Optimization of Daylight and Thermal Performance in a Membrane-Roofed Atrium Using an Interpretable Surrogate Model

Membrane materials have been widely applied in large-span roofs and atrium enclosures of commercial spaces due to their light weight, high strength, excellent light transmittance, and geometric adaptability. However, their high solar transmittance and low thermal inertia often lead to conflicts between daylight performance and thermal comfort. This study proposes an interpretable surrogate-model-based optimization framework for improving the photothermal performance of membrane-structured atrium spaces. A parametric model was developed with five design variables, including visible transmittance, solar heat gain coefficient, membrane area ratio, roof lift height, and spatial arrangement. A total of 800 simulation cases were generated using Latin hypercube sampling, followed by performance prediction using an XGBoost-based surrogate model, SHAP-based interpretation, and NSGA-II multi-objective optimization. The results show that the surrogate model accurately captures the nonlinear relationship between membrane design parameters and photothermal performance, achieving coefficients of determination of 0.90 and 0.86 for daylight compliance rate and thermal comfort performance, respectively. SHAP analysis identifies visible transmittance and membrane area ratio as dominant factors for daylight performance, while visible transmittance, area ratio, and roof lift height are critical for thermal comfort. A membrane area ratio of 0.47–0.56 provides a balanced range between daylight improvement and thermal load control, and roof lift heights above 6.55 m contribute to thermal comfort improvement. The proposed framework provides an efficient and interpretable approach for photothermal co-optimization of membrane atrium design.