SDF-SP: Semantic Dual-Order Spatiotemporal Forecasting with Simplicial Projection

Spatiotemporal forecasting must capture temporal dynamics and cross-node interactions under changing contextual conditions. Contextual semantics and historical trajectories provide complementary information, but incorporating node-specific contextual effects and combining divergent historical responses remain challenging. We propose SDF-SP, a framework that integrates semantically conditioned dual-order modelling with retrieval-based forecast correction. Its Dual-Order Spatiotemporal Encoder processes temporal-first and spatial-first branches in parallel, using context–node semantic relevance to modulate temporal features and spatial propagation. A context-conditioned gate fuses the branch representations, which a frozen pretrained language-model backbone uses to generate a base forecast. Retrieval-Augmented Simplicial Residual Projection then refines this forecast using retrieved historical trajectories. Guided by the base forecast, global and node-level projections model joint cross-node responses and individual node trajectories, respectively. Local simplicial constraints restrict interpolation to connected historical responses, and the projected forecasts are adaptively combined according to their deviations from the base forecast. Experiments on six real-world datasets spanning tourism, transportation and energy demonstrate strong forecasting performance across these domains. The code is publicly available at https://anonymous.4open.science/r/SDF-SP/.