Physics-informed neural network calibration and application for urban cooling

Mitigating the adverse effects of urban heat islands (UHI) is essential for enhancing climate resilience, public health, and energy sustainability in cities. Traditional modelling approaches, however, often face a trade-off between physical fidelity and the flexibility to integrate diverse geospatial data. This paper presents a novel physics-informed neural network (PINN) framework that bridges this gap by embedding the heat diffusion equation directly into a neural network, ensuring predictions adhere to thermodynamic principles while learning from complex urban data patterns. It includes a systematic data-fusion workflow that unifies multi-format geospatial inputs, such as land surface temperature (LST), vegetation indices, and vector-based urban morphology, into a cohesive gridded structure, enabling scalable and reproducible urban climate analysis. Validated through a case study of Paris, the model achieves strong predictive accuracy (MAE=0.3723 °C, RMSE = 0.5019 °C) and captures the city’s thermal patterns with consistent error across the observed temperature range. Comparing two targeting metrics, LST and the proposed urban heat thermal index (UHTI), shows that LST favors areas with some existing vegetation while UHTI identifies more barren, structurally vulnerable zones. Simulated green roof deployment on buildings selected by each metric yields localised surface cooling up to 4.97 °C, concentrated on the building footprints. This integrated approach thus serves as a practical scenario planning tool, quantifying the relative benefits of green infrastructure. By combining physical simulation with data-driven analytics, this research provides urban planners and policymakers with a scientifically rigorous, scalable resource to support the design of cooler, and more sustainable cities.