Modelling heterogeneous interface diffusion kinetics via a retinal-inspired hierarchical focal-PINN

To resolve the fundamental conflict between suppressing measurement noise and capturing localised kinetic features in heterogeneous interface diffusion prediction, a novel Topology-Aware Hierarchical Focal-PINN is proposed, incorporating a retinal-inspired hierarchical focusing mechanism. Mimicking the biological fovea, the model addresses the spectral bias of traditional PINNs through residual-triggered hierarchical refinement with adjacency-aware subdomain control. This architecture enables multi-scale signal separation: global regularisation suppresses unstructured instrumental noise, while micro-scale focused weighting amplifies sensitivity to localised kinetic anomalies. Experimental results on the copper-stainless steel system demonstrate that the proposed method significantly outperforms Global-PINN, reducing the Root Mean Square Error (RMSE) from 0.844 μm to 0.203 μm (∼76% reduction) and the Mean Absolute Error (MAE) by ∼68%. With a coefficient of determination (R²) reaching 0.991, the model effectively resolves the bottleneck of high-fidelity modelling for complex interfacial diffusion phenomena.