Mehdi Naima

Zhaobo Hu, Vincent Gauthier, Mehdi Naima

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.

Zhaobo Hu, Vincent Gauthier, Mehdi Naima

Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like instance normalization and its variants can mitigate temporal shifts by standardizing statistics. However, distribution shift on a graph is far more complex, involving not only the drift of individual node series but also heterogeneity across the spatial network where different nodes exhibit distinct statistical properties. To tackle this problem, we propose Reversible Residual Normalization (RRN), a novel framework that performs spatially-aware invertible transformations to address distribution shift in both spatial and temporal dimensions. Our approach integrates graph convolutional operations within invertible residual blocks, enabling adaptive normalization that respects the underlying graph structure while maintaining reversibility. By combining Center Normalization with spectral-constrained graph neural networks, our method captures and normalizes complex Spatio-Temporal relationships in a data-driven manner. The bidirectional nature of our framework allows models to learn in a normalized latent space and recover original distributional properties through inverse transformation, offering a robust and model-agnostic solution for forecasting on dynamic spatio-temporal systems.

Zhaobo Hu, Vincent Gauthier, Mehdi Naima

Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the inverse of the modified Laplacian, to naturally encode continuous multi-hop proximity and strict local centrality. To overcome the intractable $O(n^3)$ complexity of exact matrix inversion, we first utilize a truncated Neumann series to scalably approximate the DSM, which serves as the foundation for our proposed DsmNet. Furthermore, because algebraic truncation inherently causes probability mass leakage, we introduce DsmNet-compensate. This variant features a mathematically rigorous Residual Mass Compensation mechanism that analytically re-injects the truncated tail mass into self-loops, strictly restoring row-stochasticity and structural dominance. Extensive theoretical and empirical analyses demonstrate that our decoupled architectures operate efficiently in $O(K|E|)$ time and effectively mitigate over-smoothing by bounding Dirichlet energy decay, providing robust empirical validation on homophilic benchmarks. Finally, we establish the theoretical boundaries of the DSM on heterophilic topologies and demonstrate its versatility as a continuous structural encoding for Graph Transformers.