A PINN-assisted physics-guided meta-heuristic optimization method for material–energy synergy in converter steelmaking

Converter steelmaking simultaneously consumes metallic inputs and utility energy, generates recoverable BOFG and steam, and must satisfy strict endpoint-quality constraints. Existing optimization studies generally treat material utilization, energy consumption, and process quality separately, which cannot fully represent their coupled effects. This study develops a mechanism–data hybrid and physics-guided optimization framework for material–energy synergy in converter steelmaking. A synergy-degree model is established using material-flow and energy-flow order parameters. A multi-output physics-informed neural network surrogate is developed to predict BOFG, steam, endpoint carbon content, and endpoint temperature, with a thermodynamic recovery constraint incorporated into the loss function. The resulting constrained nonlinear problem is solved using the physics-guided dynamic Harris hawks optimizer (PGDHHO), which combines Tent chaotic initialization, nonlinear escape-energy scheduling, and penalty-triggered Lévy-flight repair. Using 600 industrial charges, the PINN achieves R² values of 0.972, 0.969, 0.967, and 0.961 for BOFG, steam, endpoint temperature, and endpoint carbon content, respectively. For ten test-set charges, the mean charge-level synergy improvement is 23.75%, while the mean synergy degree increases from 0.4903 to 0.6056. The average net energy consumption changes from −19.310 to −20.857 kgce/t steel, and the mean furnace-level carbon-emission reduction reaches 19.27%. In 30 independent algorithm runs, the proposed method achieves a mean fitness of 0.594 and a standard deviation of 0.004. These results demonstrate that the proposed framework improves material–energy coordination while reducing net energy consumption and carbon emissions under endpoint-quality constraints.