TempHypE-GNN: Hyperbolic Graph Neural ODEs for Hierarchical Temporal Knowledge Graphs

Pervasive systems such as IoT networks and dynamic knowledge-driven platforms demand models that can capture both temporal evolution and hierarchical structure with high fidelity. While TempHypE introduced a powerful combination of hyperbolic geometry and Neural Ordinary Differential Equations (ODEs) for continuous-time temporal reasoning, it lacks explicit mechanisms to model local graph connectivity and relational propagation. We address this limitation with TempHypE-GNN, a novel extension that integrates hyperbolic graph neural networks (GNNs) into the TempHypE framework. The GNN component enables message passing in hyperbolic space, allowing entities to aggregate neighborhood information across multi-hop relations and improving local relational reasoning under hierarchical constraints. This enhancement complements the global temporal modeling of Neural ODEs, leading to richer representations. TempHypE-GNN jointly embeds entities in the Poincaré ball to capture hierarchical dependencies, applies Neural ODEs to model continuous-time dynamics, and incorporates hyperbolic GNN layers for relational feature propagation. Experimental results on ICEWS14, ICEWS18, and GDELT demonstrate that TempHypE-GNN consistently outperforms both Euclidean models and static hyperbolic baselines. Specifically, it achieves a 17.6% relative improvement in MRR over DySAT on the GDELT dataset and an 8.5% relative increase in Hits@10 over HyperKG on ICEWS18. Furthermore, ablation studies averaged across all benchmarks show that incorporating hyperbolic GNN layers into the TempHypE architecture leads to performance gains of up to 4.3% in MRR and 5.9% in Hits@10, highlighting the added value of relational message passing in hyperbolic space. This demonstrates not only theoretical advances but also the potential for deployment in real-world domains such as IoT, smart-city analytics, and large-scale temporal knowledge management.