Spatiotemporal Water Quality Prediction Using Graph Neural Networks Based on Diffusion Decay Partial Differential Equations

Complex environmental geographical spaces exhibit characteristics such as nonlinearity, multiscale nature, and uncertainty, representing typical spatiotemporal dynamic systems. With the advent of big data, data-driven spatiotemporal prediction models have emerged. However, the high-dimensional complexity of spatiotemporal phenomena makes these models difficult to interpret. This paper proposes a river network feature identification architecture based on coupled dynamic partial differential diffusion equations and graph neural networks. By deeply analyzing the solving process of hydrodynamic-diffusion equations and graph neural networks, spatial and nonlinear information of the environmental field is embedded into the graph network. We design a message-passing network based on an aggregation sampling method for flow field information fusion, allowing multiscale flow field information to be propagated, aggregated, and updated to predict the spatiotemporal evolution of water quality. The proposed model characterizes the constraint relationship between the rate of change of water quality concentration in time and space dimensions, enhancing the model's physical consistency and interpretability.