Physics-regularized autoencoder with latent feature learning for reference evapotranspiration estimation using XGBoost

Reference evapotranspiration (ET₀) is an important variable for irrigation scheduling, agricultural water management, and hydrological applications. This study examines a Physics–Regularized Autoencoder (PRAE): a neural network that compresses daily weather variables into a small set of learned features while being encouraged to keep air temperature, relative humidity, and dew point temperature consistent with one another. The learned features were passed to XGBoost to estimate ET₀. Hourly weather data for Delhi, India, from 1 January 2000 to 31 December 2025 were converted to 9,497 daily records, and daily ET₀ was calculated with the FAO–56 Penman–Monteith method. The records were split in time order into 70% for training, 15% for validation, and 15% for testing, and the model design (number of learned features and strength of the physics term) was chosen on the validation period only. Three approaches were compared: XGBoost on the original weather variables, a standard autoencoder followed by XGBoost, and PRAE followed by XGBoost. On the test period, XGBoost on the original variables was the most accurate (RMSE 0.93 mm per day). PRAE with XGBoost (latent size six, physics weight 0.5) reached an RMSE of 1.13 mm per day (mean of five runs 1.11 ± 0.07), which is better than the standard autoencoder with XGBoost (1.27 mm per day) but not better than the original-variable baseline. The physics term lowered the dew-point inconsistency of the reconstructed data by 87% relative to the standard autoencoder (mean squared error 0.063 versus 0.495 °C 2 ). In tests with artificially removed inputs, however, PRAE showed no consistent advantage over the standard autoencoder. The size of the learned feature set had a much larger effect on accuracy than the physics term. Because ET₀ is calculated from the same weather variables that are used as model inputs, the task is the approximation of a formula-based reference value, not the independent prediction of measured evapotranspiration.