Recent studies have significantly improved the prediction accuracy of travel demand using graph neural networks. However, these studies largely ignored uncertainty that inevitably exists in travel demand prediction. To fill this gap, this study proposes a framework of probabilistic graph neural networks (Prob-GNN) to quantify the spatiotemporal uncertainty of travel demand. This Prob-GNN framework is substantiated by deterministic and probabilistic assumptions, and empirically applied to the task of predicting the transit and ridesharing demand in Chicago. We found that the probabilistic assumptions (e.g. distribution tail, support) have a greater impact on uncertainty prediction than the deterministic ones (e.g. deep modules, depth). Among the family of Prob-GNNs, the GNNs with truncated Gaussian and Laplace distributions achieve the highest performance in transit and ridesharing data. Even under significant domain shifts, Prob-GNNs can predict the ridership uncertainty in a stable manner, when the models are trained on pre-COVID data and tested across multiple periods during and after the COVID-19 pandemic. Prob-GNNs also reveal the spatiotemporal pattern of uncertainty, which is concentrated on the afternoon peak hours and the areas with large travel volumes. Overall, our findings highlight the importance of incorporating randomness into deep learning for spatiotemporal ridership prediction. Future research should continue to investigate versatile probabilistic assumptions to capture behavioral randomness, and further develop methods to quantify uncertainty to build resilient cities.

翻译：近期研究利用图神经网络显著提升了出行需求预测的准确性。然而，这些研究在很大程度上忽视了出行需求预测中不可避免的不确定性。为填补这一空白，本研究提出了一种概率图神经网络（Prob-GNN）框架，用于量化出行需求的时空不确定性。该Prob-GNN框架基于确定性与概率性假设构建，并在芝加哥的公共交通与拼车需求预测任务中进行了实证应用。研究发现，概率性假设（如分布尾部、支撑集）对不确定性预测的影响大于确定性假设（如深层模块、网络深度）。在Prob-GNN家族中，采用截断高斯分布与拉普拉斯分布的GNN在公共交通与拼车数据上取得了最优性能。即使在显著的领域偏移下（模型基于COVID前数据训练，并在新冠疫情爆发期间及之后的多个时段进行测试），Prob-GNN仍能稳定预测出行量的不确定性。Prob-GNN还揭示了不确定性的时空模式，该模式集中于下午高峰时段及出行量较大的区域。总体而言，本研究结果强调了将随机性融入深度学习对于时空出行量预测的重要性。未来研究应进一步探索多种概率性假设以捕捉行为随机性，并持续开发量化不确定性的方法以建设韧性城市。