Forward and Inverse Simulation of Pseudo-Two-Dimensional Model of Lithium-Ion Batteries Using Neural Networks
Journal:
arXiv
Published Date:
Dec 2, 2024
Abstract
In this work, we address the challenges posed by the high nonlinearity of the
Butler-Volmer (BV) equation in forward and inverse simulations of the
pseudo-two-dimensional (P2D) model using the physics-informed neural network
(PINN) framework. The BV equation presents significant challenges for PINNs,
primarily due to the hyperbolic sine term, which renders the Hessian of the
PINN loss function highly ill-conditioned. To address this issue, we introduce
a bypassing term that improves numerical stability by substantially reducing
the condition number of the Hessian matrix. Furthermore, the small magnitude of
the ionic flux \( j \) often leads to a common failure mode where PINNs
converge to incorrect solutions. We demonstrate that incorporating a secondary
conservation law for the solid-phase potential \( \psi \) effectively prevents
such convergence issues and ensures solution accuracy. The proposed methods
prove effective for solving both forward and inverse problems involving the BV
equation. Specifically, we achieve precise parameter estimation in inverse
scenarios and reliable solution predictions for forward simulations.
