Interpretation of dual time-dependent chloride diffusion in concrete based on physical information neural networks

Chloride-induced corrosion is commonly described as the "cancer" of concrete structures. Accurately calculating the distribution pattern of chloride ions within concrete at different service times is essential for conducting targeted durability design for concrete structures in chloride environments. Fick's diffusion equation makes a significant contribution to solving this problem. However, traditional analytical methods for solving diffusion differential equations are not applicable for solving the Fick diffusion equation considering the dual time-dependent effects due to the strong time-dependent effects of chloride diffusion coefficients (D) and surface chloride concentrations (C-s) in concrete. Additionally, the finite element method is very inefficient, and the accuracy of traditional machine learning methods is concerning. In this study, a feedforward neural network is constructed as a trial function and then incorporated into the Fick diffusion equation, considering the dual time-dependent effects, along with its initial and boundary conditions, to form residuals. Subsequently, a loss function is constructed based on residuals, leading to the formation of the Physical Information Neural Network (PINN) to obtain numerical solutions of the Fick equation considering the dual time-dependent effects of D and C-s. The effectiveness of the algorithm is validated through comparative analysis of the predictions from the PINN model and results obtained from finite element numerical simulations and field exposure experiments in the case studies. The results indicate that the PINN algorithm, after undergoing boundary condition concretization, maintains good predictive accuracy for the diffusion of chloride within concrete, even when considering the dual time-dependent effect of D and C-s.