Deep learning is one of the most widely used modeling approach for spatio-temporal prediction. Traditional deep learning models get discrete features or hidden states from discrete data. However such discretization method cannot work well if the data is irregularly sampled or incompletely observed. It is difficult to obtain continuous features and hidden states for deep learning models. In this paper, we demonstrate how to use neural differential equations to solve this problem. We first validated the ability of Neural Controlled Differential Equations (Neural CDE) to process real-world irregular spatiotemporal data. Neural CDE is a type of neural differential equation that can obtain continuous hidden states. To make Neural CDE can obtain the spatial correlation of spatio-temporal data, we combined Graph Attention Network (GAT) with Neural CDE to propose a new model for spatio-temporal prediction. Furthermore, we used neural differential equations to designed a module to reduce the error of the prediction results. Experimental results show our proposed model outperforms the standard baseline by up to 37.40%.

Urban traffic network is a typical complex network. Traffic states data (e.g., traffic flow, traffic occupancy, traffic speed, etc.) has strong temporal and spatial correlation. To accurately predict urban traffic state, it is very important to extract the road features in the traffic network. The existing methods use separated temporal and spatial components or Spatio-temporal fusion components to predict traffic. Graph Convolution Network (GCN) is usually used to obtain the correlation between spatial nodes or Spatio-temporal nodes. However, the message aggregation method of GCN cannot assign different weights to neighbor nodes. While Graph Attention Network (GAT) can pay attention to different neighbor nodes. To better explain the existing traffic prediction models, we carried out experiments on the model framework based on GCN. We use a new proposed GAT instead of GCN, and find that the new GAT has better performance in multi-features traffic prediction tasks. We also made a theoretical analysis on the improvement of the performance and carried out experiments on four real datasets, which can provide strong support for the theoretical analysis. Our method improves the interpretability of the Graph Neural Network (GNN) model in extracting spatial features of the traffic networks.