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

TL;DR

This paper introduces FDIFF-PINN, a novel physics-informed neural network leveraging fractional calculus to improve battery state of charge estimation by capturing complex nonlinear and memory-dependent electrochemical dynamics.

Contribution

The study develops a fractional differential equation-based neural network architecture that enhances battery SOC estimation accuracy and physical interpretability under dynamic conditions.

Findings

FDIFF-PINN outperforms traditional models in SOC estimation accuracy.

The fractional-order model effectively captures memory effects in battery dynamics.

Experimental results demonstrate robustness across temperature variations.

Abstract

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 -10$^{\circ}$C to 20$^{\circ}$C).