A physics-data hybrid model for efficient and accurate prediction of thermal recovery in high-temperature aquifer thermal energy storage

To address the intermittency challenge of renewable energy, Aquifer Thermal Energy Storage has gained significant attention due to its large capacity and excellent thermal stability. Thermal recovery efficiency is a core metric for evaluating ATES performance. However, existing prediction methods suffer from limitations such as oversimplification in mechanistic models, high computational costs of numerical simulations, and weak generalization capability of data-driven models. To bridge this gap, this paper proposes an innovative physics-data hybrid modeling paradigm—Thermal Diffusion Method—for the efficient and accurate prediction of thermal recovery efficiency in high-temperature ATES systems. The method constructs the main framework for heat loss calculation based on the first principles of thermodynamics and strategically introduces three physically meaningful efficiency coefficients to represent processes that are difficult to describe precisely by theory. Using 1188 sets of high-fidelity data generated by TOUGH2, the efficiency coefficients are calibrated once via an Annealing Particle Swarm Optimization algorithm. Systematic performance evaluation demonstrates that the TDM model significantly outperforms existing data-driven and analytical models in terms of prediction accuracy (R2 = 0.9893), generalization capability (high accuracy across all scenarios using only 1% data for calibration), and computational efficiency (119 times faster than numerical simulations). The model exhibits strong robustness to key engineering parameters, with its parameters remaining highly stable across different calibration dataset sizes. This study provides a rigorous, practical, and efficient new tool for the design and optimization of ATES systems, while validating the great potential of the physics-data hybrid modeling paradigm in solving complex engineering problems.