Physics-Guided Machine Learning for Frozen Soil Thermal Conductivity Prediction under Data Scarcity

Abstract The thermal conductivity of frozen soils is a key parameter in cold region engineering, yet reliable prediction remains difficult when measurements are limited and heterogeneous. This study develops a physics-guided machine learning (PGML) framework for predicting frozen soil thermal conductivity using a multisource database. Conventional physics-based models are first benchmarked, and the best-performing model is selected as the physics baseline. Two XGBoost-based hybrid strategies are then developed: PGML-XGBoost (Strategy I), which adaptively blends measured responses with the physics baseline during training, and PGML-XGBoost (Strategy II), which learns the residual between the physics baseline and the measured thermal conductivity. Performance is evaluated using a fixed test set and controlled degradation experiments under the Random-Record Split and the Specimen-Group Split. The purely data-driven baseline performs well under the Random-Record Split but degrades more clearly under the Specimen-Group Split. In contrast, the PGML models improve robustness under data scarcity: Strategy I more consistently preserves the goodness of fit, whereas Strategy II more effectively limits large relative errors and often achieves lower mean absolute percentage error in the most data-limited cases. Overall, physical guidance improves data efficiency and predictive stability, especially for generalization to unseen soil specimens.