A physics-informed graph neural surrogate based on flow-space decomposition for hydraulic analysis in water distribution networks

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ABSTRACT Graphical overview of the proposed physics-informed graph neural network (PIGNN). Network flows are decomposed into a demand-consistent base flow and cycle-space flows. The GNN predicts cycle flows, reconstructs hydraulic states, and is trained using an energy-dissipation loss without ground-truth flow data. Accurate and efficient hydraulic simulation is essential for water distribution network analysis. Conventional solvers such as EPANET can become computationally expensive when repeated simulations are required. Recent surrogate models reduce this cost but often struggle to enforce physical constraints and generalize across operating conditions. This study proposes a non-iterative physics-informed graph neural network (PIGNN) framework for steady-state hydraulic analysis. The method represents feasible flows as the sum of a demand-driven particular solution and a low-dimensional cycle-space component, ensuring exact mass conservation by construction while reducing the learning complexity. A graph neural network predicts the cycle coefficients from nodal demands and pipe attributes, and the complete flow field is reconstructed through a physics-based parameterization. Training is performed without hydraulic simulation labels by minimizing an energy dissipation functional derived from the Hazen–Williams formulation. Experiments on benchmark and real-world networks demonstrate high accuracy in flow and pressure prediction, stable robustness under demand perturbations, and substantial computational speedups over conventional solvers. Sensitivity analyses further show that the model captures physically meaningful hydraulic response patterns. The current formulation is developed for steady-state, demand-driven systems with a single effective water source.

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