Modern Structure-Aware Simplicial Spatiotemporal Neural Network

2026-04-17

AI Summary

Existing graph neural networks are inherently limited to modeling pairwise relationships, struggling to effectively capture higher-order topological structures while suffering from rapidly escalating computational complexity as graph size grows. To address these limitations, this work proposes a simplicial complex–based spatiotemporal neural network that, for the first time, integrates simplicial complexes into spatiotemporal modeling. By leveraging spatiotemporal random walks on high-dimensional simplicial complexes and parallelized temporal convolutions, the proposed method transcends the pairwise interaction constraints of conventional graph neural networks. This approach significantly enhances the capacity to model higher-order topological dependencies in complex systems while maintaining computational efficiency.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

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: Computational social science
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Spatiotemporal modeling has evolved beyond simple time series analysis to become fundamental in structural time series analysis. While current research extensively employs graph neural networks (GNNs) for spatial feature extraction with notable success, these networks are limited to capturing only pairwise relationships, despite real-world networks containing richer topological relationships. Additionally, GNN-based models face computational challenges that scale with graph complexity, limiting their applicability to large networks. To address these limitations, we present Modern Structure-Aware Simplicial SpatioTemporal neural network (ModernSASST), the first approach to leverage simplicial complex structures for spatiotemporal modeling. Our method employs spatiotemporal random walks on high-dimensional simplicial complexes and integrates parallelizable Temporal Convolutional Networks to capture high-order topological structures while maintaining computational efficiency. Our source code is publicly available on GitHub\footnote{Code is available at: https://github.com/ComplexNetTSP/ST_RUM.

Problem

• spatiotemporal modeling
• graph neural networks
• simplicial complexes
• high-order topological structures
• computational scalability

Innovation

• simplicial complex
• spatiotemporal modeling
• high-order topology
• temporal convolutional networks
• structure-aware neural network