# PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle model

arXiv: https://arxiv.org/abs/2312.17329 · HTML: https://mlsanity.com/paper/2312.17329/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 78 references that are in the map.
- First posted on arXiv 28 Dec 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability](https://mlsanity.com/paper/2204.12670/) (2022)
- [Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets](https://mlsanity.com/paper/2204.00997/) (2022)
- [On transfer learning of neural networks using bi-fidelity data for uncertainty propagation](https://mlsanity.com/paper/2002.04495/) (2020)
- [Neural Network Training Using ℓ1-Regularization and Bi-fidelity Data](https://mlsanity.com/paper/2105.13011/) (2021)
- [Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains](https://mlsanity.com/paper/2302.04954/) (2023)
- [Physics-constrained deep neural network method for estimating parameters in a redox flow battery](https://mlsanity.com/paper/2106.11451/) (2021)
- [Integrating Physics-Based Modeling with Machine Learning for Lithium-Ion Batteries](https://mlsanity.com/paper/2112.12979/) (2021)
- [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)
- [Uniform-in-Phase-Space Data Selection with Iterative Normalizing Flows](https://mlsanity.com/paper/2112.15446/) (2021)

## Built on by (most cited first, 6 of 6)

- [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)
- [Fixed Point Neural Acceleration and Inverse Surrogate Model for Battery Parameter Identification](https://mlsanity.com/paper/2510.24135/) (2025)
- [A Multi-Task Targeted Learning Framework for Lithium-Ion Battery State-of-Health and Remaining Useful Life](https://mlsanity.com/paper/2603.22323/) (2026)
- [Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteries](https://mlsanity.com/paper/2604.02520/) (2026)
- [Large Models for Battery Prognostics and Health Management: A Review and Future Roadmap](https://mlsanity.com/paper/2608.26111/) (2026)

## Abstract (arXiv)

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.