Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, Trondheim, Norway.
Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands.
Water Res. 2024 Sep 1;261:121933. doi: 10.1016/j.watres.2024.121933. Epub 2024 Jun 20.
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.
数据驱动的变分模型再现物理模型的输入-输出映射，同时显著减少模拟时间。这些技术在配水系统的设计、控制和优化中得到了广泛的应用。最近的研究强调了基于图神经网络的变分模型的潜力，因为它们可以有效地利用配水系统的图结构特征。此外，这些变分模型具有归纳偏差，有助于推广到看不见的拓扑结构。可转移的变分模型对于需要对许多替代布局进行高效评估的问题或训练数据稀缺的问题特别有利。然而，基于 GNN 的变分模型的可转移性仍然有限，这是由于缺乏对发生在边缘级别的物理过程的表示，即管道。为了解决这个限制，我们的工作引入了基于边缘的图神经网络，它扩展了归纳偏差的集合，并比传统的图神经网络更详细地表示链路级别的过程。这种架构在理论上与节点处质量守恒的约束有关。为了验证我们的方法，我们测试了基于边缘的网络在模拟稳态 EPANET 模拟的情况下估计管道流量和节点压力的适用性。我们首先比较了在几个基准配水系统上基于图神经网络的变分模型的有效性。然后，我们通过评估在看不见的系统上的性能来探索可转移性。对于每个配置，我们计算模型性能指标，如决定系数和相对于原始数值模型的加速。我们的结果表明，所提出的方法比基于节点的模型更准确地捕捉管道级别的物理过程。当在具有相似需求分布的看不见的水网络上进行测试时，我们的模型保留了良好的泛化性能，流量的决定系数高达 0.98，预测水头的决定系数高达 0.95。进一步的发展可能包括压力和流量的同时推导。
