graph Attention Networks

We present a cluster-based hierarchical graph attention network (HIGAT) architecture tailored for predicting deformations in 3D lattice structures under load. This architecture incorporates multi-level clustering to introduce a hierarchical edge set, enabling both local fine-granular predictions and efficient long-distance information flow within a single network forward pass, thus eliminating the practical limitation of vanilla graph neural networks (GNNs) for this and similar tasks. Moreover, we introduce a specialized graph attention scheme, optimized for geometrical data processing, which separates positional information from node latent states. We evaluate our model on a specifically generated deformation dataset containing lattice structure variations in different shapes, beam strengths, and unit cell arrangements. Our results demonstrate that this network design closely approximates the deformation predictions to those of physical simulations, achieving high fidelity in modeling real-world phenomena. In contrast to existing GNN architectures built for physical simulation approximation, the CGNN learns realistic folding behavior and lateral movement of individual lattice nodes. Accurately predicting the deformation dynamics of these structures not only streamlines the design process by serving as an efficient surrogate or complement for finite element method (FEM) simulations but also paves the way for direct inverse design optimization, enhancing design innovation and efficiency.