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.@en

Metamodels accurately reproduce the output of physics-based hydraulic models with a significant reduction in simulation times. They are widely employed in water distribution system (WDS) analysis since they enable computationally expensive applications in the design, control, and optimisation of water networks. Recent machine-learning-based metamodels grant improved fidelity and speed; however, they are only applicable to the water network they were trained on. To address this issue, we investigate graph neural networks (GNNs) as metamodels for WDSs. GNNs leverage the networked structure of WDS by learning shared coefficients and thus offering the potential of transferability. This work evaluates the suitability of GNNs as metamodels for estimating nodal pressures in steady-state EPANET simulations. We first compare the effectiveness of GNN metamodels against multi-layer perceptrons (MLPs) on several benchmark WDSs. Then, we explore the transferability of GNNs by training them concurrently on multiple WDSs. For each configuration, we calculate model accuracy and speedups with respect to the original numerical model. GNNs perform similarly to MLPs in terms of accuracy and take longer to execute but may still provide substantial speedup. Our preliminary results indicate that GNNs can learn shared representations across networks, although assessing the feasibility of truly general metamodels requires further work.

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Surrogate models replace computationally expensive simulations of physically-based models to obtain accurate results at a fraction of the time. These surrogate models, also known as metamodels, have been employed for analysis, control, and optimization of water distribution and urban drainage systems. With the advent of machine learning (ML), water engineers have increasingly resorted to these data-driven techniques to develop metamodels of urban water networks (UWNs). In this article, we review 31 recent articles on ML-based metamodeling of UWNs to outline the state-of-the-art of the field, identify outstanding gaps, and propose future research directions. For each article, we critically examined the purpose of the metamodel, the metamodel characteristics, and the applied case study. The review shows that current metamodels suffer several drawbacks, including (a) the curse of dimensionality, hindering implementation for large case studies; (b) black-box deterministic nature, limiting explainability and applicability; and (c) rigid architecture, preventing generalization across multiple case studies. We argue that researchers should tackle these issues by resorting to recent advancements in ML concerning inductive biases, robustness, and transferability. Recently developed neural network architectures, which extend deep learning methods to graph data structures, are preferred candidates for advancing surrogate modeling in UWNs. Furthermore, we foresee increasing efforts for complex applications where metamodels may play a fundamental role, such as uncertainty analysis and multi-objective optimization. Lastly, the development and comparison of ML-based metamodels can benefit from the availability of new benchmark datasets for urban drainage systems and realistic complex networks.

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