CNN Surrogate Model-Based Morphological Optimization of BIPV Curved Roofs for Carbon Reduction

In large-span curved roofs, geometric variation simultaneously affects supporting-structure material demand, building operational loads, and photovoltaic (PV) generation, but these responses are often assessed separately. Using a large-span natatorium as a case, this study developed a 20-control-point free-form building-integrated photovoltaics (BIPV) model over a 58.8 m × 37.0 m roof. Structural, energy, and PV simulations were converted into annualized structural carbon, annual operational carbon, and annual PV avoided carbon. Separate convolutional neural network (CNN) regression surrogates using ResNet18 were trained using 4000 structural samples, 1000 energy samples, and 4000 PV samples, and were coupled with three repeated non-dominated sorting genetic algorithm II (NSGA-II) searches. On independent test sets, structural R2 values were 0.9968 for roof-panel mass, 0.9048 for spherical-node mass, 0.9093 for member mass, and 0.9908 for strain energy; the energy and PV models reached 0.9973 and 0.9894. The searches yielded 1530 unique globally non-dominated candidates and showed late-generation stabilization by generation 200. Surrogate screening predicted that M2 (ID187) reduced annualized structural carbon, annual operational carbon, and the net carbon indicator by 8.44%, 3.63%, and 5.61%, respectively, while increasing annual PV avoided carbon by 2.31% relative to M1. Original-workflow recalculation of 100 Pareto candidates yielded MAPE values of 1.01–4.30%. The remaining local deviations did not materially affect candidate ranking, and ID187 retained its net carbon benefit and equal-weight compromise status within the verified set. These results apply to the sampled morphology ranges, case-specific operating assumptions, conceptual linear-elastic structural model, and the verified candidate subset.