An integrated surrogate and material optimization framework for PCM-enhanced energy piles based on EC-DeepONet

Phase change material (PCM)-enhanced energy piles can improve subsurface heat exchange through latent-heat storage, but their transient thermal response is strongly nonlinear and difficult to optimize by large-scale high-fidelity simulation alone. To address this challenge, this study develops an integrated surrogate-based evaluation and optimization framework for PCM-enhanced energy piles. A three-dimensional transient dataset is first generated using COMSOL Multiphysics and then used to train an energy-consistency-enhanced DeepONet (EC-DeepONet) for predicting continuous-time outlet-temperature curves and cumulative heat exchange. An ensemble of five sub-models is further used to screen 25,000 candidate PCM combinations in an uncertainty-aware manner. On the validation set, EC-DeepONet reduces the root mean square errors of temperature and energy prediction to 0.0508 °C and 9.87 MJ, representing reductions of approximately 20.6% and 17.8% relative to the standard DeepONet. The Spearman rank correlation coefficient reaches 0.925, indicating good consistency in material ranking. High-fidelity re-evaluation confirms that the selected optimal PCM scheme achieves a cumulative heat exchange of 436.51 MJ over 1-100 h. The results further suggest that performance improvement is associated with coordinated matching among latent heat, heat capacity, thermal conductivity, and phase-change temperature parameters, rather than the extreme value of a single variable. The entire optimization workflow requires only ∼25.55 min, which is approximately 847 times faster than exhaustive high-fidelity scanning, providing a practical route for rapid PCM preselection and design in shallow geothermal systems.