Sustainable data-driven energy management with physics-informed neural networks for optimizing delivery routes

Energy consumption during unmanned aerial vehicle (UAV) flight is an important factor for operational range, mission feasibility, and economic efficiency in aerial logistics. We develop a physics-informed neural network (PI-NN) for instantaneous-power prediction. By embedding established aerodynamic and kinematic principles directly into the neural network architecture, the PI-NN represents power as the exact sum of non-negative lift, drag, and propulsion components. On UAV flight data, PI-NN achieves R 2 = 0.9383 , MAE = 30.03 W, and MAPE = 9.31 % . Recording-level tests show a significantly lower MAE than the strongest black-box benchmark. SHAP identifies the contribution of non-electrical flight variables to individual predictions. Predicted power is converted into arc-level energy and incorporated into an energy-aware mixed-integer linear programming model. In the four-UAV, 22-task base instance, the proposed optimization model yields a feasible 209.10-Wh routing plan and satisfies the prescribed 1% optimality-gap tolerance. Benchmark comparisons, calibrated energy quantiles, and sensitivity analyses further evaluate routing performance, prediction uncertainty, and computational scalability.