Sheaf Diffusion with Adaptive Local Structure for Spatio-Temporal Forecasting

2026-04-13

AI Summary

Traditional message-passing approaches struggle to capture high-order interactions arising from local heterogeneity in spatiotemporal systems, thereby limiting predictive performance. This work reframes spatiotemporal forecasting as a problem of learning information flow within locally structured spaces and proposes a sheaf-based diffusion graph neural network. It introduces, for the first time, dynamic, locally adaptive, learnable linear restriction maps that explicitly model latent local structures. The method effectively mitigates the oversmoothing issue prevalent in deep GNNs and enhances model expressiveness. Extensive experiments on multiple real-world spatiotemporal forecasting benchmarks demonstrate state-of-the-art performance, underscoring the strong potential of sheaf-theoretic topological representations for spatiotemporal graph learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

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/.

Problem

• spatio-temporal forecasting
• local heterogeneity
• higher-order interactions
• message passing
• oversmoothing

Innovation

• sheaf diffusion
• adaptive local structure
• spatio-temporal forecasting
• graph neural networks
• dynamic restriction maps