A thermodynamics-integrated physics-guided neural network for soil temperature forecasting.

Soil temperature forecasting plays a key role in agriculture, hydrology, and climate modeling; however, existing deep learning models often show degraded performance in long-term prediction due to error accumulation, insufficient physical interpretability, and limited spatial generalization. To overcome these limitations, this study proposes a Thermodynamic-Enhanced Physics-Informed Neural Network (TE-PINN), a forecasting framework based on an LSTM backbone that integrates domain-specific physical knowledge through the Latent Thermodynamic Potential Inference (LTPI) and Multi-Pathway Physics-Guided Loss Integration (MPPGLI) modules. LTPI applies free-energy principles and dissipation constraints to characterize internal thermal dynamics, addressing the difficulty of LSTM in capturing long-range temporal dependencies. MPPGLI provides a multi-path physics-guided loss formulation that effectively narrows the discrepancy between predictions and observations, improving robustness. TE-PINN exhibits slower performance degradation across multi-day forecast horizons and maintains stable predictive behavior across datasets from different latitudes. In comparison with both shallow and deep baseline models, the results indicate that introducing thermodynamic priors substantially improves the accuracy and physical consistency of soil temperature forecasting.