Sheaf Diffusion with Adaptive Local Structure for Spatio-Temporal Forecasting

Spatio-temporal systems often exhibit highly heterogeneous and non-intuitive responses to localized disruptions, limiting the effectiveness of conventional message passing approaches in modeling higher-order interactions under local heterogeneity. This paper reformulates spatio-temporal forecasting as the problem of learning information flow over locally structured spaces, rather than propagating globally aligned node representations. We introduce a spatio-temporal sheaf diffusion graph neural network (ST-Sheaf GNN) that embeds graph topology into sheaf-theoretic vector spaces connected by learned linear restriction maps. Unlike prior work that relies on static or globally shared transformations, our model learns dynamic restriction maps that evolve over time and adapt to local spatio-temporal patterns to enable substantially more expressive interactions. By explicitly modeling latent local structure, the proposed framework efficiently mitigates the oversmoothing phenomenon in deep GNN architectures. We evaluate our framework on a diverse set of real-world spatio-temporal forecasting benchmarks spanning multiple domains. Experimental results demonstrate state-of-the-art performance, highlighting the effectiveness of sheaf-theoretic topological representations as a powerful foundation for spatio-temporal graph learning. The code is available at: https://anonymous.4open.science/r/ST-SheafGNN-6523/.