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arXiv · 2512.12285

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

Lujuan Dang·Zilai Wang
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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).

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Lujuan Dang, Zilai Wang. 2025-12-13. Fractional Differential Equation Physics-Informed Neural Network and Its Application in Battery State Estimation. https://arxiv.org/abs/2512.12285

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