Graph neural network-based surrogate modeling for fast and scalable simulations of meshed district heating networks

District heating networks are key to the decarbonization of heating, yet their high capital costs and long payback periods hinder investments. Simulation-based applications such as real-time control optimization, which rely on scenario analysis or uncertainty quantification, can reduce costs and risks but face prohibitive computational burdens when numerous forward evaluations are required. Graph neural network-based surrogates are promising for improving simulation speed, but their local receptive fields cannot resolve the global interdependencies governing pressure balance across internal loops in meshed networks. Moreover, most existing surrogates are fully data-driven, sacrificing physical guarantees on thermal dynamics. This work presents a model that overcomes these limitations by reformulating the problem in terms of cycle flows and using a condensed graph representation that allows shallower architectures to capture global dynamics. This learned hydraulic solver is coupled with a physics-based Lagrangian thermal model optimized for parallel execution. The framework is validated on the district heating network of Verbier, Switzerland, comprising 165 substations and six internal loops per line. On synthetic test data spanning the full operational envelope, the surrogate matches physics-based solver accuracy in over 97% of cases, maintaining pressure residuals below 100 Pa, while achieving an 85-fold speedup (2187 versus 25 hydraulic steps per second). Validation against real-world monitoring data shows thermal predictions comparable to high-fidelity simulation tools with the speed of fully data-driven models. The resulting throughput and accuracy make the proposed framework suitable for applications requiring high simulation speed while maintaining physical fidelity. • A graph neural network surrogate enables fast simulation of meshed heating networks. • Achieves 85x speedup over iterative solvers with 97% convergence rate. • Validated on monitoring data shows negligible discrepancies with physics-based tools.