# Fractional Differential Equation Physics-Informed Neural Network and Its Application in Battery State Estimation

arXiv: https://arxiv.org/abs/2512.12285 · HTML: https://mlsanity.com/paper/2512.12285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 24 references that are in the map.
- First posted on arXiv 13 Dec 2025.

## Builds on (most cited first, 1 of 1)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)

## Abstract (arXiv)

Accurate estimation of the State of Charge (SOC) is critical for ensuring the safety, reliability, and performance optimization of lithium-ion battery systems. Conventional data-driven neural network models often struggle to fully characterize the inherent complex nonlinearities and memory-dependent dynamics of electrochemical processes, significantly limiting their predictive accuracy and physical interpretability under dynamic operating conditions. To address this challenge, this study proposes a novel neural architecture termed the Fractional Differential Equation Physics-Informed Neural Network (FDIFF-PINN), which integrates fractional calculus with deep learning. The main contributions of this paper include: (1) Based on a fractional-order equivalent circuit model, a discretized fractional-order partial differential equation is constructed. (2) Comparative experiments were conducted using a dynamic charge/discharge dataset of Panasonic 18650PF batteries under multi-temperature conditions (from -10circC to 20circC).