A GNN-Enhanced PINN Framework Driven by Constrained Graph-Point Coupling for Two-Dimensional Material Wavefield Propagation

Physics-informed neural networks (PINNs) have difficulty fully exploiting discrete spatial neighborhood information, while conventional graph neural networks (GNNs) cannot readily compute higher-order partial derivatives directly at arbitrary continuous collocation points. To address these challenges, this study proposes a GNN-enhanced PINN framework based on constrained graph-to-point coupling for two-dimensional wavefield propagation in materials. The framework uses a PINN to represent the continuous base wavefield and a GNN to extract local spatial information. Interpolation, constrained residual correction, and learnable gating are integrated into the graph-to-point coupling process, combining discrete graph representations with continuous physical constraints while preserving the initial boundary compatibility of the correction. A two-dimensional wave benchmark in a homogeneous medium shows that, compared with a baseline PINN, the framework reduces full space–time prediction errors and improves predictions of propagating wavefronts and boundary-reflection structures. These results provide a feasible approach to material wavefield solution that combines spatial neighborhood information with continuous physical constraints.