Data-efficient machine learning-based surrogate modeling of g-functions for borehole thermal energy storage

Borehole thermal energy storage is a mature technology for seasonal waste heat storage, improving district heating competitiveness, and reducing winter peak demand. Precise design and control of large-scale borehole fields are critical for optimizing capital and operational costs. In g-function-based borehole analysis, prediction accuracy strongly depends on the use of realistic boundary conditions, which can introduce substantial computational cost. In this study, a machine learning-based surrogate model was developed to address this challenge. Extreme gradient boosting and Gaussian process regression were employed for surrogate modeling, while both direct training and a residual training strategy based on learning the logarithmic difference between g-functions generated under two boundary conditions were evaluated under limited training data conditions. The results showed that although increasing the dataset size generally improved prediction accuracy, residual training substantially enhanced data efficiency. Depending on the model and dataset size, 65% to 83% of cases achieved mean absolute percentage error values below 1% using residual training, compared with 17% to 51% for direct training. The propagation of g-function prediction errors was further assessed through a 10-year system-level simulation. The average temperature mean absolute error ranged from 0.27 K to 0.76 K for direct training and decreased to 0.12 K to 0.22 K for residual training. In addition, the surrogate models reduced the average case evaluation time by 75% compared with direct simulation. These results demonstrate that the proposed surrogate modeling framework enables accurate and computationally efficient design and simulation of large-scale borehole fields with reduced data generation and training requirements.