Transferable and data efficient metamodeling of storm water system nodal depths using auto-regressive graph neural networks.

Storm water systems (SWSs) are essential infrastructure providing multiple services including environmental protection and flood prevention. Typically, utility companies rely on computer simulators to properly design, operate, and manage SWSs. However, multiple applications in SWSs are highly time-consuming. Researchers have resorted to cheaper-to-run models, i.e. metamodels, as alternatives of computationally expensive models. With the recent surge in artificial intelligence applications, machine learning has become a key approach for metamodelling urban water networks. Specifically, deep learning methods, such as feed-forward neural networks, have gained importance in this context. However, these methods require generating a sufficiently large database of examples and training their internal parameters. Both processes defeat the purpose of using a metamodel, i.e., saving time. To overcome this issue, this research focuses on the application of inductive biases and transfer learning for creating SWS metamodels which require less data and retain high performance when used elsewhere. In particular, this study proposes an auto-regressive graph neural network metamodel of the Storm Water Management Model (SWMM) from the Environmental Protection Agency (EPA) for estimating hydraulic heads. The results indicate that the proposed metamodel requires a smaller number of examples to reach high accuracy and speed-up, in comparison to fully connected neural networks. Furthermore, the metamodel shows transferability as it can be used to predict hydraulic heads with high accuracy on unseen parts of the network. This work presents a novel approach that benefits both urban drainage practitioners and water network modeling researchers. The proposed metamodel can help practitioners on the planning, operation, and maintenance of their systems by offering an efficient metamodel of SWMM for computationally intensive tasks like optimization and Monte Carlo analyses. Researchers can leverage the current metamodel's structure for developing new surrogate model architectures tailored to their specific needs or start paving the way for more general foundation metamodels of urban drainage systems.