A deep spatio-temporal Graph Attention Network to learn nonlinear operators for traffic prediction

Accurate long-horizon traffic prediction is critical for intelligent transportation systems, yet it remains challenging due to the highly nonlinear spatio-temporal dependencies and complex temporal evolution of traffic networks. Existing sequence-to-sequence prediction models often suffer from error accumulation and degraded accuracy in long-horizon forecasts. To address these challenges, we propose the Deep Spatial-Temporal Graph Attention Operator Network (DSTGAON), which integrates operator learning with graph attention mechanisms for traffic speed prediction. Inspired by the Mori–Zwanzig formalism from statistical mechanics, DSTGAON models long-horizon traffic evolution from the perspective of nonlinear operator approximation and non-Markovian memory effects. Specifically, the framework extracts key spatio-temporal features from historical traffic states using a branch network and encodes future temporal query information via a trunk network; the outputs of the two networks are fused through a dot product to predict traffic state over specified future horizons. This design provides a structured approach to capture dynamic spatial correlations, temporal dependencies, and nonlinear traffic evolution, thereby significantly enhancing long-horizon prediction performance. Extensive experiments on benchmark traffic datasets demonstrate that DSTGAON outperforms state-of-the-art baselines, particularly in long-horizon forecasting, and additional fitting and stability analyses further confirm its reliability under diverse traffic conditions.