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arxiv: 2604.16580 · v1 · submitted 2026-04-17 · 💻 cs.LG · cs.AI

Continuous ageing trajectory representations for knee-aware lifetime prediction of lithium-ion batteries across heterogeneous dataset

Agnieszka Pregowska , Stefan Marynowicz This is my paper

Pith reviewed 2026-05-10 09:05 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords lithium-ion batteriesbattery ageingknee point detectionremaining useful life predictioncontinuous trajectory modelingdegradation featuresheterogeneous datasetsearly-life prediction
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The pith

Continuous representations of battery ageing trajectories enable consistent knee-point detection and early remaining useful life prediction across heterogeneous datasets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a framework that models battery voltage-capacity and capacity-cycle data as continuous functions rather than discrete points. This approach extracts features such as curvature and knee locations in a way that is consistent even when data comes from different labs and cycling conditions. Across more than 250 cells from public datasets, it finds that the cycle at which the knee appears strongly predicts when the battery reaches end of life. The method also shows that these predictions can be made reliably using only the first 5 to 20 cycles, with the estimates becoming stable as more early data is included. This matters because better early prediction of battery lifetime helps with safer and more efficient use in electric vehicles and grid storage, where data is often limited and inconsistent.

Core claim

The central discovery is that continuous functional representations of ageing trajectories enable the consistent identification of degradation transitions such as the knee point, which correlates with end-of-life at Pearson coefficients of 0.75-0.84 across heterogeneous datasets, and that knee-related features extracted from partial early trajectories support uncertainty-aware remaining useful life predictions that stabilize within the first 5-20 cycles while remaining robust to cross-dataset shifts.

What carries the argument

Continuous functional representations of voltage-capacity and capacity-cycle trajectories, which permit consistent extraction of degradation descriptors including curvature, plateau length, and knee metrics independent of dataset discretization.

Load-bearing premise

The continuous representations learned from the data accurately reflect the underlying physical degradation processes without introducing artifacts from the choice of model form or fitting procedure, and that the knee point remains a reliable universal marker across unseen conditions.

What would settle it

A new battery dataset collected under different operating conditions where the Pearson correlation between identified knee onset and end-of-life falls below 0.7, or where RUL predictions from the first 5 cycles deviate significantly from actual values without stabilizing.

Figures

Figures reproduced from arXiv: 2604.16580 by Agnieszka Pregowska, Stefan Marynowicz.

Figure 1
Figure 1. Figure 1: Workflow of the proposed battery ageing analysis framework. Heterogeneous [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: EOL distribution analysis: (a) empirical histogram showing strong right–skewness [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Kaplan-Meier survival analysis: (a) survival function for all datasets combined, [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Relationships between EOL, knee, and initial capacity: (a) EOL [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Latent representations of degradation: (a) PCA latent space coloured by degradation [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Relationship between degradation indicators: (a) scatter of EOL versus initial [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of (a) curve curvature across dataset types, revealing protocol-dependent [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) PCA latent space with K-means clusters showing distinct degradation modes, [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cross-dataset generalisation: (a) RMSE heatmap for the Random Forest model, (b) [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: INR model analysis: (a) validation RMSE comparison across INR architectures [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) SHAP summary plot showing feature importance for the EOL regression model, [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
read the original abstract

Accurate assessment of lithium-ion battery ageing is challenged by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven models across datasets. In particular, robust identification of degradation transitions, such as the knee point, and reliable early-life prediction of remaining useful life (RUL) remain open problems. This study proposes a unified framework for battery ageing analysis based on continuous representations of voltage-capacity and capacity-cycle trajectories learned from heterogeneous public datasets (NASA, CALCE, ISU-ILCC). The continuous formulation enables consistent extraction of degradation descriptors, including curvature, plateau length and knee-related metrics, while reducing sensitivity to dataset-specific discretisation. Across more than 250 cells, statistically significant correlations between knee onset and end-of-life (Pearson 0.75-0.84) are observed. Additional early-life analysis confirms that knee-related features retain predictive value when estimated from partial trajectories. Early-life models provide increasingly stable RUL predictions as the number of observed cycles increases, with meaningful predictive performance emerging within the first 5-20 cycles and remain robust under cross-dataset domain shift. The framework integrates continuous modelling, feature extraction and uncertainty-aware prediction, providing an interpretable and dataset-consistent approach demonstrating robustness across heterogeneous dataset types. Compared with conventional discrete or feature-based methods, the proposed representation reduces sensitivity to sampling resolution and improves cross-dataset consistency. The study is limited to laboratory-scale datasets and capacity-based end-of-life definitions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes a unified framework for lithium-ion battery ageing analysis based on continuous representations of voltage-capacity and capacity-cycle trajectories learned from heterogeneous public datasets (NASA, CALCE, ISU-ILCC). It enables consistent extraction of degradation descriptors including curvature, plateau length and knee-related metrics, reports statistically significant Pearson correlations (0.75-0.84) between knee onset and end-of-life across >250 cells, and shows that knee-related features retain predictive value for remaining useful life (RUL) when estimated from partial trajectories, with meaningful performance emerging in the first 5-20 cycles and robustness under cross-dataset domain shift. The approach is positioned as reducing sensitivity to sampling resolution compared to discrete methods while integrating continuous modelling, feature extraction and uncertainty-aware prediction.

Significance. If the continuous representations prove free of systematic artifacts and the predictive results are supported by transparent validation, the work could contribute an interpretable, dataset-consistent method for handling cell-to-cell variability and protocol heterogeneity in battery lifetime prediction. The reported cross-dataset correlations and early-cycle emergence of predictive power would be of practical interest for RUL estimation, provided the claims are grounded in detailed methodological reporting and ablation evidence.

major comments (3)
  1. [Methods / Abstract] The abstract and methods description provide no details on the specific functional forms chosen for the continuous representations, their parameterization, regularization, fitting procedures, or how training/validation splits were handled across the heterogeneous datasets. Without these, it is impossible to evaluate whether the reported knee metrics and 5-20-cycle predictive performance arise from the data or from model-specific smoothness priors.
  2. [Results / Experiments] No ablation is presented comparing the continuous basis to alternative families (e.g., different splines, polynomials, or Gaussian processes), regularization strengths, or physics-based references such as equivalent-circuit or SEI-growth models. This omission leaves open the possibility that the claimed cross-dataset consistency and reduced sensitivity to sampling resolution are partly artifacts of the chosen representation rather than universal degradation features.
  3. [Results] The central claims rest on representations learned from the same datasets used for feature extraction and RUL prediction. Although cross-dataset domain-shift testing is mentioned, the manuscript does not report independent held-out validation, error bars on the Pearson coefficients, or statistical tests that would separate data-driven artifacts from genuine predictive signal.
minor comments (1)
  1. [Abstract] The abstract states that the framework provides 'uncertainty-aware prediction' but supplies no quantitative details on how uncertainty is quantified or propagated into the RUL forecasts.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback, which has helped clarify several aspects of our work. We address each major comment below and have revised the manuscript to improve transparency, add supporting analyses, and strengthen the validation evidence.

read point-by-point responses

  1. Referee: [Methods / Abstract] The abstract and methods description provide no details on the specific functional forms chosen for the continuous representations, their parameterization, regularization, fitting procedures, or how training/validation splits were handled across the heterogeneous datasets. Without these, it is impossible to evaluate whether the reported knee metrics and 5-20-cycle predictive performance arise from the data or from model-specific smoothness priors.

    Authors: We agree that greater explicitness is required for reproducibility. In the revised manuscript we have expanded the Methods section to specify the functional forms (piecewise-linear bases with C1 continuity for capacity-cycle trajectories and low-order polynomial bases for voltage-capacity curves), parameterization (knot locations and coefficient vectors), regularization (L2 penalty on second derivatives), fitting procedure (regularized least-squares solved via QR decomposition with 5-fold cross-validation for hyperparameter selection), and split strategy (per-dataset 80/20 train/test with leave-one-dataset-out for domain-shift evaluation). The abstract has been updated to reference these modeling choices. These additions make clear that the reported knee metrics and early-cycle RUL performance are driven by observed data patterns rather than imposed smoothness priors. revision: yes

  2. Referee: [Results / Experiments] No ablation is presented comparing the continuous basis to alternative families (e.g., different splines, polynomials, or Gaussian processes), regularization strengths, or physics-based references such as equivalent-circuit or SEI-growth models. This omission leaves open the possibility that the claimed cross-dataset consistency and reduced sensitivity to sampling resolution are partly artifacts of the chosen representation rather than universal degradation features.

    Authors: We acknowledge that explicit ablations would further support the claims. We have added an ablation study to the supplementary material that compares our representation against cubic splines of varying knot counts, polynomial bases of degrees 3–7, and Gaussian-process regression with RBF and Matérn kernels, together with a sweep over regularization strengths. The results confirm that the chosen continuous basis yields the highest cross-dataset consistency in knee detection and the lowest sensitivity to sampling resolution. For physics-based references we have added a discussion section relating the extracted curvature and plateau features to expected signatures of SEI-growth models in the literature; a direct head-to-head comparison with equivalent-circuit models was not performed because our focus is on protocol-agnostic, data-driven descriptors that remain applicable when mechanistic assumptions do not hold uniformly across heterogeneous datasets. revision: partial

  3. Referee: [Results] The central claims rest on representations learned from the same datasets used for feature extraction and RUL prediction. Although cross-dataset domain-shift testing is mentioned, the manuscript does not report independent held-out validation, error bars on the Pearson coefficients, or statistical tests that would separate data-driven artifacts from genuine predictive signal.

    Authors: The cross-dataset domain-shift protocol already implements independent held-out validation: models are trained on two datasets and evaluated on the third unseen dataset. In the revision we have added bootstrapped 95 % confidence intervals (error bars) for all reported Pearson coefficients and performed two-sided t-tests confirming statistical significance (p < 0.001). A new subsection explicitly tabulates the train/test splits and shows that the early-cycle RUL predictive performance remains stable under these stricter validation conditions, thereby separating genuine signal from potential data-driven artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper learns continuous functional representations of voltage-capacity and capacity-cycle trajectories from the input datasets, extracts knee-related descriptors (curvature, plateau length, onset), computes empirical Pearson correlations with separately defined EOL (0.75-0.84), and trains early-life RUL predictors on partial trajectories. These steps are standard empirical fitting followed by statistical analysis and cross-dataset testing; no equation or procedure reduces the reported correlations or predictive performance to the inputs by construction. Cross-dataset domain-shift evaluation supplies independent grounding, and no self-citation chain or uniqueness theorem is invoked as load-bearing justification. The framework therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides limited visibility; the central claim rests on the assumption that continuous functional forms can be fitted to discrete battery data without loss of predictive information and that knee-related metrics are transferable across protocols.

axioms (1)
  • domain assumption Battery aging trajectories can be accurately captured by continuous functions that enable consistent extraction of degradation descriptors such as curvature and knee points.
    Invoked when proposing continuous representations to reduce sensitivity to dataset-specific discretisation.

pith-pipeline@v0.9.0 · 5557 in / 1395 out tokens · 106895 ms · 2026-05-10T09:05:15.391437+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    Hu, J., Fu, P., Wei, Z. et al. Early prediction of lithium-ion battery degra- dation with a generative pre-trained transformer. Nat Commun 17, 126 (2026). https://doi.org/10.1038/s41467-025-66819-0

    work page doi:10.1038/s41467-025-66819-0 2026

  2. [2]

    (2023) Transparent and Interpretable State of Health Forecasting of Lithium-Ion Batteries with Deep Learning and Saliency Maps, International Journal of Energy Research 9922475

    von Bulow, F., Hahn, Y., Meyes, R., Meisen, T. (2023) Transparent and Interpretable State of Health Forecasting of Lithium-Ion Batteries with Deep Learning and Saliency Maps, International Journal of Energy Research 9922475. https://doi.org/10.1155/2023/9922475. 36

    work page doi:10.1155/2023/9922475 2023

  3. [3]

    A., Li, R., OKane, S

    Nazeeruddin, M. A., Li, R., OKane, S. E., Marinescu, M., & Offer, G. J. (2025). Lithium-ion battery degradation: Introducing the concept of reser- voirs to design for lifetime. arXiv preprint https://arxiv.org/abs/2512.15440

    work page arXiv 2025

  4. [4]

    Guangxu Zhang, Xuezhe Wei, Siqi Chen, Guangshuai Han, Jiangong Zhu, and Haifeng Dai ACS Applied Energy Materials 2022 5 (5), 6462-6471 https://doi.org/10.1021/acsaem.2c00957

    work page doi:10.1021/acsaem.2c00957 2022

  5. [5]

    Chen, L., Xu, C., Bao, X. et al. (2023) State-of-health estimation of Lithium-ion battery based on back-propagation neural network with adaptive hidden layer. Neural Comput & Applic 35, 14169-14182. https://doi.org/10.1007/s00521-023-08471-7

    work page doi:10.1007/s00521-023-08471-7 2023

  6. [6]

    (2022) The Application of Artificial Intelligence in the Effective Battery Life Cycle in the Closed Circular Economy Model- A Perspective

    Pregowska, A., Osial, M., Urbanska, W. (2022) The Application of Artificial Intelligence in the Effective Battery Life Cycle in the Closed Circular Economy Model- A Perspective. Recycling 7, 81. https://doi.org/10.3390/recycling7060081

    work page doi:10.3390/recycling7060081 2022

  7. [7]

    (2012) A comparative study of equivalent cir- cuit models for Li-ion batteries, Journal of Power Sources 198, 359-367

    Hu, X., Li, S., Peng, H. (2012) A comparative study of equivalent cir- cuit models for Li-ion batteries, Journal of Power Sources 198, 359-367. https://doi.org/10.1016/j.jpowsour.2011.10.013

    work page doi:10.1016/j.jpowsour.2011.10.013 2012

  8. [8]

    (2016) Review of simplified Pseudo-two-Dimensional models of lithium-ion batteries, Journal of Power Sources 327, 44-55

    Jokar, A., Rajabloo, B., Desilets, M., Lacroix, M. (2016) Review of simplified Pseudo-two-Dimensional models of lithium-ion batteries, Journal of Power Sources 327, 44-55. https://doi.org/10.1016/j.jpowsour.2016.07.036

    work page doi:10.1016/j.jpowsour.2016.07.036 2016

  9. [9]

    Wei, Y., Wu, D. (2023) Prediction of state of health and remaining useful life of lithium-ion battery using graph convolutional network with dual attention mechanisms, Reliability Engineering & System Safety 230, 108947. https://doi.org/10.1016/j.ress.2022.108947

    work page doi:10.1016/j.ress.2022.108947 2023

  10. [10]

    (2025) Prediction of the Remaining Useful Life of Lithium-Ion Batter- ies Based on Mode Decomposition and ED-LSTM, Batteries 11, 86

    Song, B., Yue, G., Guo, D., Wu, H., Sun, Y., Li, Y., Zhou, B. (2025) Prediction of the Remaining Useful Life of Lithium-Ion Batter- ies Based on Mode Decomposition and ED-LSTM, Batteries 11, 86. https://doi.org/10.3390/batteries11030086. 37

    work page doi:10.3390/batteries11030086 2025

  11. [11]

    (2021) Lithium- ion battery data and where to find it, Energy and AI 5, 100081

    dos Reis, G., Strange, C., Yadav, M., Li, S. (2021) Lithium- ion battery data and where to find it, Energy and AI 5, 100081. https://doi.org/10.1016/j.egyai.2021.100081

    work page doi:10.1016/j.egyai.2021.100081 2021

  12. [12]

    (2024) Data-Driven State of Health Interval Prediction for Lithium-Ion Batteries

    Song, Z., Zhang, H., Jia, J. (2024) Data-Driven State of Health Interval Prediction for Lithium-Ion Batteries. Electronics 13, 3991. https://doi.org/10.3390/electronics13203991

    work page doi:10.3390/electronics13203991 2024

  13. [13]

    Mildenhall B., Srinivasan P.P., Tancik M., Barron J.T., Ramamoorthi R., Ng R. (2021). NeRF: representing scenes as neural radiance fields for view synthesis, Commun. ACM 65, 1, 99–106. https://doi.org/10.1145/3503250

    work page doi:10.1145/3503250 2021

  14. [14]

    (2019) Algorithm to Determine the Knee Point on Capacity Fade Curves of Lithium-Ion Cells

    Diao, W., Saxena, S., Han, B., Pecht, M. (2019) Algorithm to Determine the Knee Point on Capacity Fade Curves of Lithium-Ion Cells. Energies 12,

    work page 2019

  15. [15]

    https://doi.org/10.3390/en12152910

    work page doi:10.3390/en12152910

  16. [16]

    (2023) Nonlinear aging knee-point prediction for lithium–on batteries faced with different application scenarios, eTransportation 18, 100270

    You, H., Zhu, J., Wang, X., Jiang, B., Wei, X., Dai, H. (2023) Nonlinear aging knee-point prediction for lithium–on batteries faced with different application scenarios, eTransportation 18, 100270. https://doi.org/10.1016/j.etran.2023.100270

    work page doi:10.1016/j.etran.2023.100270 2023

  17. [17]

    Sitzmann V., Martel J., Bergman A., Lindell D., Wetzstein G. (2020). Implicit Neural Representations with Periodic Activation Functions, in: Advances in Neural Information Processing Systems, Larochelle H., Ranzato M., Hadsell R., Balcan M.F., Lin H. (Eds.), Curran Associates, Inc., Article 33, 7462–7473

    work page 2020

  18. [18]

    P., Mildenhall B., Fridovich-Keil S., Raghavan N., Singhal U., Ramamoorthi R, Barron J

    Tancik M., Srinivasan P. P., Mildenhall B., Fridovich-Keil S., Raghavan N., Singhal U., Ramamoorthi R, Barron J. T., Ng R., (2020). Fourier features let networks learn high frequency functions in low dimensional domains, in: Proceedings of the 34th International Conference on Neural Information Processing Systems (NIPS ’20). Curran Associates Inc., Red Ho...

    work page 2020

  19. [19]

    A., Majid, M.A

    Mouais, T., Kittaneh, O. A., Majid, M.A. (2021) Choosing the Best Lifetime Model for Commercial Lithium-Ion Batteries, Journal of Energy Storage 41, 102827. https://doi.org/10.1016/j.est.2021.102827

    work page doi:10.1016/j.est.2021.102827 2021

  20. [20]

    (2025) A Comprehensive Review on Lithium-Ion Battery Lifetime Prediction and Aging Mechanism Analysis

    Madani, S.S., Shabeer, Y., Allard, F., Fowler, M., Ziebert, C., Wang, Z., Pan- chal, S., Chaoui, H., Mekhilef, S., Dou, S.X., et al. (2025) A Comprehensive Review on Lithium-Ion Battery Lifetime Prediction and Aging Mechanism Analysis. Batteries 11, 127. https://doi.org/10.3390/batteries11040127

    work page doi:10.3390/batteries11040127 2025

  21. [21]

    Park J.J., Florence P., Straub J., Newcombe R., Lovegrove S. (2019). DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation, IEEE/CVF Conference on Computer Vision and Pat- tern Recognition (CVPR), Long Beach, CA, USA, pp. 165–174. https://doi.org/10.1109/CVPR.2019.00025

    work page doi:10.1109/cvpr.2019.00025 2019

  22. [22]

    Mescheder L., Oechsle M., Niemeyer M., Nowozin S., Geiger A. (2019). Occupancy Networks: Learning 3D Reconstruction in Func- tion Space,IEEE/CVF Conference on Computer Vision and Pat- tern Recognition (CVPR), Long Beach, CA, USA, pp. 4455–4465. https://doi.org/10.1109/CVPR.2019.00459

    work page doi:10.1109/cvpr.2019.00459 2019

  23. [23]

    Pregowska A., Larecki W., Szczepanski J. (2025) Application of Neural Networks for Determine the Radiation Pressure in Two-Moment Radia- tion Hydrodynamics in Slab Geometry, Computer Assisted Methods in Engineering and Science, 1–24. https://doi.org/10.24423/cames.2025.1960

    work page doi:10.24423/cames.2025.1960 2025

  24. [24]

    https://doi.org/10.1007/s00591-025-00399-4

    Dietrich, F., Schilders, W.(2025)Scientificmachinelearning.MathSemester- ber 72, 89–115. https://doi.org/10.1007/s00591-025-00399-4

    work page doi:10.1007/s00591-025-00399-4 2025

  25. [25]

    A review on prognostics and health management (PHM) methods of lithium-ion batteries, Renewable and Sustainable Energy Re- views 116, 109405

    Meng, H., Li, Y.F. A review on prognostics and health management (PHM) methods of lithium-ion batteries, Renewable and Sustainable Energy Re- views 116, 109405. https://doi.org/10.1016/j.rser.2019.109405

    work page doi:10.1016/j.rser.2019.109405 2019

  26. [26]

    (2024) State of Health Estimation for Lithium-Ion Batteries Using an Explainable 39 XGBoost Model with Parameter Optimization

    Xiao, Z., Jiang, B., Zhu, J., Wei, X., Dai, H. (2024) State of Health Estimation for Lithium-Ion Batteries Using an Explainable 39 XGBoost Model with Parameter Optimization. Batteries 10, 394. https://doi.org/10.3390/batteries10110394

    work page doi:10.3390/batteries10110394 2024

  27. [27]

    (2016) Critical review of state of health estimation methods of Li-ion batteries for real applications," Renew- able and Sustainable Energy Reviews, Elsevier, vol

    Berecibar, M., Gandiaga, I., Villarreal, I., Omar, N., Van Mierlo, J., Van den Bossche, P. (2016) Critical review of state of health estimation methods of Li-ion batteries for real applications," Renew- able and Sustainable Energy Reviews, Elsevier, vol. 56(C), 572–587. https://doi.org/10.1016/j.rser.2015.11.042

    work page doi:10.1016/j.rser.2015.11.042 2016

  28. [28]

    Attia, P.M., Grover, A., Jin, N. et al. (2020) Closed-loop optimization of fast-charging protocols for batteries with machine learning. Nature 578, 397–402. https://doi.org/10.1038/s41586-020-1994-5

    work page doi:10.1038/s41586-020-1994-5 2020

  29. [29]

    Severson, K.A., Attia, P.M., Jin, N. et al. (2019) Data-driven prediction of battery cycle life before capacity degradation. Nat Energy 4, 383–391. https://doi.org/10.1038/s41560-019-0356-8

    work page doi:10.1038/s41560-019-0356-8 2019

  30. [30]

    Chen, Z., Sun, M., Shu, X., Shen, J., Xiao, R. (2018). On-board state of health estimation for lithium-ion batteries based on random forest. 2018 IEEE International Conference on Industrial Technology (ICIT), 175–1759

    work page 2018

  31. [31]

    (2025) Ma- chine Learning-Based State-of-Health Estimation of Battery Management Systems Using Experimental and Simulation Data

    Al-Rahamneh, A., Izco, I., Serrano-Hernandez, A., Faulin, J. (2025) Ma- chine Learning-Based State-of-Health Estimation of Battery Management Systems Using Experimental and Simulation Data. Mathematics 13, 2247. https://doi.org/10.3390/math13142247

    work page doi:10.3390/math13142247 2025

  32. [32]

    Thelen, A., Huan, X., Paulson, N. et al. Probabilistic machine learning for battery health diagnostics and prognostics-review and perspectives. npj Mater. Sustain. 2, 14. https://doi.org/10.1038/s44296-024-00011-1

    work page doi:10.1038/s44296-024-00011-1

  33. [33]

    (2016) Dropout as a Bayesian approximation: representing model uncertainty in deep learning

    Gal, Y., Ghahramani, Z. (2016) Dropout as a Bayesian approximation: representing model uncertainty in deep learning. In Proceedings of the 33rd International Conference on International Conference on Machine Learning 48 (ICML’16). JMLR.org, 1050–1059. 40

    work page 2016

  34. [34]

    Kendall, A., Gal, A. (2017) What uncertainties do we need in Bayesian deep learning for computer vision? In Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS’17). Curran Associates Inc., Red Hook, NY, USA, 5580–5590

    work page 2017

  35. [35]

    (2023) Uncertainty-aware remaining useful life prediction for predic- tive maintenance using deep learning, Procedia CIRP 118, 116–12

    Xuan, Q.L., Adhisantoso, Y.G., Munderloh, M., Ostermann, J. (2023) Uncertainty-aware remaining useful life prediction for predic- tive maintenance using deep learning, Procedia CIRP 118, 116–12. https://doi.org/10.1016/j.procir.2023.06.021

    work page doi:10.1016/j.procir.2023.06.021 2023

  36. [36]

    Breiman, L., Friedman, J., Olshen, R.A., Stone, C.J. (1984). Clas- sification and Regression Trees (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781315139470

    work page doi:10.1201/9781315139470 1984

  37. [37]

    Kuleshov, V., Fenner, N., Ermon, S. (2018). Accurate Uncertainties for Deep Learning Using Calibrated Regression. ArXiv, abs/1807.00263

    work page Pith review arXiv 2018

  38. [38]

    (2021) Re- maining useful life prediction of lithium-ion batteries based on Monte Carlo Dropout and gated recurrent unit, Energy Reports 7, 2862–2871

    Wei, M., Gu, H., Ye, M., Wang, Q., Xu, X., Wu, C. (2021) Re- maining useful life prediction of lithium-ion batteries based on Monte Carlo Dropout and gated recurrent unit, Energy Reports 7, 2862–2871. https://doi.org/10.1016/j.egyr.2021.05.019

    work page doi:10.1016/j.egyr.2021.05.019 2021

  39. [39]

    and Liu, O

    Attia, P.M., Bills, A., Planella, F.B., Dechent, P., Dos Reis, G., Dubarry, M., Gasper, P., Gilchrist, R., Greenbank, S., Howey, D. and Liu, O. (2022). “Knees” in lithium-ion battery aging trajectories. Journal of The Electro- chemical Society, 169(6), https://doi.org/060517.10.1149/1945-7111/ac6d13

    work page doi:10.1149/1945-7111/ac6d13 2022

  40. [40]

    et al (2024)

    Jia, X., Zhang, C., Li, Y. et al (2024). Knee-point-conscious battery aging trajectory prediction of lithium-ion based on physics-guided machine learn- ing. IEEE Transactions on Transportation Electrification, 10(1): 1056-1069. http://dx.doi.org/10.1109/TTE.2023.3266386

    work page doi:10.1109/tte.2023.3266386 2024

  41. [41]

    D. N. T. How, M. A. Hannan, M. S. Hossain Lipu and P. J. Ker, State of Charge Estimation for Lithium-Ion Batteries Using Model-Based and 41 Data-Driven Methods: A Review, in IEEE Access, vol. 7, pp. 136116-136136, 2019, https://doi.org/10.1109/ACCESS.2019.2942213

    work page doi:10.1109/access.2019.2942213 2019

  42. [42]

    Lu, Yu and Zhou, Sida and Zhou, Xinan and Yang, Shichun and Liu, Mingyan and Liu, Xinhua and Ling, Heping and Lian, Yubo. (2023). A novel method of prediction for capacity and remaining use- ful life of lithium-ion battery based on multi-time scale Weibull accel- erated failure time regression. Journal of Energy Storage, 68, 107589. https://doi.org/10.101...

    work page doi:10.1016/j.est.2023.107589 2023

  43. [43]

    (2018) Incremental Capacity Analysis on Commercial Lithium-Ion Batteries using Support Vector Regression: A Parametric Study

    Feng, X., Weng, C., He, X., Wang, L., Ren, D., Lu, L., Han, X., Ouyang, M. (2018) Incremental Capacity Analysis on Commercial Lithium-Ion Batteries using Support Vector Regression: A Parametric Study. Energies 11, 2323. https://doi.org/10.3390/en11092323

    work page doi:10.3390/en11092323 2018

  44. [44]

    Lv, Zhe and Si, Huinan and Yang, Zhe and Cui, Jiawen and He, Zhichao and Wang, Lei and Li, Zhe and Zhang, Jianbo. (2025). Simplified Mecha- nistic Aging Model for Lithium Ion Batteries in Large-Scale Applications. Materials, 18(6), 1342. https://doi.org/10.3390/ma18061342

    work page doi:10.3390/ma18061342 2025

  45. [45]

    (2025) In Situ Estimation of Li-Ion Battery State of Health Using On-Board Electrical Measurements for Electromobility Applications

    Bustos, J.E.G., Schiele, B.B., Baldo, L., Masserano, B., Jaramillo-Montoya, F., Troncoso-Kurtovic, D., Orchard, M.E., Perez, A., Silva, J.F. (2025) In Situ Estimation of Li-Ion Battery State of Health Using On-Board Electrical Measurements for Electromobility Applications. Batteries 11, 451. https://doi.org/10.3390/batteries11120451

    work page doi:10.3390/batteries11120451 2025

  46. [46]

    (2022) State-of-health estimation of Li- ion batteries in the early phases of qualification tests: An in- terpretable machine learning approach

    Lee, G., Kim, J., Lee, C. (2022) State-of-health estimation of Li- ion batteries in the early phases of qualification tests: An in- terpretable machine learning approach. Expert Syst. Appl. 197, C. https://doi.org/10.1016/j.eswa.2022.116817

    work page doi:10.1016/j.eswa.2022.116817 2022

  47. [47]

    and Liu, K

    Xu, D., Ma, S., Ji, X., Han, X., Lin, J. and Liu, K. (2025), A SHapley Additive exPlanations-Based Data-Driven Approach for Lithium-Ion Battery State of Health Estimation Using Ultrasound Technology. Energy Technol 13, 2500673. https://doi.org/10.1002/ente.202500673. 42

    work page doi:10.1002/ente.202500673 2025

  48. [48]

    https://data.nasa.gov/dataset/li-ion-battery-aging-datasets

    work page

  49. [49]

    https://calce.umd.edu/battery-data

    work page

  50. [50]

    https://iastate.figshare.com/articles/dataset/_b_ISU- ILCC_Battery_Aging_Dataset_b_/22582234

    work page

  51. [51]

    https://doi.org/10.25380/iastate.22582234

    work page doi:10.25380/iastate.22582234

  52. [52]

    https://doi.org/10.6084/m9.figshare.11888115

    work page doi:10.6084/m9.figshare.11888115

  53. [53]

    (2023) Dataset for rapid state of health estimation of lithium batteries using EIS and machine learning: Training and validation

    Rashid, M., Faraji-Niri, M., Sansom, J., Sheikh, M., Widanage, D., Marco, J. (2023) Dataset for rapid state of health estimation of lithium batteries using EIS and machine learning: Training and validation. Data Brief. 48, 109157. doi: 10.1016/j.dib.2023.109157

    work page doi:10.1016/j.dib.2023.109157 2023

  54. [54]

    (2024)Lithium-ion battery state of health and failure analysis with mixture weibull and equivalent circuit model

    Hu, W., Qian, Q. (2024)Lithium-ion battery state of health and failure analysis with mixture weibull and equivalent circuit model. iScience 27(6), 109980. https://doi.org/10.1016/j.isci.2024.109980

    work page doi:10.1016/j.isci.2024.109980 2024

  55. [55]

    Chu, Ch.-H., Lee, Ch.-J., Yeh, H.-Y. (2020) Developing Deep Survival Model for Remaining Useful Life Estimation Based on Convolutional and Long Short-Term Memory Neural Networks, Wireless Communications and Mobile Computing 8814658. https://doi.org/10.1155/2020/8814658

    work page doi:10.1155/2020/8814658 2020

  56. [56]

    Huang, Y., Zhang, P., Lu, J., Xiong, R., & Cai, Z. (2024). A transferable long-term lithium-ion battery aging trajectory prediction model considering internal resistance and capacity regeneration phenomenon. Applied Energy, 360, 122825

    work page 2024

  57. [57]

    (2022) Mechanism and properties of emerging nanos- tructured hydrogen storage materials

    Liu S, Shui J. (2022) Mechanism and properties of emerging nanos- tructured hydrogen storage materials. Battery Energy 1, 20220033. https://doi.org/10.1002/bte2.20220033. 43

    work page doi:10.1002/bte2.20220033 2022