Physics-informed digital twin for optimal operation of solar air source heat pump-based district heating systems

District heating systems (DHS) are increasingly required to support low-carbon building energy supply; however, conventional fossil-fuel-based DHS suffer from high energy consumption, thermal losses and limited flexibility under variable solar availability and heating demand. Solar air-source heat pump systems improve renewable heat utilization, but their practical operation is challenged by intermittent solar irradiance, nonlinear coupling among the solar collector, heat pump, thermal storage and load-side distribution loop and the need for accurate real-time state estimation and control. Existing rule-based and proportional–integral–derivative (PID) strategies lack predictive capability, while conventional model predictive control (MPC) and digital-twin approaches often rely on simplified linear or quasi-static models that cannot fully capture heat-pump nonlinearities, model uncertainty and thermodynamic constraints. To address these limitations, this paper proposes a physics-informed digital-twin district heating system (PI-DT-DHS) based on a physics-informed neural network (PINN) for a solar air-source heat pump. The proposed framework models the solar air heater, evaporator, condenser, thermal storage tank and load-side loop using coupled thermodynamic energy-balance equations, while the PINN embeds supervised reference-data fitting, physics residuals, boundary conditions, energy conservation and operational constraints into the learning process. The trained digital twin is further combined with a constrained optimization layer to minimize compressor power, auxiliary heating, load-temperature deviation and storage-temperature fluctuation under operational limits. Simulation results demonstrate that the proposed PI-DT-DHS reduces compressor energy to 19.7 kWh , auxiliary heating to 8.9 kWh , storage loss to 2.4 kWh and distribution loss to 2.0 kWh , while increasing useful heat delivery to 39.5 kWh compared with other district heating configurations.