# Comparative Study of Neural Surrogate Architectures for Autoregressive Prediction of Internal Battery States

arXiv: https://arxiv.org/abs/2606.20053 · HTML: https://mlsanity.com/paper/2606.20053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [A Learned Representation For Artistic Style](https://mlsanity.com/paper/1610.07629/) (2016)
- [MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling](https://mlsanity.com/paper/2304.14422/) (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)
- [Forward and Inverse Simulation of Pseudo-Two-Dimensional Model of Lithium-Ion Batteries Using Neural Networks](https://mlsanity.com/paper/2412.13200/) (2024)

## Abstract (arXiv)

The Doyle-Fuller-Newman (DFN) model resolves internal electrochemical states in lithium-ion batteries with high fidelity. However, the numerical solution of its governing equations is computationally prohibitive for real-time deployment, limiting scalability from individual cells to pack and fleet-scale applications. While machine learning surrogates can substantially reduce inference latency through GPU acceleration, most existing approaches learn solution approximations tied to specific operating conditions rather than learning generalizable state-evolution dynamics. This work presents a systematic comparison of four neural network architectures (MLP, ResNet, U-Net, FNO) formulated as autoregressive state-transition operators that predict full DFN internal states across a wide range of operating conditions. To ensure a controlled architectural comparison, all models are trained under a unified framework using multi-step unrolling and current-conditioning, isolating the impact of spatial inductive bias. Results demonstrate that the U-Net's multi-scale feature hierarchy achieves a mean final-step nRMSE of 3% averaged across all internal state variables after 300-step autoregressive rollouts, while providing a 5.38x speed-up over the numerical solver. These findings highlight spatial inductive bias as a critical determinant of surrogate performance, advancing the development of surrogates for internal state observability for next-generation battery management systems and digital twins.