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

arXiv: https://arxiv.org/abs/2601.06195 · HTML: https://mlsanity.com/paper/2601.06195/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 2 of 2)

- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)

## Built on by (most cited first, 3 of 3)

- [When Smaller Wins: Dual-Stage Distillation and Pareto-Guided Compression of Liquid Neural Networks for Edge Battery Prognostics](https://mlsanity.com/paper/2601.06227/) (2026)
- [Interpretable Battery Aging without Extra Tests via Neural-Assisted Physics-based Modelling](https://mlsanity.com/paper/2604.01229/) (2026)
- [PhyMamba: Physics-Modulated Mamba for Robust Battery Health Prognostics](https://mlsanity.com/paper/2608.27978/) (2026)

## Abstract (arXiv)

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.