CAG-NSPDE: Continuous adaptive graph neural stochastic partial differential equations for traffic flow forecasting

Traffic flow forecasting, which aims to predict future traffic flow given historical data, is crucial for the planning and construction of urban transportation infrastructure. Existing methods based on discrete dynamic graphs are unable to model the smooth evolution of spatial relationships and usually have high computational cost. In addition, they ignore the effect of stochastic noise on the modeling of temporal dependencies, which lead to poor predictive performance on complex intelligent transportation systems. To address these issues, we propose continuous adaptive graph neural stochastic partial differential equation (CAG-NSPDE). A continuous graph is constructed based on learnable continuous adaptive node embeddings for the modeling of evolution of spatial dependencies. To explicitly model the effect of noise, a novel architecture based on stochastic partial differential equation (SPDE) is proposed. It can simultaneously extract features from the temporal and frequency domains by reducing SPDEs to a system of ODEs in Fourier space. We perform extensive experiments on four real-world datasets and the results demonstrate the superiority of CAG-NSPDE compared with state-of-the-arts.