A Systematic Benchmark of Physics-Informed Neural NetworkStrategies for Stiff Ion Transport in Lithium Symmetric Cells

Abstract

The Poisson–Nernst–Planck (PNP) system governs ion transport in lithium-ion battery electrolytes and presents a canonical stiff coupled PDE challenge: extreme coefficient ratios, sharp electric double-layer boundary layers, and nonlinear coupling between the Poisson and Nernst–Planck equations. Physics-informed neural networks (PINNs) are appealing because they require no mesh and handle forward and inverse problems in one framework, but spectral bias and multi-task loss imbalance have limited their accuracy on stiff PNP systems. We present the first systematic, simulation-only benchmark of eleven PINN configurations, organised into four strategy groups (adaptive loss weighting, spectral bias mitigation, spatio-temporal decomposition, and physics enrichment), on a physically parametrised one-dimensional PNP model for a lithium symmetric cell, implemented in NVIDIA PhysicsNeMo Sym and validated against a high-resolution finite volume method reference. Root-mean-square errors span 10⁻² to 10⁻⁴: Neural Tangent Kernel (NTK) adaptive weighting achieves the lowest errors (RMSE = 6.6×10⁻⁴ for anion concentration), while the balanced residual decay rate (BRDR) scheme matches NTK within 10% RMSE for concentrations while reducing wall-clock time by 3.2 ± 0.4 h per run. Loss landscape geometry corroborates the RMSE ranking. An open-source PhysicsNeMo Sym implementation is released for reuse in electrochemical modelling.