Forward and Inverse Simulation of Pseudo-Two-Dimensional Model of Lithium-Ion Batteries Using Neural Networks

TL;DR

This paper develops a neural network framework to improve forward and inverse simulations of lithium-ion batteries by addressing the nonlinearity of the Butler-Volmer equation, enhancing stability and accuracy.

Contribution

Introduces a bypassing term and a secondary conservation law within PINNs to stabilize solutions and prevent convergence failures in modeling lithium-ion batteries.

Findings

Enhanced numerical stability with reduced Hessian condition number.

Accurate parameter estimation in inverse problems.

Reliable forward simulation predictions.

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.