Physics-informed neural networks for the point defect model: Solving and inverting passive-film growth kinetics

Predicting how passive oxide films grow and break down is central to corrosion science and the long-term integrity of structural alloys, and the point defect model (PDM) is the standard kinetic description: a stiff, coupled system of Nernst–Planck, Poisson, and Butler–Volmer equations on a moving boundary; solving it conventionally requires specialized finite-element (FEM) solvers and identifying its kinetic parameters requires costly experimental campaigns. Physics-informed neural networks (PINNs) are compelling here because they natively assimilate data and invert for unknown parameters, so one measurement can replace an FEM solution and yield what kinetics FEM cannot. We show that PINNs solve the PDM and recover its parameters from sparse data. The problem is difficult for reasons common to stiff multiphysics systems: widely separated scales, stiff boundary conditions, and convergence to non-physical solution branches. We address these with physics-based non-dimensionalization, which extends stable simulation from about 1 to 250 h; NTK adaptive weighting, which compresses a four-to-six-order loss imbalance to roughly one; and a single validated anchor that selects the physical branch and brings film-thickness error to below 2.2% at all five potentials. Stiff boundary-condition enforcement remains an open problem. Robustness comes from resampling the anchor each step; accuracy saturates beyond ten anchors; and the physics loss tolerates 5% measurement noise. Crucially, recoverability tracks stiffness: a boundary-stiff kinetic constant is identifiable from film-thickness data while a weakly coupled interior coefficient is not. By turning sparse measurements into full fields and inferred kinetics, this approach reduces the experimental and computational burden of characterizing passive-film growth.