Transfer learning-enhanced rapid prediction of heat transfer fields in diverse porous media under Robin boundary conditions

Accurate prediction of temperature distributions in porous materials is critical for energy and aerospace thermal management. Conventional numerical solvers are accurate but computationally prohibitive for real-time use. A Physics-Constrained Attention U-Net (PCAU) has been developed, integrating heat transfer governing equations with transfer learning to predict temperatures in diverse porous structures under Robin boundary conditions. Compared with U-Net, MobileNet, and PINN, PCAU reduces the mean relative error by up to 79% and improves R2 above 0.91. Its transfer learning capability further enables accurate predictions across various microstructures, improving performance by 41.8–79.0% while requiring only 8% of the original training data. Notably, high accuracy is maintained even when boundary conditions and porosity values extend beyond the training ranges. This framework enables efficient, high-fidelity thermal field predictions across diverse porous media, offering a practical foundation for optimization and digital twin applications in energy thermal management.