  Dynamic demand prediction is crucial for the efficient operation and
management of urban transportation systems. Extensive research has been
conducted on single-mode demand prediction, ignoring the fact that the demands
for different transportation modes can be correlated with each other. Despite
some recent efforts, existing approaches to multimodal demand prediction are
generally not flexible enough to account for multiplex networks with diverse
spatial units and heterogeneous spatiotemporal correlations across different
modes. To tackle these issues, this study proposes a multi-relational
spatiotemporal graph neural network (ST-MRGNN) for multimodal demand
prediction. Specifically, the spatial dependencies across modes are encoded
with multiple intra- and inter-modal relation graphs. A multi-relational graph
neural network (MRGNN) is introduced to capture cross-mode heterogeneous
spatial dependencies, consisting of generalized graph convolution networks to
learn the message passing mechanisms within relation graphs and an
attention-based aggregation module to summarize different relations. We further
integrate MRGNNs with temporal gated convolution layers to jointly model
heterogeneous spatiotemporal correlations. Extensive experiments are conducted
using real-world subway and ride-hailing datasets from New York City, and the
results verify the improved performance of our proposed approach over existing
methods across modes. The improvement is particularly large for demand-sparse
locations. Further analysis of the attention mechanisms of ST-MRGNN also
demonstrates its good interpretability for understanding cross-mode
interactions.
