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

Source: [Physics-Informed Neural Network for Diffusion-Reaction Problems with Dead-Core Formation in Catalyst Slabs](<https://www.sota2.com/research/paper/6a210674c10484bac23eff71>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-04T05:00:05.280Z

Authors: Piotr Skrzypacz, Kaisar Tangirbergen, Jan Valdman

Published: 2026-05-23T05:39:46.000Z

## 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. The model exhibits a free-boundary structure, where an unknown interface separates a dead-core region with vanishing concentration from an active region with positive concentration. We propose a Physics-Informed Neural Network (PINN) framework that incorporates a structured, hard-constrained trial solution embedding the asymptotic behavior near the interface. The dead-core location is treated as a trainable parameter, enabling the simultaneous approximation of the concentration profile and identification of the free boundary without explicit interface tracking. The method is validated against analytical solutions and high-precision numerical shooting. Numerical experiments demonstrate that the approach accurately captures both the solution profile and the free-boundary location while maintaining a computationally manageable training cost.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.02599>)

[PDF](<https://arxiv.org/pdf/2606.02599.pdf>)