[论文解读] EntroLnn: Entropy-Guided Liquid Neural Networks for Operando Refinement of Battery Capacity Fade Trajectories

Wei Li, Wei Zhang+1 more|arXiv (Cornell University)|Jan 8, 2026

Advanced Battery Technologies Research被引用 0

一句话总结

EntroLnn 通过熵引导的可变形液态神经网络实时 refine 整个电池容量衰退轨迹，在有限数据和轻量化计算下实现高精度。对于 CFT，MAE 为 0.004577；使用熵特征进行的 18 循环 EoL 预测。

ABSTRACT

Battery capacity degradation prediction has long been a central topic in battery health analytics, and most studies focus on state of health (SoH) estimation and end of life (EoL) prediction. This study extends the scope to online refinement of the entire capacity fade trajectory (CFT) through EntroLnn, a framework based on entropy-guided transformable liquid neural networks (LNNs). EntroLnn treats CFT refinement as an integrated process rather than two independent tasks for pointwise SoH and EoL. We introduce entropy-based features derived from online temperature fields, applied for the first time in battery analytics, and combine them with customized LNNs that model temporal battery dynamics effectively. The framework enhances both static and dynamic adaptability of LNNs and achieves robust and generalizable CFT refinement across different batteries and operating conditions. The approach provides a high fidelity battery health model with lightweight computation, achieving mean absolute errors of only 0.004577 for CFT and 18 cycles for EoL prediction. This work establishes a foundation for entropy-informed learning in battery analytics and enables self-adaptive, lightweight, and interpretable battery health prediction in practical battery management systems.

研究动机与目标

• 将容量衰退轨迹建模扩展到 SoH 和 EoL 之外的 operando CFT 精炼.
• 引入来自在线温度场的基于熵的特征以实现物理可解释性.
• 开发可变形的 LNN（静态与动态），以在不同电池和工作条件下自适应.
• 展示数据高效、可泛化的电池健康建模，所需传感最少。

提出的方法

• 从温度与空间区间定义熵 S，以总结降解过程中的热不均匀性。
• 将 dS/dV 作为 SoH 建模的主要特征。
• 使用一个轻量级的两层 1D-CNN 提取 dS/dV 的模式。
• 将熵导出特征与基于物理信息的指标在注意力驱动的多输入 MLP 中融合，用于 SoH 估计。
• 在参考电池上训练静态 LNN 以实现短期 CFT 精炼，在在线自适应的前提下训练动态 LNN 以实现长期精炼。
• 两阶段部署：静态 LNN 处理早期循环；动态 LNN 通过滑动窗口将 CFT 推进至 EoL。

Figure 1. The holistic framework of EntroLnn . The model integrates multiple features of LIBs, including temperature curves, entropy features derived from temperature profiles, and additional attributes extracted from entropy curves. EntroLnn adapts to real-time CFT refinement across different batte

实验结果

研究问题

• RQ1 熵基温度特征是否能在多样化电池上实现准确的 operando SoH 与 CFT 精炼？
• RQ2 静态和动态 LNN 如何在有限的早期循环数据下对未见电池实现良好泛化？
• RQ3 在最少数据和轻量模型条件下，CFT 精炼与 EoL 预测可达到的准确度是多少？
• RQ4 operando 熵引导学习是否提升对传感器噪声与不同工作条件的鲁棒性？

主要发现

Method	MAE (SoH)	MAE (EoL)	Data Storage	Parameters (M)
BFRN	0.004775	200 (with 10% data)	0.36 GB for 10 cycles	6.05
BTL	0.02709 (with 30% data)	–	–	–
DRRN	0.012	–	–	0.69
TLPH	–	47.67	–	7.36
DCNN	–	65.00	–	2.39
EntroLnn (ours)	0.004577 (with 10% data)	18 (with 10% data)	239KB for 2,134 cycles	0.25

• EntroLnn 在 10% 数据下实现 CFT 精炼的 MAE 为 0.004577。
• 在 10% 数据下，EoL 预测 MAE 为 18 个循环。
• 静态 LNN 在跨电池的短期精炼中达到高精度，SoH 达到 ~98% 的平均 SoH 演化 MAE 约 0.0025。
• 动态 LNN 将精炼扩展到 EoL，短期与中期电池的总体 CFT MAE 低于 0.0058，MAPE ~0.6%。
• 基于熵特征的逐点 SoH 估计 MAE 为 0.0086，显著优于仅使用温度时的 0.0158。
• 基于熵的特征实现轻量级、传感器高效建模（2,134 循环的数据存储 239 KB；参数量 0.25M）。

Figure 2. The original data extraction from the dataset, which consists of 124 batteries. The extracted data include the SoH, voltage, and surface temperature profiles.