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<p>Water Distribution Networks (WDNs) are large-scale, spatially irregular systems composed of interconnected nodes and pipes shaped by urban infrastructure. Despite their critical role in public health and urban resilience, WDNs often lag behind other utilities in terms of digitization and integration into smart city frameworks. This work presents a generative, data-driven method for reconstructing the full hydraulic state—pressures at nodes and flows in pipes—using a feedforward neural network with radial basis function (RBF) activations. The model is trained on synthetic data generated via hydraulic simulations and uses sparse real-time measurements from a limited number of strategically placed pressure and flow sensors. Unlike classical RBF Neural Networks, which rely on fixed spatial centers and local interpolation, the proposed architecture enables full-field inference through a single forward pass. The RBF activations capture spatial dependencies while allowing the network to generalize across the entire topology of the WDN. The approach achieves high-precision reconstruction performance, with Mean Squared Errors on the order of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(10^{-13}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>13</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> and Mean Absolute Errors around <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(10^{-7}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, confirming the method’s accuracy and stability. So, RBF-NNs emerge as a particularly effective solution, as they efficiently capture local-to-global spatial dependencies inherent in the dynamic behavior of WDNs, contributing to the broader integration of AI-driven solutions in infrastructure management.</p>

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Reconstruction of hydraulic states in water distribution systems via radial basis function neural networks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月20日

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  • Vittorio Bauduin,
  • Salvatore Cuomo

摘要

Water Distribution Networks (WDNs) are large-scale, spatially irregular systems composed of interconnected nodes and pipes shaped by urban infrastructure. Despite their critical role in public health and urban resilience, WDNs often lag behind other utilities in terms of digitization and integration into smart city frameworks. This work presents a generative, data-driven method for reconstructing the full hydraulic state—pressures at nodes and flows in pipes—using a feedforward neural network with radial basis function (RBF) activations. The model is trained on synthetic data generated via hydraulic simulations and uses sparse real-time measurements from a limited number of strategically placed pressure and flow sensors. Unlike classical RBF Neural Networks, which rely on fixed spatial centers and local interpolation, the proposed architecture enables full-field inference through a single forward pass. The RBF activations capture spatial dependencies while allowing the network to generalize across the entire topology of the WDN. The approach achieves high-precision reconstruction performance, with Mean Squared Errors on the order of \(10^{-13}\) 10 - 13 and Mean Absolute Errors around \(10^{-7}\) 10 - 7 , confirming the method’s accuracy and stability. So, RBF-NNs emerge as a particularly effective solution, as they efficiently capture local-to-global spatial dependencies inherent in the dynamic behavior of WDNs, contributing to the broader integration of AI-driven solutions in infrastructure management.