Urban flow prediction with spatial–temporal neural ODEs

With the recent advances in deep learning, data-driven methods have shown compelling performance in various application domains enabling the Smart Cities paradigm. Leveraging spatial–temporal data from multiple sources for (citywide) traffic forecasting is a key to strengthen the smart city management in areas such as urban traffic control, abnormal event detection, etc. Existing approaches of traffic flow prediction mainly rely on the development of various deep neural networks –e.g., Convolutional Neural Networks such as ResNet are used for modeling spatial dependencies among different regions, whereas recurrent neural networks are increasingly implemented for temporal dynamics modeling. Despite their advantages, the existing approaches suffer from limitations of intensive computations, lack of capabilities to properly deal with missing values, and simplistic integration of heterogeneous data. In this paper, we propose a novel urban flow prediction framework by generalizing the hidden states of the model with continuous-time dynamics of the latent states using neural ordinary differential equations (ODE). Specifically, we introduce a discretize-then-optimize approach to improve and balance the prediction accuracy and computational efficiency. It not only guarantees the prediction error but also provides high flexibility for decision-makers. Furthermore, we investigate the factors, both intrinsic and extrinsic, that affect the city traffic volume and use separate neural networks to extract and disentangle the influencing factors, which avoids the brute-force data fusion in previous works. Extensive experiments conducted on the real-world large-scale datasets demonstrate that our method outperforms the state-of-the-art baselines, while requiring significantly less memory cost and fewer model parameters.