Multiscale physics-informed modeling and hybrid intelligent control of urban district heating networks

District heating (DH) networks exhibit strong multi-physics coupling, transport delays, and user heterogeneity that complicate prediction and control. This study develops a physics-constrained, multi-scale state-space model of the primary–secondary network, plate heat exchanger, buried twin-pipes, and room/building thermal dynamics, and couples it with a hybrid Temporal Convolutional Network-Fuzzy Cognitive Map (TCN-FCM) predictor whose hyperparameters are globally tuned by the Black Kite Algorithm (BKA). A prediction-driven Proportional–Integral–Derivative (PID) controller is then tuned using the Whale Optimization Algorithm (WOA) to coordinate primary-side valve opening. The framework is validated on a real DH system serving 28 buildings (153000 m2) over an entire heating season. Thermal-hydraulic simulation accurately reproduces secondary-loop behavior (return temperature errors concentrated within ±0.2 °C; supply mostly within ±0.3 °C). For short-term (48 h) forecasting, the BKA-TCN-FCM achieves RMSE = 0.35, MAE = 0.28, and MAPE = 0.58 %, outperforming ablations and benchmarks, including TCN-Long Short-Term Memory (LSTM), TCN-Gated Recurrent Unit (GRU), and TCN-Support Vector Regression (SVR). For medium-term (160 h) horizons, it sustains robust accuracy (RMSE = 0.393, MAE = 0.335, MAPE = 0.7 %). Closed-loop tests show that the WOA-PID delivers rapid responses with effective overshoot suppression and small steady-state error; over 48 h and 160 h windows, valve actuation remains closely synchronized with supply temperature, which is maintained within a narrow band (≈47.6–48.4 °C). By fusing physical constraints, causal interpretability, and metaheuristic optimization, the proposed framework provides an accurate, scalable, and explainable foundation for intelligent DH operation and low-carbon heating.