A Systematic Benchmark of Physics-Informed Neural Network Architectures for the Stiff Poisson-Nernst-Planck System: Adaptive LossWeighting and Multi-Scale Resolution
The Poisson Nernst Planck PNP system constitutes a canonical stiff coupled PDE problem where the charge density prefactor produces extreme coefficient ratios and the electric double layer imposes sharp boundary layers. Physics informed neural networks PINNs are appealing here because they require no mesh and differentiate through the physics automatically. Spectral bias and multi task loss imbalance however have limited their accuracy on stiff PNP systems. We present the first systematic data free benchmark of eleven PINN configurations organised into four strategy groups on a physically parametrised one dimensional PNP model for a lithium symmetric cell implemented within NVIDIA PhysicsNeMo Sym and validated against a finite volume method FVM reference. Root mean square errors RMSE span across architectures. The balanced residual decay rate BRDR scheme matches Neural Tangent Kernel NTK performance for concentration fields while reducing mean wall clock time making it the preferable strategy under compute constraints. Loss landscape geometry corroborates the RMSE ranking. We release an open source PhysicsNeMo Sym implementation for reuse on stiff coupled PDE problems in computational mechanics.