# PINN surrogate of Li-ion battery models for parameter inference. Part II: Regularization and application of the pseudo-2D model

arXiv: https://arxiv.org/abs/2312.17336 · HTML: https://mlsanity.com/paper/2312.17336/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 104 references that are in the map.
- First posted on arXiv 28 Dec 2023.

## Builds on (most cited first, 19 of 19)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets](https://mlsanity.com/paper/2204.00997/) (2022)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [Physics-constrained deep neural network method for estimating parameters in a redox flow battery](https://mlsanity.com/paper/2106.11451/) (2021)
- [Bayesian Parameter Estimation Applied to the Li-ion Battery Single Particle Model with Electrolyte Dynamics](https://mlsanity.com/paper/2001.09890/) (2020)
- [Identifiability and parameter estimation of the single particle lithium-ion battery model](https://mlsanity.com/paper/1702.02471/) (2017)
- [Inferring electrochemical performance and parameters of Li-ion batteries based on deep operator networks](https://mlsanity.com/paper/2205.03508/) (2022)
- [Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model](https://mlsanity.com/paper/2306.01010/) (2023)
- [Analysis of sloppiness in model simulations: unveiling parameter uncertainty when mathematical models are fitted to data](https://mlsanity.com/paper/2203.15184/) (2022)
- [Ensemble flow reconstruction in the atmospheric boundary layer from spatially limited measurements through latent diffusion models](https://mlsanity.com/paper/2303.00836/) (2023)
- [Learning from Integral Losses in Physics Informed Neural Networks](https://mlsanity.com/paper/2305.17387/) (2023)
- [Unlocking Extra Value from Grid Batteries Using Advanced Models](https://mlsanity.com/paper/2009.11615/) (2020)
- [Estimating State of Charge for xEV batteries using 1D Convolutional Neural Networks and Transfer Learning](https://mlsanity.com/paper/2011.00841/) (2020)

## Built on by (most cited first, 5 of 5)

- [Detection of False Data Injection Attacks (FDIA) on Power Dynamical Systems With a State Prediction Method](https://mlsanity.com/paper/2409.04609/) (2024)
- [Forward and Inverse Simulation of Pseudo-Two-Dimensional Model of Lithium-Ion Batteries Using Neural Networks](https://mlsanity.com/paper/2412.13200/) (2024)
- [Optimizing Energy Management of Smart Grid using Reinforcement Learning aided by Surrogate models built using Physics-informed Neural Networks](https://mlsanity.com/paper/2510.17380/) (2025)
- [Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteries](https://mlsanity.com/paper/2604.02520/) (2026)
- [Comparative Study of Neural Surrogate Architectures for Autoregressive Prediction of Internal Battery States](https://mlsanity.com/paper/2606.20053/) (2026)

## Abstract (arXiv)

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of 2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to 2mV for the SPM surrogate and 10mV for the P2D surrogate which could be mitigated with additional data.