Spatial PDE-aware Selective State-space with Nested Memory for Mobile Traffic Grid Forecasting

Traffic forecasting in cellular networks is a challenging spatiotemporal prediction problem due to strong temporal dependencies, spatial heterogeneity across cells, and the need for scalability to large network deployments. Traditional cell-specific models incur prohibitive training and maintenance costs, while global models often fail to capture heterogeneous spatial dynamics. Recent spatiotemporal architectures based on attention or graph neural networks improve accuracy but introduce high computational overhead, limiting their applicability in large-scale or real-time settings. We study spatiotemporal grid forecasting, where each time step is a 2D lattice of traffic values, and predict the next grid patch using previous patches. We propose NeST-S6, a convolutional selective state-space model (SSM) with a spatial PDE-aware core, implemented in a nested learning paradigm: convolutional local spatial mixing feeds a spatial PDE-aware SSM core, while a nested-learning long-term memory is updated by a learned optimizer when one-step prediction errors indicate unmodeled dynamics. On the mobile-traffic grid (Milan dataset) at three resolutions (202, 502, 1002), NeST-S6 attains lower errors than a strong Mamba-family baseline in both single-step and 6-step autoregressive rollouts. Under drift stress tests, our model's nested memory lowers MAE by 48-65% over a no-memory ablation. NeST-S6 also speeds full-grid reconstruction by 32 times and reduces MACs by 4.3 times compared to competitive per-pixel scanning models, while achieving 61% lower per-pixel RMSE.