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交通需求预测的精度。然而，这些研究普遍忽略了交通需求预测中固有的不确定性。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，用于量化交通需求的时空不确定性。该概率图神经网络框架基于确定性与概率性假设，并在芝加哥公共交通与共享出行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（如深度模块、网络深度）。在概率图神经网络家族中，采用截断高斯分布与拉普拉斯分布的图神经网络在公共交通与共享出行数据上表现最佳。即便在显著的领域偏移条件下，以疫情前数据训练并跨越新冠疫情期及其后的多个时期进行测试时，概率图神经网络仍能稳定预测出行需求的不确定性。此外，概率图神经网络揭示了不确定性的时空模式，该模式集中于下午高峰时段与客流量较大的区域。总体而言，本研究结果凸显了在时空出行需求预测的深度学习中引入随机性的重要性。未来研究应持续探索多样化的概率性假设以捕捉行为随机性，并进一步开发不确定性量化方法以建设韧性城市。