EntroLnn: Entropy-Guided Liquid Neural Networks for Operando Refinement of Battery Capacity Fade Trajectories

TL;DR

This work reframes battery health modeling by online-refining the entire capacity fade trajectory (CFT) rather than solely estimating state of health (SoH) or end of life (EoL). It introduces EntroLnn, which combines entropy-guided features derived from operando temperature fields with transformable liquid neural networks, employing a static LNN based on a reference battery for short-term refinement and a dynamic LNN for long-term adaptation across multiple cells. Experimental results on the MIT-Stanford dataset show strong performance: CFT refinement MAEs around 0.0046 and EoL predictions within about 18 cycles, with high generalization across batteries and operating conditions while using minimal data and lightweight computation. The approach demonstrates a practical, interpretable, and transferable framework for real-time battery health analytics, and establishes entropy-informed learning as a foundation for physics-guided ML in energy systems.

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.

Figures (4)

• 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 batteries and maintains high generalizability and stable performance.
• 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.
• Figure 3: The operando temperature curve refinement and pointwise SoH estimation results. EntroLnn adapts to each battery and identifies the corresponding heat generation model. Without entropy feature guidance, the pointwise SoH estimation produces significantly higher errors.
• Figure 4: CFT operando refinement for different batteries. The experimental results can be grouped into three categories corresponding to long-, mid-, and short-life batteries, to illustrate the transformable CFT refinement from the original dataset. The shaded region represents the SoH range from 100% to 98%. EntroLnn accurately models the CFTs across different batteries.