Fick's law as a custom kernel in support vector regression: How to fully represent chloride concentration profiles in concrete structures

ABSTRACT Reinforced concrete structures exposed to the marine environment are susceptible to degradation due to chloride-induced corrosion. Traditional service life prediction models for these structures are commonly based on Fick's laws of diffusion, adjusting only the diffusion zone of chloride concentration profiles. This study investigates the use of machine learning to evaluate alternative models that explicitly account for both the convection and diffusion zones. To this end, chloride profiles were selected worldwide from structures with 10 to 100 years of exposure to natural degradation in the marine environment, across various exposure zones, or subjected to deicing salts. The machine learning technique employed was Support Vector Regression (SVR), and, in addition to standard kernels, the solution to Fick's second law, the Modified Holliday Equation, the Modified Ricker Curve, and the Double Exponential Model were evaluated as custom kernels. For comparison, these formulations were also implemented as custom basis functions for Kernel Ridge Regression (KRR) as a linear regularized regression in a predefined functional space. These customized approaches are developed following the standard structure of an estimator in the scikit-learn library. The results demonstrate that SVR was capable of adequately fitting field data of chloride concentration, as well as identifying the model with the best statistical performance. In addition to the custom kernels, the Fick and Holliday custom basis functions, together with the Radial Basis Function standard kernel, exhibited the best statistical and physical performance, capturing the key patterns of chloride concentration profiles in real-world applications. Both the Fick-based formulations successfully captured the convection and diffusion zones, outperforming traditional diffusion models, while the Holliday basis function showed strong consistency with physically meaningful parameters, such as the peak depth. Overall, the proposed machine learning approaches are shown to be consistent with the fundamental mechanisms governing chloride transport in concrete.