Cross-City LST Prediction with Physics-Informed Neural Networks: Few-Shot Gains from NYC\u2192Austin and Austin\u2192NYC

A physics-informed neural network (Residual-PINN) is developed for mapping urban land-surface temperature (LST), blending flexible data-driven learning with a steady-state heat constraint enforced via a spatial Laplacian penalty. Inputs include Landsat-8 C2 L2 indices the Normalized Difference Vegetation Index (NDVI), Normalized Difference Water Index (NDWI), Normalized Difference Built-up Index (NDBI), Normalized Difference Impervious Index (NDII), and Normalized Impervious Surface Index (NDISI), alongside a Digital Elevation Model (DEM) and meteorology. The study window is the warm season May\u2013September 2023, with Landsat data with cloud cover less than 10% and standard L2 QA filtering. Feature engineering adds seasonality (sin\/cos of day-of-year), selected interactions, quadratic terms, and neighborhood context via ring statistics in three annuli (0\u2013300, 300\u2013500, 500\u20131000 m). Evaluation is leakage\u2011aware and identical across models: 3-fold GroupKFold over spatial blocks with a 300 m exclusion buffer, reporting OOF RMSE\/MAE\/R\u00b2 (mean \u00b1 SD). Compared with the Histogram Gradient Boosting Regressor (HGBR) baseline, the PINN yields physics-consistent maps and achieves monotonic few-shot gains under cross-city transfer (Austin\u2194NYC): with only \u22485\u201310% labeled target pixels, most of the gap to fully local training is recovered. The framework is transferable, sample-efficient, and interpretable, and it is released with a minimal reproducibility package.