Towards transferable metamodels for water distribution systems with edge-based graph neural networks

Data-driven metamodels reproduce the input-output mapping of physics-based models while significantly reducing simulation times. Such techniques are widely used in the design, control, and optimization of water distribution systems. Recent research highlights the potential of metamodels based on Graph Neural Networks as they efficiently leverage graph-structured characteristics of water distribution systems. Furthermore, these metamodels possess inductive biases that facilitate generalization to unseen topologies. Transferable metamodels are particularly advantageous for problems that require an efficient evaluation of many alternative layouts or when training data is scarce. However, the transferability of metamodels based on GNNs remains limited, due to the lack of representation of physical processes that occur on edge level, i.e. pipes. To address this limitation, our work introduces Edge-Based Graph Neural Networks, which extend the set of inductive biases and represent link-level processes in more detail than traditional Graph Neural Networks. Such an architecture is theoretically related to the constraints of mass conservation at the junctions. To verify our approach, we test the suitability of the edge-based network to estimate pipe flowrates and nodal pressures emulating steady-state EPANET simulations. We first compare the effectiveness of the metamodels on several benchmark water distribution systems against Graph Neural Networks. Then, we explore transferability by evaluating the performance on unseen systems. For each configuration, we calculate model performance metrics, such as coefficient of determination and speed-up with respect to the original numerical model. Our results show that the proposed method captures the pipe-level physical processes more accurately than node-based models. When tested on unseen water networks with a similar distribution of demands, our model retains a good generalization performance with a coefficient of determination of up to 0.98 for flowrates and up to 0.95 for predicted heads. Further developments could include simultaneous derivation of pressures and flowrates.