Courtyard design for energy efficiency and thermal comfort: machine learning insights across hot and warm climates

Courtyards, long used as a passive climate-control element in vernacular housing, are increasingly reinterpreted in modern residential design, yet their quantified impact on energy use and comfort remains poorly documented. This study investigates how courtyard design affects energy efficiency and thermal comfort in villas across five hot and warm climates: Cairo, Riyadh, Gizan, Miami, and Sevilla. Using nearly 29,000 parametric simulations, design variables (geometry, window-to-wall ratio (WWR), glazing, insulation, and orientation) were systematically tested. Random Forest models achieved R² > 0.99 for both annual cooling demand and discomfort hours, with Shapley Additive explanations (SHAP) analysis revealing variable importance. Results show that compact courtyards with low WWR, external insulation, and high-performance glazing reduce cooling demand under 75 kWh/m² year. In contrast, elongated courtyards with higher WWR reduce discomfort to under 70 h annually in hot-dry climates, though often at the cost of increased cooling demand in hot-humid regions. Courtyard dimensions accounted for less than 3% of outcome variance, compared with > 40% for WWR and insulation. This study combines large-scale simulation with interpretable machine learning to quantify courtyard performance across climates. The findings provide climate-specific, evidence-based design guidance and demonstrate a pathway toward performance-based building codes that integrate courtyard design for hot regions.