AGF-PINN-HC: Hard-constrained enhanced physics-informed neural networks for multi-pipe heat transfer in artificial ground freezing

Artificial ground freezing (AGF) is widely applied in civil engineering to construct temporary frozen curtains for stability and groundwater control. Accurate prediction of the temperature field induced by multiple freezing pipes is essential for the safe and efficient design of AGF systems. To overcome the convergence degradation of standard physics-informed neural networks (PINNs), we propose a novel hard-constrained PINN framework (AGF-PINN-HC), which explicitly embeds Dirichlet boundary conditions into the network architecture using distance-based weighting functions. This formulation automatically guarantees boundary satisfaction and eliminates the loss competition between PDE residuals and boundary conditions, thereby enhancing training stability and solution accuracy. The proposed framework is validated through numerical experiments on both canonical (triple-pipe) and complex freezing configurations (circular, square, and horseshoe-shaped). AGF-PINN-HC achieves high-fidelity temperature predictions and accurately reconstructs isotherms under varying pipe layouts. Notably, the framework demonstrates strong generalization under nonuniform boundary conditions, with no structural modifications. In addition, by integrating transfer learning, the training time is reduced by up to 90% for new boundary scenarios, while maintaining predictive accuracy. These results highlight the first demonstration of a robust and boundary-aware PINN solution for practical AGF design, offering a promising tool for thermal analysis and rapid optimization in complex geotechnical applications.