LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

arXiv:2607.03682v1 Announce Type: cross Abstract: Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized. This creates a structural mismatch for standard physics-informed neural networks (PINNs), whose trial spaces are not designed to match the value--derivative structure of such layers. We propose a Layer-Resolving XNet Physics-Informed Neural Network (LRX-PINN) based on integrated Cauchy activations. The proposed basis is transition-type at the solution level, while its derivative