Reconstructing nodal pressures in water distribution systems with graph neural networks

Knowing the pressure at all times in each node of a water distribution system (WDS) facilitates safe and efficient operation. Yet, complete measurement data cannot be collected due to the limited number of instruments in a real-life WDS. The data-driven methodology of reconstructing all the nodal pressures by observing only a limited number of nodes is presented in the paper. The reconstruction method is based on K-localized spectral graph filters, wherewith graph convolution on water networks is possible. The effect of the number of layers, layer depth and the degree of the Chebyshev-polynomial applied in the kernel is discussed taking into account the peculiarities of the application. In addition, a weighting method is shown, wherewith information on friction loss can be embed into the spectral graph filters through the adjacency matrix. The performance of the proposed model is presented on 3 WDSs at different number of nodes observed compared to the total number of nodes. The weighted connections prove no benefit over the binary connections, but the proposed model reconstructs the nodal pressure with at most 5% relative error on average at an observation ratio of 5% at least. The results are achieved with shallow graph neural networks by following the considerations discussed in the paper.