Graph Neural Networks for State Estimation in Water Distribution Systems: Application of Supervised and Semisupervised Learning

Xing, Lu; Sela, Lina

doi:10.1061/(asce)wr.1943-5452.0001550

Cited by 23 publications

(11 citation statements)

References 38 publications

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“…1) Signal reconstruction, including interpolation and denoising: We often observe a corrupted version of the graph signal only at a subset of nodes. This may be the case of noisy measurements in sensor [32], power [34], or water networks [47], or when a few ratings are available in a recommender system [43]. We want to denoise the signal or interpolate the missing values by relying on the neighboring signal values and the graph structure.…”

Section: B Signals Defined On Graphsmentioning

confidence: 99%

“…Comparing (47) with (31), we see that the Tikhonov filter is an order one rational filter with frequency response h(λ) = (1 + γλ) −1 . This frequency response also helps understanding the role of parameter γ; the optimal solution in ( 47) is a low-pass graph filter and the higher γ, the more low-pass the filter.…”

Section: Filtering By Regularizationmentioning

confidence: 99%

“…This is again an inverse graph filtering, but it does not necessarily admit a straightforward spectral analogy as (47) and (49).…”

Section: Filtering By Regularizationmentioning

confidence: 99%

“…The role of the regularization parameter γ is discussed from a bias-variance perspective in [108] and from a graph-kernel perspective in [109]. Differently, [110] generalizes (47) to the case where each node has its own regularization parameters (i.e. a vector of parameters γ), yielding a rational node varying filter [cf.…”

Section: Filtering By Regularizationmentioning

confidence: 99%

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Graph Filters for Signal Processing and Machine Learning on Graphs

Isufi¹,

Gama²,

Shuman³

et al. 2022

Preprint

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Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks. Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. In this article, we provide a comprehensive overview of graph filters, including the different filtering categories, design strategies for each type, and trade-offs between different types of graph filters. We discuss how to extend graph filters into filter banks and graph neural networks to enhance the representational power; that is, to model a broader variety of signal classes, data patterns, and relationships. We also showcase the fundamental role of graph filters in signal processing and machine learning applications. Our aim is that this article serves the dual purpose of providing a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations between signal processing, machine learning, and application domains.

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Section: B Signals Defined On Graphsmentioning

confidence: 99%

Section: Filtering By Regularizationmentioning

confidence: 99%

“…This is again an inverse graph filtering, but it does not necessarily admit a straightforward spectral analogy as (47) and (49).…”

Section: Filtering By Regularizationmentioning

confidence: 99%

Section: Filtering By Regularizationmentioning

confidence: 99%

See 2 more Smart Citations

Graph Filters for Signal Processing and Machine Learning on Graphs

Isufi¹,

Gama²,

Shuman³

et al. 2022

Preprint

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show abstract

“…In WDSs, Tsiami and Makropoulos (2021) employed this architecture for cyber‐physical attack detection using a graph created from sensors in the water system. Xing and Sela (2022) used the GNN to create a model for state estimation based on the layout of the WDS. Although showcased for simulated case studies, the ML models in these articles have been developed for usage in real scenarios.…”

Section: Research Directionsmentioning

confidence: 99%

Machine Learning‐Based Surrogate Modeling for Urban Water Networks: Review and Future Research Directions

Garzón

Kapelan

Langeveld

et al. 2022

Water Resources Research

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Urban water networks (UWNs) comprise drinking water distribution and urban drainage systems (WDS and UDS). The former are responsible for supplying drinking water to cities and the latter for evacuating wastewater and stormwater runoff. These infrastructures are a fundamental part of the city and are directly linked to its development (Brown et al., 2009). Each of these systems faces challenges to improve and maintain quality service in a dynamic urban environment under a widening range of climatic conditions; especially, in a climate-changing situation. Designing, optimizing, and intervening in these systems requires approximating their hydraulic behavior. Many models have been developed in the past years for simulating UWNs, for example, SOBEK (Deltares, n.d.), WaterCAD (Bentley®, n.d.), EPA-SWMM (Rossman, 2010), among others. Traditional modeling approaches are either based on accurate description of the physical processes (e.g., EPANET;Rossman et al., 2000) or rely on simplified conceptual models (e.g., SIMPOL;Dempsey et al., 1997); nonetheless, the former usually entail computationally expensive calculations while the latter lack fidelity, that is, level of detail. Applications such as optimization, real-time modeling, and uncertainty analysis need efficient models for evaluating the performance

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