Physics-Informed Neural Network for Diffusion-Reaction Problems with Dead-Core Formation in Catalyst Slabs

Abstract

This work investigates a nonlinear two-point boundary value problem arising in diffusion--reaction processes in catalyst slabs with power-law kinetics and fractional reaction order. For sufficiently large Thiele modulus, the solution develops a dead-core region separated from the active region by an unknown free boundary. We propose a structured Physics-Informed Neural Network (PINN) framework that incorporates the asymptotic behavior at the dead-core interface into a hard-constrained trial solution and treats the interface location as a trainable parameter. The concentration profile and free boundary are therefore approximated simultaneously without explicit interface tracking or penalty-based enforcement of the interface conditions. The method is validated against the exact solution for power-law kinetics and a high-precision numerical shooting method. Numerical experiments covering near-critical and strongly supercritical regimes demonstrate accurate recovery of both the concentration profile and dead-core location, together with robustness to random initialization and collocation sampling. While classical shooting is more efficient for the present one-dimensional benchmark, the proposed formulation provides a flexible framework for extensions to multidimensional geometries and problems for which analytical solutions are unavailable.

15 pages, 3 figures, 4 tables, proceeding of PPAM conference 2026 in Poznan