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

Traffic forecasting requires modeling complex temporal dynamics and long-range spatial dependencies over large sensor networks. Existing methods typically face a trade-off between expressiveness and efficiency: Transformer-based models capture global dependencies well but suffer from quadratic complexity, while recent selective state-space models are computationally efficient yet less effective at modeling spatial interactions in graph-structured traffic data. We propose FAST, a unified framework that combines attention and state-space modeling for scalable spatiotemporal traffic forecasting. FAST adopts a Temporal-Spatial-Temporal architecture, where temporal attention modules capture both short- and long-term temporal patterns, and a Mamba-based spatial module models long-range inter-sensor dependencies with linear complexity. To better represent heterogeneous traffic contexts, FAST further introduces a learnable multi-source spatiotemporal embedding that integrates historical traffic flow, temporal context, and node-level information, together with a multi-level skip prediction mechanism for hierarchical feature fusion. Experiments on PeMS04, PeMS07, and PeMS08 show that FAST consistently outperforms strong baselines from Transformer-, GNN-, attention-, and Mamba-based families. In particular, FAST achieves the best MAE and RMSE on all three benchmarks, with up to 4.3% lower RMSE and 2.8% lower MAE than the strongest baseline, demonstrating a favorable balance between accuracy, scalability, and generalization.

Accurate traffic forecasting is crucial for intelligent transportation systems, supporting effective traffic management, congestion reduction, and informed urban planning. However, traditional models often fail to adequately capture the intricate spatio-temporal dependencies present in traffic data. To overcome these limitations, we introduce GAMMA-Net, a novel approach that integrates Graph Attention Networks (GAT) with multi-axis Selective State Space Models (Mamba). The GAT component uses a self-attention mechanism to dynamically adjust the influence of nodes within the traffic network, enabling adaptive spatial dependency modeling based on real-time conditions. Simultaneously, the Mamba module efficiently models long-term temporal and spatial dynamics without the heavy computational cost of conventional recurrent architectures. Extensive experiments on several benchmark traffic datasets, including METR-LA, PEMS-BAY, PEMS03, PEMS04, PEMS07, and PEMS08, show that GAMMA-Net consistently outperforms existing state-of-the-art models across different prediction horizons, achieving up to a 16.25% reduction in Mean Absolute Error (MAE) compared to baseline models. Ablation studies highlight the critical contributions of both the spatial and temporal components, emphasizing their complementary role in improving prediction accuracy. In conclusion, the GAMMA-Net model sets a new standard in traffic forecasting, offering a powerful tool for next-generation traffic management and urban planning. The code for this study is available at https://github.com/hdy6438/GAMMA-Net

Traffic prediction is difficult due to the complex interplay of temporal evolution, spatial interactions, and delayed spatio-temporal propagation over road networks. Existing methods either model spatial and temporal dependencies separately or employ unified spatio-temporal structures, but they often insufficiently characterize how neighboring sensors at historical timestamps influence a target node, while complex joint models may incur high computation. This paper proposes STEI-PCN, an efficient pure convolutional network based on spatio-temporal encoding and relation inference. It first builds a local causal joint spatio-temporal graph to restrict candidate interactions, then uses absolute position and relative distance encodings to infer dynamic edge weights. A single-layer graph convolution with a position-aware gated activation unit captures local joint dependencies, and temporal dilated causal convolutions complement long-range temporal patterns. A multi-view prediction module fuses raw, local propagation, and long-range temporal representations for direct multi-step forecasting. Experiments on PeMS03, PeMS04, PeMS07, PeMS08, and PeMS-Bay under multiple horizons show that STEI-PCN achieves competitive accuracy with moderate parameters and low training and inference costs. Ablation and fluctuation analyses further verify the contributions of the main components and empirically analyze the effects of the training-stage constraints under sharp speed changes. Our code is available at a GitHub link https://github.com/Jessez2/STEI-PCN.