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

arXiv: https://arxiv.org/abs/2412.13200 · HTML: https://mlsanity.com/paper/2412.13200/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?](https://mlsanity.com/paper/2206.02016/) (2022)
- [PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle model](https://mlsanity.com/paper/2312.17329/) (2023)
- [Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model](https://mlsanity.com/paper/2306.01010/) (2023)
- [PINN surrogate of Li-ion battery models for parameter inference. Part II: Regularization and application of the pseudo-2D model](https://mlsanity.com/paper/2312.17336/) (2023)
- [A fast solver for the pseudo-two-dimensional model of lithium-ion batteries](https://mlsanity.com/paper/2111.09251/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Theory-guided Weighted L2 Loss for solving the BGK model via Physics-informed neural networks](https://mlsanity.com/paper/2604.04971/) (2026)
- [Comparative Study of Neural Surrogate Architectures for Autoregressive Prediction of Internal Battery States](https://mlsanity.com/paper/2606.20053/) (2026)

## Abstract (arXiv)

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.