Evaluation of graph neural networks for urban drainage metamodeling: Key components and transferability analysis

Simulating urban drainage hydraulics is computationally demanding, limiting its application in tasks that require real-time or repeated simulations. Graph Neural Networks (GNNs) are promising metamodels, but the effect of their internal components and transferability potential remain underexplored. This study addresses these gaps through two main contributions: (1) a systematic evaluation of key architectural components, including graph layer type, processor depth, and prediction window with links to physical transport dynamics; and (2) transferability experiments across domains (across two distinct drainage networks) and tasks (from head to flow prediction). As case studies, we selected two combined sewer networks in The Netherlands that differ in their hydraulic dynamics. We find that metamodels with moderate depth and a ten-step prediction window achieve high accuracy (RMSE of 2-5 cm for hydraulic heads and 0.02 m³/s for flowrates). They also reach speed-ups of up to four orders of magnitude higher compared to the physics-based model, SWMM, when executing parallel simulations in GPU. Based on our two case studies, we find that pre-trained metamodels with full fine-tuning effectively adapt to a new task within the same domain, whereas cross-domain transfer requires appropriate normalization and fine-tuning. Furthermore, joint training on both case studies enables the metamodel to capture representations of both systems, suggesting potential for more general applicability. These findings demonstrate that metamodel architecture can reflect physical system behavior and offer practical guidance for building fast, accurate, and generalizable GNN-based metamodels-establishing a foundation for their use in applications such as uncertainty analysis, design optimization, and nowcasting.