Physics-informed Neural Network for Predicting the Moisture Diffusion and Parameter Inversion in Stone Heritage

Water vapor is a critical factor affecting the long-term durability of porous stone materials used in historic buildings and archaeological sites. To extend the service life of these materials, it is essential to investigate the mechanisms of water vapor migration within them. This study proposes a multi-domain physics-informed neural network (PINN) framework that integrates physical constraints and data-driven modeling to simulate water vapor diffusion and identify transient diffusion coefficients. The results demonstrate that the PINN model accurately predicts relative humidity distributions in stone samples under both laboratorycontrolled and in-situ conditions, achieving mean RMSE values of 1.39 and 3.05, respectively. The inferred diffusion coefficients are consistent with those experimentally determined for Yungang Grotto sandstone, both on the order of 10−7. The PINN framework exhibits improved applicability and computational efficiency. This work presents a robust analytical framework and workflow for characterizing water vapor diffusion behavior and extracting vapor diffusion parameters in porous stone materials.