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

• URL: http://arxiv.org/abs/2512.12285v1
• Date: Sat, 13 Dec 2025 11:11:03 GMT
• Title: Fractional Differential Equation Physics-Informed Neural Network and Its Application in Battery State Estimation
• Abstract summary: The State of Charge (SOC) is critical for ensuring the safety, reliability, and performance optimization of lithium-ion battery systems.<n> Conventional data-driven neural network models often struggle to fully characterize the inherent complex nonlinearities and memory-dependent dynamics of electrochemical processes.<n>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.
• Score: 2.3977651066739374
• License: http://creativecommons.org/licenses/by/4.0/
• 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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