Physics-Informed Regression Modelling for Vertical Facade Surface Temperature: A Tropical Case Study on Solar-reflective Material

Urban heat islands (UHIs) pose a critical challenge in densely populated cities and tropical climates where large amounts of energy are used to meet the cooling demand. To address this, Building and Construction Authority (BCA) of Singapore provides incentives for passive cooling such as using of solar-reflective material in its Green Mark guidelines. Thus, understanding about its real-world effectiveness in tropical urban environments is required. This study evaluated the effectiveness of solar-reflective cool paint using a hybrid modelling framework combining a transient physical model and data driven model through field measurements. Several machine learning algorithms were compared including multiple-linear regression (MLR), random forest regressor (RF), AdaBoost regressor (AB), extreme gradient boosting regressor (XGB), and TabPFN regressor (TPR). The results indicated that the transient physical model overestimated facade temperatures in the lower temperature ranges. The physics-informed MLR achieved best performance with improved accuracy for pre-cool paint (R2=0.96, RMSE=0.83C) and post-cool paint (R2=0.95, RMSE=0.65C) scenarios, reducing RMSE by 26% and 44%, respectively. The hybrid model also effectively predicted hourly heat fluxes revealing substantial reductions in surface temperature and heat storage with increasing albedo. The maximum net heat flux q_net was reduced by about 30-65 W/m2 in the post-cool paint stage (albedo = 0.73) compared to the pre-cool paint stage (albedo = 0.31). As albedo increases from 0.1 to 0.9, the sensitivity analysis predicts that the maximum daytime surface temperature will decrease by about 11C and the peak heat release of the net heat flux will decrease significantly from about 161 W/m2 to 27 W/m2.

💡 Research Summary

Urban heat islands (UHIs) are a pressing problem in densely populated tropical cities, where high cooling demand drives substantial energy consumption and carbon emissions. Singapore’s Building and Construction Authority (BCA) promotes passive cooling measures such as high‑albedo (solar‑reflective) paints under its Green Mark scheme, yet the real‑world performance of these coatings on vertical façades remains poorly quantified. This study addresses that gap by conducting a year‑long field experiment on an institutional building in Singapore, measuring façade surface temperature with thermocouples and infrared imaging, and recording ambient meteorological variables (global horizontal irradiance, air temperature, relative humidity, wind speed) using a mobile weather station. The building was monitored before (pre‑cool paint, albedo ≈ 0.31) and after (post‑cool paint, albedo ≈ 0.73) the application of a commercial solar‑reflective cool paint.

A hybrid modelling framework was developed that couples a transient physics‑based heat‑balance model with data‑driven regression techniques. The physics model solves a one‑dimensional transient conduction‑convection‑radiation problem for the façade, using incident solar radiation simulated via the Ladybug‑Grasshopper plugin. Validation against measured temperatures revealed a systematic over‑prediction in the lower temperature range (RMSE ≈ 1.1 °C), likely due to simplified treatment of convective resistance and surface roughness.

To correct these systematic biases, the residuals (measured – physics) were modeled with several machine‑learning regressors: multiple linear regression (MLR), random forest (RF), AdaBoost (AB), extreme gradient boosting (XGB), and TabPFN (TPR). The dataset was split 80 % for training and 20 % for testing; hyper‑parameters were tuned via cross‑validation. All physics‑informed models outperformed the physics‑only baseline, but the physics‑informed MLR achieved the best balance of accuracy, interpretability, and robustness, delivering R² = 0.96 (pre‑cool) and 0.95 (post‑cool) with RMSE = 0.83 °C and 0.65 °C respectively—reductions of 26 % and 44 % in error compared with the standalone physics model. The other algorithms yielded comparable R² (0.93–0.99) but showed higher variance and less transparent coefficient structures.

Using the MLR‑based hybrid model, hourly heat‑flux components (radiative, conductive, convective) and net heat flux (q_net) were estimated. The post‑cool paint stage exhibited a reduction in peak q_net of 30–65 W m⁻² relative to the pre‑cool stage, reflecting both lower solar absorption and enhanced infrared emission. Sensitivity analysis varying façade albedo from 0.1 to 0.9 demonstrated a non‑linear response: maximum daytime surface temperature decreased by roughly 11 °C, and the peak q_net dropped dramatically from about 161 W m⁻² to 27 W m⁻². The analysis indicates that once albedo exceeds ~0.5, additional gains in heat‑island mitigation become increasingly pronounced.

Key insights from the study include: (1) physics‑informed regression markedly improves temperature prediction while preserving physical consistency; (2) high‑albedo cool paint on vertical façades can lower surface temperatures by 2–3 °C and cut net heat gain by up to 65 W m⁻², translating into meaningful reductions in building cooling loads; (3) the hybrid framework offers a computationally efficient alternative to full‑scale CFD or EnergyPlus simulations for long‑term urban‑scale assessments; and (4) the quantified albedo‑temperature‑heat‑flux relationships provide actionable guidance for policymakers aiming to set minimum façade albedo targets.

The paper concludes that integrating transient physics models with data‑driven regression, particularly simple linear models constrained by physics, yields a powerful tool for evaluating and optimizing passive cooling strategies on vertical building surfaces. Future work should extend the approach to multiple building typologies, explore combined roof‑façade strategies, and integrate real‑time IoT sensor streams for adaptive building energy management.