Modeling Urban Land Surface Temperature Using Physics-Informed Neural Networks (PINNs)

Abstract. A compact physics-informed neural network (PINN) is developed to (i) quantify city-scale accuracy of 30 m urban land surface temperature (LST) maps, (ii) identify influential predictors, and (iii) contrast climate-dependent patterns between New York City (NYC) (humid to sub-humid) and Austin, Texas (humid subtropical). Inputs combine selected Landsat-8 spectral indices, a digital elevation model, and meteorological covariates. LST targets are retrieved from Landsat-8 thermal band 10 (single-channel), quality-screened, and resampled to 30 m for May–September 2023. The loss combines data mean squared error term with a lightweight temporal smoothness prior implemented as a finite-difference term (Δ𝑇⁄Δ𝑡) on same-pixel pairs to reflect heat storage behaviour and discourage unrealistically rapid day to day changes. On the study pixels (in-sample), performance reaches R² = 0.88 (RMSE = 1.2 °C) in NYC and R² = 0.91 (RMSE = 0.9 °C) in Austin; errors are approximately Gaussian with minimal bias. Feature patterns differ by climate: vegetation-related signals dominate cooling in NYC, whereas shortwave-radiation and impervious-surface proxies (e.g., NDBI/NDISI) are strongest in Austin. These findings show that a shallow PINN with a minimal temporal constraint yields accurate, interpretable LST maps suitable for urban-heat-island assessment and climate-sensitive heat-mitigation planning.