  The district heating network (DHN) is essential in enhancing the operational
flexibility of integrated energy systems (IES). Yet, it is hard to obtain an
accurate and concise DHN model for the operation owing to complicated network
features and imperfect measurements. Considering this, this paper proposes a
physical-ly informed data-driven aggregate model (AGM) for the DHN, providing a
concise description of the source-load relationship of DHN without exposing
network details. First, we derive the analytical relationship between the state
variables of the source and load nodes of the DHN, offering a physical
fundament for the AGM. Second, we propose a physics-informed estimator for the
AGM that is robust to low-quality measurements, in which the physical
constraints associated with the parameter normalization and sparsity are
embedded to improve the accuracy and robustness. Finally, we propose a
physics-enhanced algorithm to solve the nonlinear estimator with non-closed
constraints efficiently. Simulation results verify the effectiveness of the
proposed method.
