A novel HGCN-transformer spatio-temporal model for multi-modal freight demand forecasting and OD matrix estimation

Accurate forecasting of freight volumes and OD matrix estimation help to precisely characterize the magnitude and spatial direction of freight flows, which is crucial for alleviating transport supply–demand mismatches and improving hub-corridor-network coordination and network flow assignment. Existing studies typically focus either on freight volume forecasting or OD matrix estimation, and thus lack a unified framework that can jointly estimate the scale and spatial distribution of freight demand. Meanwhile, OD observations between cities are difficult to obtain and are often incomplete and heterogeneous in statistical definitions, which forces OD matrix estimation research to rely heavily on conventional benchmarks such as gravity models. To address these gaps, this paper proposes an integrated and interpretable two-stage framework for freight volume forecasting and OD matrix estimation. In the freight volume forecasting stage, we develop an HGCN-Transformer model that integrates a Hierarchical Graph Convolution Network and a Transformer. Specifically, the HGCN extracts spatial structural features from multimodal heterogeneous topologies, while the Transformer captures temporal dependencies in freight time series and employs a cross-modal attention mechanism to model interactions across transport modes. Meanwhile, exogenous factors are incorporated to account for their impacts on freight demand. Building on these forecasts, the OD matrix estimation stage introduces GNN-Explainer-derived edge-importance scores as an interpretation-informed allocation proxy, and mode-specific OD matrix estimates are then generated under the constraints of the forecasted freight volumes; further external comparative validation is conducted using the available OD observations, together with a production-constrained gravity model, a uniform allocation mechanism, and a distance-decay-based allocation mechanism as benchmarks. The rolling-origin out-of-sample evaluation over 2021–2023 suggests that, based on the average values of out-of-sample evaluation metrics over three test years, the proposed model, relative to the best baseline, reduces MAPE by 8.57%, 18.61%, and 9.69% on the highway, railway, and waterway datasets, respectively, while improving R2 by 1.50%, 0.98%, and 0.64%, respectively. The OD validation results further show that, when GNN-Explainer-derived edge-importance scores are used as an interpretation-informed allocation proxy, the resulting OD matrix estimates exhibit higher overall consistency with the actual OD characteristics and outperform the other benchmark allocation mechanisms overall.