Accelerating gas-network feasibility screening with a physics-informed graph neural network surrogate

Large-scale gas-network scenario evaluation is a computational bottleneck in integrated energy-system planning, particularly when gas infrastructure interacts with power, heat, hydrogen, and sector-coupling pathways. Conventional nonlinear hydraulic solvers provide reliable feasibility assessment but are costly for stochastic screening, whereas unconstrained learning-based surrogates may produce hydraulically infeasible states. This study develops a physics-informed graph neural network surrogate for steady-state gas-network simulation and feasibility screening. The model uses an edge-centric architecture to predict pipe-level squared-pressure differences and flows. A differentiable projection layer enforces nodal mass conservation on predicted flows, while a Laplacian reconstruction maps edge pressure differences to topologically consistent nodal pressures. The framework is evaluated on GasLib-134, GasLib-135, and GasLib-582 using stochastically generated operating scenarios. On the meshed 582-node benchmark trained with 5000 scenarios, the surrogate achieves a pressure mean absolute error of 1.05~bar, corresponding to 1.3\% of the realized pressure range, with $R^2 = 0.981$. Projected-flow predictions reach $R^2 = 0.972$, and mass-balance residuals are reduced to numerical precision, on the order of $10^{-5}$--$10^{-4}$~Nm$^3$/s. Compared with the MYNTS reference solver, inference is reduced from seconds to milliseconds, with the largest benchmark evaluated in less than 40~ms. Loadability and out-of-distribution stress-test evaluations demonstrate robust feasibility screening under high-load conditions, while strongly localized demand concentrations are identified as cases requiring solver-based verification near feasibility limits. The framework provides a physically constrained planning accelerator for high-volume scenario screening and prioritization.