Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations

This paper models message passing in graph neural networks as hyperbolic PDEs, creating a dynamical system that explicitly captures the graph's topological structure through eigenvector-based solution spaces. This approach enhances interpretability, aligns with spectral GNNs, and improves performance across various graph tasks by enabling explicit extraction of topological features.