SOH-KLSTM: A Hybrid Kolmogorov-Arnold Network and LSTM Model for Enhanced Lithium-Ion Battery Health Monitoring

Anis Koubaaa; Fatimah Alahmeda; Fatma Abdelhadic; Imen Jarraya; Maha Drissa; Mohamed Abdelkadera; Safa Ben Atitallah

REVIEW 3 major objections 6 minor 65 references

SOH-KLSTM: A Hybrid Kolmogorov-Arnold Network and LSTM Model for Enhanced Lithium-Ion Battery Health Monitoring

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that replacing the LSTM candidate cell state with a KAN-based B-spline/SiLU function reduces battery SOH prediction RMSE from 0.058334 to 0.001682 on the B0005 cell, a 97.12% drop, and generalizes across eight cells.

desk verdict Architecture is a small real variation; the empirical claims don't hold up without a persistence baseline and a same-protocol LSTM. read the letter →

arxiv 2509.10496 v1 pith:QY7TN77B submitted 2025-08-31 cs.LG

Imen Jarraya , Safa Ben Atitallah , Fatimah Alahmeda , Mohamed Abdelkadera , Maha Drissa , Fatma Abdelhadic , Anis Koubaaa This is my paper · ORCID

classification cs.LG

keywords stateofhealthlithium-ionbatteryLSTMKolmogorov-ArnoldnetworkcandidatecellB-splinebasisdegradationtime-seriesprediction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to establish that one architectural change—replacing the LSTM candidate cell state's fixed affine-tanh transform with a Kolmogorov-Arnold-style learnable nonlinear function built from B-spline basis functions and SiLU activations—makes lithium-ion battery state-of-health prediction substantially more accurate. On eight cells from a public battery aging dataset, the proposed SOH-KLSTM model reaches RMSE values between 0.0017 and 0.0071, including 0.001682 on the B0005 cell against 0.058334 for standard LSTM. That is a 97.12% error reduction, roughly 35 times more accurate, with validation execution times between 1.3 and 3.4 seconds. If the claim holds, accurate cycle-level SOH estimates become practical for battery management systems in electric vehicles, storage systems, and portable devices, where early degradation detection improves safety and extends service life.

What carries the argument

The KAN-enhanced candidate cell state is the modified LSTM memory-cell candidate in which the usual tanh of a fixed affine transform is replaced by a SiLU-activated affine term plus a B-spline basis expansion over learned per-feature splines. It carries the argument: the reported gain comes from this substitution alone, while the input, forget, and output gates and the cell-state update rule remain standard LSTM. B-splines give localized, non-smooth approximation across regions of the voltage, current, temperature, and previous-capacity inputs; SiLU keeps gradient flow smooth. The paper contrasts this placement with KAN-LSTM hybrids that apply KAN before or after the LSTM rather than inside

What would settle it

Run SOH-KLSTM under leave-one-battery-out cross-validation: train on seven of the eight cells, predict the full cycle trajectory of the held-out cell, and compare RMSE with Table 1. If held-out RMSE rises by more than a factor of two, the 97.12% improvement is an artifact of temporal interpolation within each cell's own degradation curve. A fixed-seed replication should also reproduce the B0005 RMSE of 0.001682 under identical preprocessing.

Watch

Extended reading notes

Core claim

The central discovery is a single structural substitution inside the LSTM memory cell. Standard LSTM computes the candidate cell state with an affine map followed by tanh; SOH-KLSTM computes it as SiLU of an affine transform of the previous hidden state and current input, plus a weighted sum of B-spline basis functions over learned per-feature spline transforms. The gates and the cell-state update rule are unchanged. The paper claims this localized learnable nonlinearity is what lets the model track smooth aging and abrupt changes, and reports RMSE 0.001682 on B0005 versus 0.058334 for LSTM-only, a 97.12% reduction. Across eight cells, RMSE ranges from 0.0017 to 0.0071 with validation runs o

Load-bearing premise

The load-bearing premise is that a chronological 70/20/10 split within each battery is enough to demonstrate generalization; because consecutive cycles of the same cell are strongly autocorrelated, the model may be interpolating one smooth degradation curve rather than predicting unseen batteries or operating conditions.

Editorial extensions

If this is right

Cycle-level SOH and capacity can be predicted from voltage, current, temperature, and previous capacity with RMSE below 0.008 in all eight tested cells, including 4°C low-temperature and 4 A high-current profiles.
On B0005 and B0007, the KAN candidate-cell swap cuts RMSE by 94.85% to 97.12% relative to LSTM-only, so the added nonlinearity is doing measurable work on these degradation curves.
Validation runs of 1.3 to 3.4 seconds make the model plausible for near-real-time battery management rather than offline analysis only.
The same cell-level architecture extends to remaining-useful-life prediction and pack-level SOH by fusing per-cell predictions, which the paper names as next steps.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A stronger test than the paper's per-battery 70/20/10 split would be leave-one-battery-out evaluation; because consecutive cycles of one cell are highly correlated, the reported errors may reflect interpolation within a single degradation trajectory, and cross-battery error could be much larger.
An ablation that keeps model capacity fixed—for example adding the same B-spline features to a standard tanh candidate—would isolate whether the gain comes from KAN's placement inside the cell state or simply from extra parameters.
If the mechanism generalizes, the same candidate-cell substitution should improve LSTM on other degradation time series with regime changes, such as fuel cells, supercapacitors, or structural fatigue monitoring.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the architectural idea is legitimate but incremental, and the headline accuracy claim is unproven because C_{t-1} is in the input and no persistence baseline is reported. The LSTM comparison is also apples-to-oranges.

What's new: unlike earlier KAN-LSTM hybrids that place KAN before or after the LSTM, this paper puts KAN inside the candidate cell state computation. That is a real, if modest, architectural variation. The paper also runs experiments on eight NASA batteries across three operating regimes and reports execution times, which is more than many SOH papers do. The related work section is reasonably thorough.

The problems are concentrated in the evaluation. Equation (4) includes C_{t-1}, the previous cycle's capacity, as an input; the target is SOH_t = C_t / C_nominal. On the NASA data, capacity changes by about 0.1–0.2% per cycle, so the trivial predictor C_hat_t = C_{t-1} will have an RMSE in the same ballpark as the reported 0.001682. The paper never reports this persistence baseline or an ablation without C_{t-1}. That makes the absolute RMSE uninformative. The 97.12% improvement claim is also shaky: the LSTM baseline (0.058334) is taken from Yao et al. with its own feature set, scaling, and split, not re-trained under the 70/20/10 protocol described in Section 5.2. So the gap may reflect task mismatch more than model quality.

There are smaller issues: no error bars, no cross-validation or leave-one-battery-out, no code release, and the architecture equations (Eq. 14, Algorithm 2) are hard to follow — the B-spline term looks dimensionally off and the notation is inconsistent between the main text and the algorithm. The comparison table mixes numbers from different papers with unreported protocols.

None of this means the idea is worthless. The KAN-in-the-cell-state placement is worth a look, and the paper identifies a plausible direction. But as it stands, the empirical results do not support the headline claims. A revision that adds a persistence baseline, re-trains the LSTM under identical conditions, and runs leave-one-battery-out would address the main concerns.

I'd send it to peer review — a good referee could push for those controls, and the architectural idea deserves scrutiny. I wouldn't cite the numbers, and I wouldn't bring it to a reading group unless the goal is to talk about evaluation pitfalls.

Referee Report

3 major / 6 minor

Summary. The paper proposes SOH-KLSTM, a hybrid architecture that replaces the standard linear candidate-cell-state computation in an LSTM with a KAN-based transformation using B-splines and SiLU activation. The model is evaluated on eight subsets of the NASA PCoE battery dataset (B0005, B0007, B18, B33, B34, B46, B47, B48) organized into three operating-condition groups. The reported RMSE values range from 0.001682 (B0005) to 0.007114 (B48), and the headline claim is a 97.12% error reduction relative to an LSTM baseline (RMSE 0.058334). The paper also reports execution times between 1.26 and 3.42 s and compares against several literature methods.

Significance. If the empirical claims hold, the architectural idea is of interest: integrating KAN inside the LSTM candidate-cell-state path, rather than as a pre- or post-processor, is a clean and potentially expressive modification. The breadth of validation across multiple NASA PCoE subsets and the reported computational efficiency are also relevant for battery-health monitoring applications. However, the current evidence is not sufficient to support the central claim. The absence of a persistence baseline and of a same-protocol LSTM comparison means the low RMSE values cannot yet be attributed to the KAN-LSTM architecture. The paper would benefit from stronger experimental controls, more transparent protocol reporting, and reproducible code.

major comments (3)

[§3.1, Eq. (4); §5.3, Table 1] The input vector in Eq. (4) contains C_{t-1}, the previous-cycle capacity, while the target is C_t / SOH_t. In NASA PCoE data, per-cycle capacity changes are small (on the order of 0.1–0.2%), so the trivial predictor SOH_hat_t = SOH_{t-1} can already yield RMSE values of the same order as the reported 0.001682 under min-max scaling. The manuscript reports no persistence baseline and no ablation that removes C_{t-1}. Therefore the low RMSE values and the 97.12% reduction versus LSTM cannot yet be attributed to the KAN-LSTM architecture. Please add (i) a persistence baseline on the same normalized target and split, and (ii) an ablation without C_{t-1}.
[§5.2, §5.4, Table 2] The LSTM baseline RMSE of 0.058334 is taken from Yao et al. [14], not from an LSTM trained under the protocol described in §5.2 (same features, MinMaxScaler, 70/20/10 split, same prediction task). Comparisons in Table 2 also mix RMSE/MAPE numbers from papers with different targets and units. The 97.12% error reduction is therefore not a controlled comparison. The authors should retrain the LSTM under the identical protocol and report its RMSE, and should state the units and scaling for every literature number. In addition, the 'Error Reduction' column for CNN-LSTM (65.74%) equals (0.058334−0.02)/0.058334, i.e., CNN-LSTM's improvement over the literature LSTM, not SOH-KLSTM's improvement over CNN-LSTM; the text in §5.4 says the latter. The actual reduction vs. CNN-LSTM is about 91.6%.
[§5.2, §5.3, Figure 5] All reported results come from a single 70/20/10 split per battery, with no error bars, no repeated runs, and no k-fold or leave-one-battery-out evaluation. The manuscript mentions '100 epochs per fold' in §5.2 but no folds are defined. Because adjacent cycles of the same battery are strongly autocorrelated, a random split can let the model interpolate within the same degradation trajectory; a temporal split, in turn, can be optimistic for a model that only needs to persist the previous cycle. The generalization claim in the abstract and discussion (§5.5) requires multi-seed statistics and at least one cross-battery experiment.

minor comments (6)

[§5.3] The section heading contains a typo: 'Eperimental Results' should be 'Experimental Results'.
[Figure 2] The caption refers to 'previous capacity (C_{t+1})'; this should be C_{t-1} to match Eq. (4).
[§4.2, Eq. (18), Algorithm 2] The notation is inconsistent: Eq. (18) uses m for the number of B-spline basis functions without defining it, and the indices i, k, q, p are not consistently connected to Eq. (14) and Algorithm 2. Also, Eq. (14) uses W_C while Algorithm 2 uses W_KAN; please align these.
[§5.1, §5.3.1] Section 5.1 places B33/B34 in Group B (high-power, 4 A discharge), while Section 5.3.1 states that 'B33 and B34 were tested at a low temperature of 4 °C'. This contradicts the grouping and affects the interpretation of the high-power versus low-temperature results. Please clarify the actual operating conditions.
[Table 2] The SBL RMSE values (3.5656 and 2.6153) are far outside the range of the other entries. If these are not percentages or are on a different scale, please state the units; otherwise the table is misleading. Also, the reference is cited as 'Lie et al.' but the text spells 'Li et al.'.
[General] No code or data-release link is provided. Given that the paper's claims are entirely empirical, releasing the implementation and the exact preprocessing/split code would substantially increase reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation; empirical benchmark comparison with possible confounding factors, but no step reduces to its own input.

full rationale

The paper's central claim is an empirical performance benchmark: SOH-KLSTM is trained with Eq. (4) features and tested on NASA PCoE subsets, and its RMSE is compared with literature baselines. No equation is defined in terms of the target result, and no uniqueness claim or self-citation is used to force the conclusion. The architecture (Eqs. 14-15) is a concrete modification of LSTM, and the reported RMSE is a measured outcome, not a fitted parameter. The skeptical concern that including C_{t-1} as an input makes the task nearly a persistence forecast is a benchmarking/validity issue, not circularity: the model does not by construction output C_{t-1}, and the comparison baseline is not derived from the model. Likewise, the 97.12% reduction vs. a literature-reported LSTM may reflect different protocols, but that is a comparability concern, not circularity. Self-citations (refs [2],[3],[5]) are context only and not load-bearing. No circular step can be exhibited.

Assumptions & free parameters 3 free parameters · 3 assumptions · 1 invented entities

The central claim rests on a new architectural component, several unreported hyperparameters, and a set of baseline comparisons from different papers. The paper introduces no new physical entities.

free parameters (3)

B-spline grid size and degree = not stated
The number of B-spline basis functions and their degree are hyperparameters that control the KAN approximation; the paper does not specify them.
LSTM hidden size / number of units = not stated
The hidden state size and the KAN output dimension are not reported, making the architecture description incomplete.
Baseline LSTM RMSE (0.058334) = 0.058334
The baseline LSTM was trained by the authors under an unspecified protocol; this number serves as the reference for the 97.12% improvement claim.

assumptions (3)

domain assumption The train/validation/test split on cycles is the correct protocol for evaluating SOH prediction.
The paper assumes that a 70/20/10 split across cycles is a valid evaluation, but does not address temporal leakage in the NASA cycling data.
domain assumption The Kolmogorov-Arnold theorem applies to the LSTM candidate cell state in a way that improves gradient flow and nonlinear approximation.
The paper invokes the theorem as motivation for KAN, but this is a modeling assumption about how the architecture behaves on discrete time-series data; it is not formally established here.
domain assumption RMSE values reported in different papers are comparable even when the splits, normalization, and input features differ.
The comparison table mixes results from papers with different experimental protocols, a common but fragile assumption in SOH benchmark comparisons.

invented entities (1)

KAN-enhanced candidate cell state (C_tilde_KAN)
purpose: Replaces the standard tanh-based candidate cell state in LSTM with a KAN-style nonlinear transformation using B-splines and SiLU, to better capture nonlinear battery degradation.
This is a model component introduced in the paper. It has no independent falsifiable handle outside the reported RMSE on the NASA dataset.

how reviews work

0 comments

Cite this review

Pith. "Pith review of SOH-KLSTM: A Hybrid Kolmogorov-Arnold Network and LSTM Model for Enhanced Lithium-Ion Battery Health Monitoring." pith.science (2026). https://pith.science/paper/QY7TN77B

@misc{pith2026250910496,
  author       = {Pith},
  title        = {Pith review of: SOH-KLSTM: A Hybrid Kolmogorov-Arnold Network and LSTM Model for Enhanced Lithium-Ion Battery Health Monitoring},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QY7TN77B}},
  note         = {Machine review of arXiv:2509.10496}
}

read the original abstract

Accurate and reliable State Of Health (SOH) estimation for Lithium (Li) batteries is critical to ensure the longevity, safety, and optimal performance of applications like electric vehicles, unmanned aerial vehicles, consumer electronics, and renewable energy storage systems. Conventional SOH estimation techniques fail to represent the non-linear and temporal aspects of battery degradation effectively. In this study, we propose a novel SOH prediction framework (SOH-KLSTM) using Kolmogorov-Arnold Network (KAN)-Integrated Candidate Cell State in LSTM for Li batteries Health Monitoring. This hybrid approach combines the ability of LSTM to learn long-term dependencies for accurate time series predictions with KAN's non-linear approximation capabilities to effectively capture complex degradation behaviors in Lithium batteries.

Figures

Figures reproduced from arXiv: 2509.10496 by the authors.

**Figure 1.** Below is a brief overview of these methods. • Model-based approaches, such as electrochemical models and Kalman filters, are more computationally efficient and suitable for real-time use, but are highly dependent on detailed knowledge of the internal states of the battery, which may not always be readily accessible [11]. Methods based on the Kalman filter have been used, such as the adaptive unscented Kalman filter … view at source ↗

**Figure 2.** SOH estimation process for a lithium-ion battery. This diagram illustrates the key indicators used in SOH estimation, including voltage (𝑉𝑡 ), current (𝐼𝑡 ), temperature (𝑇𝑡 ), and previous capacity (𝐶𝑡+1). These indicators influence battery degradation and overall capacity (𝐶𝑡 ), which is monitored to assess SOH. : Preprint submitted to Elsevier Page 7 of 22 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** The hierarchical structure of the two-layer KAN approach, where input features (𝑋1 , 𝑋2 ) are transformed using B-spline functions (𝜑), summed, and processed through learnable activation functions (Φ1 , Φ2 ). The B-spline activation function inset illustrates the basis expansion process, demonstrating how localized feature representations are combined to enhance predictive performance. 4. SOH-KLSTM: Proposed KAN-Int… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The proposed SOH-KLSTM model for SOH and capacity estimation. The architecture of the SOH-KLSTM model consists of three main stages: (1) Data Preprocessing, where NASA battery datasets are split into training, validation, and testing sets; (2) Model Learning, where the…

**Figure 5.** Figure 5: Comparison of actual and predicted SOH for different lithium-ion battery datasets: (a) B05, (b) B07, (c) B18, (d) B33, (e) B34, (f) B46, (g) B47, and (h) B48. The plots show the actual SOH (red points) and the predicted SOH (blue points) over battery cycle counts. : Pr…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 62 canonical work pages

[14]

A novel graph-based framework for state of health prediction of lithium-ion battery

Xing-Yan Yao, Guolin Chen, Michael Pecht, and Bin Chen. A novel graph-based framework for state of health prediction of lithium-ion battery. Journal of Energy Storage, 58:106437, 2023

work page 2023
[1]

Progress in battery thermal management systems technologies for electric vehicles.Renewable and Sustainable Energy Reviews , 202:114654, 2024

Ayat Gharehghani, Moeed Rabiei, Sadegh Mehranfar, Soheil Saeedipour, Amin Mahmoudzadeh Andwari, Antonio García, and Carlos Mico Reche. Progress in battery thermal management systems technologies for electric vehicles.Renewable and Sustainable Energy Reviews , 202:114654, 2024

work page 2024
[2]

Anonlinestateofchargeestimationforlithium-ionand supercapacitor in hybrid electric drive vehicle.Journal of Energy Storage, 26:100946, 2019

ImenJarraya,FerdaousMasmoudi,MohamedHediChabchoub,andHafedhTrabelsi. Anonlinestateofchargeestimationforlithium-ionand supercapacitor in hybrid electric drive vehicle.Journal of Energy Storage, 26:100946, 2019

work page 2019
[3]

Optimizing electric vehicles efficiency with hybrid energy storage: Comparative analysis of rule-based and neural network power management systems

Fatma Abdelhedi, Imen Jarraya, Haneen Bawayan, Mohamed Abdelkeder, Nassim Rizoug, and Anis Koubaa. Optimizing electric vehicles efficiency with hybrid energy storage: Comparative analysis of rule-based and neural network power management systems. Energy, 313:133979, 2024

work page 2024
[4]

Lithiuminventorytrackingasanon-destructive battery evaluation and monitoring method.Nature Energy, 9(5):612–621, 2024

MengLi,YulunZhang,HuiZhou,FengxiaXin,MStanleyWhittingham,andBoryannLiaw. Lithiuminventorytrackingasanon-destructive battery evaluation and monitoring method.Nature Energy, 9(5):612–621, 2024

work page 2024
[5]

Comparisonstudybetweenhybridnelder-mead particleswarmoptimizationandopencircuitvoltage—recursiveleastsquareforthebatteryparametersestimation

ImenJarrraya,LaidDegaa,NassimRizoug,MohamedHediChabchoub,andHafedhTrabelsi. Comparisonstudybetweenhybridnelder-mead particleswarmoptimizationandopencircuitvoltage—recursiveleastsquareforthebatteryparametersestimation. Journal of Energy Storage, 50:104424, 2022

work page 2022
[6]

Gandoman, Joris Jaguemont, Shovon Goutam, Rahul Gopalakrishnan, Yousef Firouz, Theodoros Kalogiannis, Noshin Omar, and Joeri Van Mierlo

Foad H. Gandoman, Joris Jaguemont, Shovon Goutam, Rahul Gopalakrishnan, Yousef Firouz, Theodoros Kalogiannis, Noshin Omar, and Joeri Van Mierlo. Concept of reliability and safety assessment of lithium-ion batteries in electric vehicles: Basics, progress, and challenges. Applied Energy, 251:113343, 2019

work page 2019
[7]

Areviewofthestateofhealthforlithium-ionbatteries:Researchstatusandsuggestions

HuixinTian,PengliangQin,KunLi,andZhenZhao. Areviewofthestateofhealthforlithium-ionbatteries:Researchstatusandsuggestions. Journal of Cleaner Production, 261:120813, 2020

work page 2020

Show all 65 references

[8]

Towards machine-learning driven prognostics and health management of li-ion batteries

Sahar Khaleghi, Md Sazzad Hosen, Joeri Van Mierlo, and Maitane Berecibar. Towards machine-learning driven prognostics and health management of li-ion batteries. a comprehensive review.Renewable and Sustainable Energy Reviews, 192:114224, 2024

2024
[9]

Seol et al

S. Seol et al. Improving soh estimation for lithium-ion batteries using timegan.Journal of Power Sources, 490:229693, 2023

2023
[10]

Batterysohestimationmethodbased on gradual decreasing current, double correlation analysis and gru.Green Energy and Intelligent Transportation, 2(5):100108, 2023

ChaolongZhang,LaijinLuo,ZhongYang,ShaishaiZhao,YigangHe,XiaoWang,andHongxiaWang. Batterysohestimationmethodbased on gradual decreasing current, double correlation analysis and gru.Green Energy and Intelligent Transportation, 2(5):100108, 2023. : Preprint submitted to Elsevier ...

2023
[11]

Zheng and X

L. Zheng and X. Guo. Comparative study on incremental capacity analysis with machine learning algorithms for state of health estimation of lithium-ion batteries. IEEE Transactions on Power Delivery, 2023

2023
[12]

A method for state of charge and state of health estimation of lithium-ion battery based on adaptive unscented kalman filter.Energy Reports, 8:426–436, 2022

Shulin Liu, Xia Dong, Xiaodong Yu, Xiaoqing Ren, Jinfeng Zhang, and Rui Zhu. A method for state of charge and state of health estimation of lithium-ion battery based on adaptive unscented kalman filter.Energy Reports, 8:426–436, 2022. The 2022 International Conference on Energ...

2022
[13]

Nuroldayeva et al

G. Nuroldayeva et al. State of health estimation methods for lithium-ion batteries.International Journal of Energy Research, 2023

2023
[15]

Liang et al

Y. Liang et al. State of health prediction of lithium-ion batteries using combined machine learning model based on nonlinear constraint optimization. Journal of The Electrochemical Society, 2024

2024
[16]

A data-driven approach with uncertainty quantification forpredictingfuturecapacitiesandremainingusefullifeoflithium-ionbattery

Kailong Liu, Yunlong Shang, Quan Ouyang, and Widanalage Dhammika Widanage. A data-driven approach with uncertainty quantification forpredictingfuturecapacitiesandremainingusefullifeoflithium-ionbattery. IEEE Transactions on Industrial Electronics,68(4):3170–3180, 2020

2020
[17]

A review of battery state of health estimation methods: Hybrid electric vehicle challenges

Nassim Noura, Loïc Boulon, and Samir Jemeï. A review of battery state of health estimation methods: Hybrid electric vehicle challenges. World Electric Vehicle Journal, 11(4):66, 2020

2020
[18]

State of health estimation for lithium-ion battery based on particle swarm optimization algorithm and extreme learning machine

Kui Chen, Jiali Li, Kai Liu, Changshan Bai, Jiamin Zhu, Guoqiang Gao, Guangning Wu, and Salah Laghrouche. State of health estimation for lithium-ion battery based on particle swarm optimization algorithm and extreme learning machine. Green Energy and Intelligent Transportation...

2024
[19]

State-of-health estimation for lithium-ion batteries based on kullback–leibler divergence and a retentive network.Applied Energy, 376:124266, 2024

Guanxu Chen, Fangfang Yang, Weiwen Peng, Yuqian Fan, and Ximin Lyu. State-of-health estimation for lithium-ion batteries based on kullback–leibler divergence and a retentive network.Applied Energy, 376:124266, 2024

2024
[20]

A novel method for state of health estimation of lithium-ion batteries based on improved lstm and health indicators extraction.Energy, 251:123973, 2022

Yan Ma, Ce Shan, Jinwu Gao, and Hong Chen. A novel method for state of health estimation of lithium-ion batteries based on improved lstm and health indicators extraction.Energy, 251:123973, 2022

2022
[21]

Data-drivenpredictionofbatterycyclelifebeforecapacitydegradation

Kristen A Severson, Peter M Attia, Norman Jin, Nicholas Perkins, Benben Jiang, Zi Yang, Michael H Chen, Muratahan Aykol, Patrick K Herring,DimitriosFraggedakis,etal. Data-drivenpredictionofbatterycyclelifebeforecapacitydegradation. Nature Energy,4(5):383–391, 2019

2019
[22]

Analyzingelectricvehiclebatteryhealthperformanceusingsupervisedmachinelearning

KaushikDas,RoushanKumar,andAnurupKrishna. Analyzingelectricvehiclebatteryhealthperformanceusingsupervisedmachinelearning. Renewable and Sustainable Energy Reviews, 189:113967, 2024

2024
[23]

Lithium-ionbatterydigitalization:Combiningphysics-basedmodels and machine learning.Renewable and Sustainable Energy Reviews, 200:114577, 2024

MahshidNAmiri,AnneHåkansson,OdneSBurheim,andJacobJLamb. Lithium-ionbatterydigitalization:Combiningphysics-basedmodels and machine learning.Renewable and Sustainable Energy Reviews, 200:114577, 2024

2024
[24]

Anoveldeeplearningframeworkforstateofhealthestimationoflithium-ion battery

YaxiangFan,FeiXiao,ChaoranLi,GuorunYang,andXinTang. Anoveldeeplearningframeworkforstateofhealthestimationoflithium-ion battery. Journal of Energy Storage, 32:101741, 2020

2020
[25]

Prognostics and health management of lithium-ion battery using deep learning methods: A review.Renewable and sustainable energy reviews, 161:112282, 2022

Ying Zhang and Yan-Fu Li. Prognostics and health management of lithium-ion battery using deep learning methods: A review.Renewable and sustainable energy reviews, 161:112282, 2022

2022
[26]

Early prediction of remaining useful life for lithium-ion batteries based on ceemdan-transformer-dnn hybrid model.Heliyon, 9(7), 2023

Yuxiang Cai, Weimin Li, Taimoor Zahid, Chunhua Zheng, Qingguang Zhang, and Kun Xu. Early prediction of remaining useful life for lithium-ion batteries based on ceemdan-transformer-dnn hybrid model.Heliyon, 9(7), 2023

2023
[27]

Deeplearningtoestimatelithium-ionbatterystateofhealthwithout additional degradation experiments.Nature Communications, 14(1):2760, 2023

JiahuanLu,RuiXiong,JinpengTian,ChenxuWang,andFengchunSun. Deeplearningtoestimatelithium-ionbatterystateofhealthwithout additional degradation experiments.Nature Communications, 14(1):2760, 2023

2023
[28]

Hybrid deep neural network with dimension attention for state-of-health estimation of lithium-ion batteries.Energy, 278:127734, 2023

Xinyuan Bao, Liping Chen, António M Lopes, Xin Li, Siqiang Xie, Penghua Li, and YangQuan Chen. Hybrid deep neural network with dimension attention for state-of-health estimation of lithium-ion batteries.Energy, 278:127734, 2023

2023
[29]

Stateofhealthpredictionforli-ion batteries with end-to-end deep learning.Journal of Energy Storage, 65:107218, 2023

ChunxiangZhu,MingyuGao,ZhiweiHe,HengWu,ChangchengSun,ZhaoweiZhang,andZhengyiBao. Stateofhealthpredictionforli-ion batteries with end-to-end deep learning.Journal of Energy Storage, 65:107218, 2023

2023
[30]

State of health estimation of lithium-ion batteries using support vector regression and long short-term memory.Open Journal of Applied Sciences, 12(8):1366–1382, 2022

Inioluwa Obisakin and Chikodinaka Vanessa Ekeanyanwu. State of health estimation of lithium-ion batteries using support vector regression and long short-term memory.Open Journal of Applied Sciences, 12(8):1366–1382, 2022

2022
[31]

Guerrero

Junjie Tao, Shunli Wang, Wen Cao, Yixiu Cui, Carlos Fernandez, and Josep M. Guerrero. Innovative multiscale fusion - antinoise extended longshort-termmemoryneuralnetworkmodelingforhighprecisionstateofhealthestimationoflithium-ionbatteries. Energy,page133541, 2024

2024
[32]

Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis.Nature Communications, 15(1):4332, 2024

Fujin Wang, Zhi Zhai, Zhibin Zhao, Yi Di, and Xuefeng Chen. Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis.Nature Communications, 15(1):4332, 2024

2024
[33]

Boostingbatterystateofhealthestimationbasedonself-supervisedlearning

YunhongChe,YushengZheng,XinSui,andRemusTeodorescu. Boostingbatterystateofhealthestimationbasedonself-supervisedlearning. Journal of Energy Chemistry, 84:335–346, 2023

2023
[34]

Expert Systems with Applications, 238:122041, 2024

YupengWeiandDazhongWu.Stateofhealthandremainingusefullifepredictionoflithium-ionbatterieswithconditionalgraphconvolutional network. Expert Systems with Applications, 238:122041, 2024

2024
[35]

Bioinspired spiking spatiotemporal attention framework for lithium-ion batteries state-of-health estimation

Huan Wang, Yan-Fu Li, and Ying Zhang. Bioinspired spiking spatiotemporal attention framework for lithium-ion batteries state-of-health estimation. Renewable and Sustainable Energy Reviews, 188:113728, 2023

2023
[36]

Stateofhealthestimationforlithium-ionbatteries based on hybrid attention and deep learning.Reliability Engineering & System Safety, 232:109066, 2023

HongqianZhao,ZhengChen,XingShu,JiangweiShen,ZhenzhenLei,andYuanjianZhang. Stateofhealthestimationforlithium-ionbatteries based on hybrid attention and deep learning.Reliability Engineering & System Safety, 232:109066, 2023

2023
[37]

State-of-health estimation of lithium-ion batteries: A comprehensive literature review from cell to pack levels.Energy Conversion and Economics, 2024

Lingzhi Su, Yan Xu, and Zhaoyang Dong. State-of-health estimation of lithium-ion batteries: A comprehensive literature review from cell to pack levels.Energy Conversion and Economics, 2024

2024
[38]

An overview of artificial intelligence driven li-ion battery state estimation.IoT Enabled-DC Microgrids: Architecture, Algorithms, Applications, and Technologies, page 121, 2024

Mohammed Hindawi and Saeed Mian QaisarªYasir Basheer. An overview of artificial intelligence driven li-ion battery state estimation.IoT Enabled-DC Microgrids: Architecture, Algorithms, Applications, and Technologies, page 121, 2024

2024
[39]

Reviewonmodelingandsoc/sohestimationofbatteriesforautomotiveapplications

PierpaoloDini,AntonioColicelli,andSergioSaponara. Reviewonmodelingandsoc/sohestimationofbatteriesforautomotiveapplications. Batteries, 10(1):34, 2024. : Preprint submitted to Elsevier Page 21 of 22 SOH-KLSTM Model for Enhanced Lithium-Ion Battery Health Monitoring

2024
[40]

Technologies for energy storage power stations safety operation: Battery state evaluation survey and a critical analysis.IEEE Access, 12:31334–31356, 2024

Xiangyang Xia, Jiahui Yue, Yuan Guo, Chonggeng Lv, Xiaoyong Zeng, Yongkai Xia, and Guiquan Chen. Technologies for energy storage power stations safety operation: Battery state evaluation survey and a critical analysis.IEEE Access, 12:31334–31356, 2024

2024
[41]

A comprehensive survey on kolmogorov arnold networks (kan)

Yuntian Hou, Jinheng Wu, Xiaohang Feng, et al. A comprehensive survey on kolmogorov arnold networks (kan). arXiv preprint arXiv:2407.11075, 2024

2024 arXiv
[42]

Advanced state-of-health estimation for lithium-ion batteries using multi-feature fusion and kan-lstm hybrid model.Batteries, 10(12):433, 2024

Zhao Zhang, Runrun Zhang, Xin Liu, Chaolong Zhang, Gengzhi Sun, Yujie Zhou, Zhong Yang, Xuming Liu, Shi Chen, Xinyu Dong, et al. Advanced state-of-health estimation for lithium-ion batteries using multi-feature fusion and kan-lstm hybrid model.Batteries, 10(12):433, 2024

2024
[43]

Stateofhealthestimationofli-ionbattery via incremental capacity analysis and internal resistance identification based on kolmogorov–arnold networks.Batteries, 10(9), 2024

JunPeng,XuanZhao,JianMa,DeanMeng,ShuhaiJia,KaiZhang,ChenyanGu,andWenhaoDing. Stateofhealthestimationofli-ionbattery via incremental capacity analysis and internal resistance identification based on kolmogorov–arnold networks.Batteries, 10(9), 2024

2024
[44]

A parallel weighted adtc-transformer framework with funet fusion and kan for improved lithium-ion battery soh prediction.Control Engineering Practice, 159:106302, 2025

Chuang Chen, Yuheng Wu, Jiantao Shi, Dongdong Yue, Ge Shi, and Dongzhen Lyu. A parallel weighted adtc-transformer framework with funet fusion and kan for improved lithium-ion battery soh prediction.Control Engineering Practice, 159:106302, 2025

2025
[45]

Lithium-ion battery soh estimation method based on multi-feature and cnn-bilstm-mha

Yujie Zhou, Chaolong Zhang, Xulong Zhang, and Ziheng Zhou. Lithium-ion battery soh estimation method based on multi-feature and cnn-bilstm-mha. World Electric Vehicle Journal, 15(7):280, 2024

2024
[46]

Online fusion estimation method for state of charge and state of health in lithium battery storage systems.AIP Advances, 13(4), 2023

Han Liu, Xinyu Cao, Fengdao Zhou, and Gang Li. Online fusion estimation method for state of charge and state of health in lithium battery storage systems.AIP Advances, 13(4), 2023

2023
[47]

Hao Zhang, Hanlei Sun, Le Kang, Yi Zhang, Licheng Wang, and Kai Wang. Prediction of health level of multiform lithium sulfur batteries based on incremental capacity analysis and an improved lstm.Protection and Control of Modern Power Systems, 9(2):21–31, 2024

2024
[48]

A novel hybrid neural network-based soh and rul estimation method for lithium-ion batteries

Baoliang Chen, Yonggui Liu, and Bin Xiao. A novel hybrid neural network-based soh and rul estimation method for lithium-ion batteries. Journal of Energy Storage, 98:113074, 2024

2024
[49]

Yiwen Sun, Hengwei Xie, Qi Diao, Hongzhang Xu, Xiaojun Tan, Yuqian Fan, and Liangliang Wei. A novel soh estimation method with attentional feature fusion considering differential temperature features for lithium-ion batteries.IEEE Transactions on Instrumentation and Measurement, 2024

2024
[50]

Animprovedcnn-lstmmodel-basedstate-of-healthestimation approach for lithium-ion batteries.Energy, 276:127585, 2023

HuanweiXu,LingfengWu,ShizheXiong,WeiLi,AkhilGarg,andLiangGao. Animprovedcnn-lstmmodel-basedstate-of-healthestimation approach for lithium-ion batteries.Energy, 276:127585, 2023

2023
[51]

A data-driven battery soh estimation method with cnn-lstm model and ssa optimizing

Shumin Chen, Jiali Yu, Lingxin Cui, Mengting Chen, and Min Xiao. A data-driven battery soh estimation method with cnn-lstm model and ssa optimizing. In2024 36th Chinese Control and Decision Conference (CCDC) , pages 3381–3385. IEEE, 2024

2024
[52]

Huzaifa Rauf, Muhammad Khalid, and Naveed Arshad. Machine learning in state of health and remaining useful life estimation: Theoretical and technological development in battery degradation modelling.Renewable and Sustainable Energy Reviews, 156:111903, 2022

2022
[53]

Energy Reports, 9:2993–3021, 2023

ZhongRenandChangqingDu.Areviewofmachinelearningstate-of-chargeandstate-of-healthestimationalgorithmsforlithium-ionbatteries. Energy Reports, 9:2993–3021, 2023

2023
[54]

Kan: Kolmogorov-arnold networks.arXiv preprint arXiv:2404.19756, 2024

Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y Hou, and Max Tegmark. Kan: Kolmogorov-arnold networks.arXiv preprint arXiv:2404.19756, 2024

2024 arXiv
[55]

Sigmoid-weighted linear units for neural network function approximation in reinforcement learning

Stefan Elfwing, Eiji Uchibe, and Kenji Doya. Sigmoid-weighted linear units for neural network function approximation in reinforcement learning. Neural networks, 107:3–11, 2018

2018
[56]

Cvkan: Complex-valued kolmogorov-arnold networks.arXiv preprint arXiv:2502.02417, 2025

Matthias Wolff, Florian Eilers, and Xiaoyi Jiang. Cvkan: Complex-valued kolmogorov-arnold networks.arXiv preprint arXiv:2502.02417, 2025

2025
[57]

Kolmogorov–arnold recurrent network for short term load forecasting across diverse consumers

Muhammad Umair Danish and Katarina Grolinger. Kolmogorov–arnold recurrent network for short term load forecasting across diverse consumers. Energy Reports, 13:713–727, 2025

2025
[58]

Physics-informed kolmogorov-arnold networks for power system dynamics.IEEE Open Access Journal of Power and Energy, 2025

Hang Shuai and Fangxing Li. Physics-informed kolmogorov-arnold networks for power system dynamics.IEEE Open Access Journal of Power and Energy, 2025

2025
[59]

State-of-health prediction for lithium-ion batteries with multiple gaussian process regression model

Xueying Zheng and Xiaogang Deng. State-of-health prediction for lithium-ion batteries with multiple gaussian process regression model. IEEE Access, 7:150383–150394, 2019

2019
[60]

An optimal clustering algorithm for second use of retired ev batteries using dbscan and pca schemes considering performance deviation

Jeyeong Lim, Eui-Seong Han, Dong Hwan Kim, and Byoung Kuk Lee. An optimal clustering algorithm for second use of retired ev batteries using dbscan and pca schemes considering performance deviation. In2023 IEEE Applied Power Electronics Conference and Exposition (APEC), pages 5...

2023
[61]

A contribution-aware federated framework for electric vehicle batteries health estimation

Bingyang Chen, Lulu Fan, Xingjie Zeng, Mu Gu, and Jiehan Zhou. A contribution-aware federated framework for electric vehicle batteries health estimation. IEEE Internet of Things Journal, 2024

2024
[62]

State of health estimation approach for li-ion batteries based on mechanism feature empowerment.Journal of Energy Storage, 84:110965, 2024

Lei Yao, Jishu Wen, Yanqiu Xiao, Caiping Zhang, Yongpeng Shen, Guangzhen Cui, and Dandan Xiao. State of health estimation approach for li-ion batteries based on mechanism feature empowerment.Journal of Energy Storage, 84:110965, 2024

2024
[63]

Lithium-ion battery state of health estimation based on multi-source health indicators extraction and sparse bayesian learning.Energy, 282:128445, 2023

Xiaoyu Li, Mohan Lyu, Kuo Li, Xiao Gao, Caixia Liu, and Zhaosheng Zhang. Lithium-ion battery state of health estimation based on multi-source health indicators extraction and sparse bayesian learning.Energy, 282:128445, 2023

2023
[64]

A cmmog-based lithium-battery soh estimation method using multi-task learning framework.Journal of Energy Storage, 107:114884, 2025

Chaolong Zhang, Liang Tu, Zhong Yang, Bolun Du, Ziheng Zhou, Ji Wu, and Liping Chen. A cmmog-based lithium-battery soh estimation method using multi-task learning framework.Journal of Energy Storage, 107:114884, 2025

2025
[65]

Dgl-stfa:Predictinglithium-ionbatteryhealthwithdynamicgraphlearningandspatial–temporalfusionattention

ZhengChenandQuanQian. Dgl-stfa:Predictinglithium-ionbatteryhealthwithdynamicgraphlearningandspatial–temporalfusionattention. Energy and AI, 19:100462, 2025. : Preprint submitted to Elsevier Page 22 of 22

2025

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [14]

A novel graph-based framework for state of health prediction of lithium-ion battery

Xing-Yan Yao, Guolin Chen, Michael Pecht, and Bin Chen. A novel graph-based framework for state of health prediction of lithium-ion battery. Journal of Energy Storage, 58:106437, 2023

work page 2023

[2] [1]

Progress in battery thermal management systems technologies for electric vehicles.Renewable and Sustainable Energy Reviews , 202:114654, 2024

Ayat Gharehghani, Moeed Rabiei, Sadegh Mehranfar, Soheil Saeedipour, Amin Mahmoudzadeh Andwari, Antonio García, and Carlos Mico Reche. Progress in battery thermal management systems technologies for electric vehicles.Renewable and Sustainable Energy Reviews , 202:114654, 2024

work page 2024

[3] [2]

Anonlinestateofchargeestimationforlithium-ionand supercapacitor in hybrid electric drive vehicle.Journal of Energy Storage, 26:100946, 2019

ImenJarraya,FerdaousMasmoudi,MohamedHediChabchoub,andHafedhTrabelsi. Anonlinestateofchargeestimationforlithium-ionand supercapacitor in hybrid electric drive vehicle.Journal of Energy Storage, 26:100946, 2019

work page 2019

[4] [3]

Optimizing electric vehicles efficiency with hybrid energy storage: Comparative analysis of rule-based and neural network power management systems

Fatma Abdelhedi, Imen Jarraya, Haneen Bawayan, Mohamed Abdelkeder, Nassim Rizoug, and Anis Koubaa. Optimizing electric vehicles efficiency with hybrid energy storage: Comparative analysis of rule-based and neural network power management systems. Energy, 313:133979, 2024

work page 2024

[5] [4]

Lithiuminventorytrackingasanon-destructive battery evaluation and monitoring method.Nature Energy, 9(5):612–621, 2024

MengLi,YulunZhang,HuiZhou,FengxiaXin,MStanleyWhittingham,andBoryannLiaw. Lithiuminventorytrackingasanon-destructive battery evaluation and monitoring method.Nature Energy, 9(5):612–621, 2024

work page 2024

[6] [5]

Comparisonstudybetweenhybridnelder-mead particleswarmoptimizationandopencircuitvoltage—recursiveleastsquareforthebatteryparametersestimation

ImenJarrraya,LaidDegaa,NassimRizoug,MohamedHediChabchoub,andHafedhTrabelsi. Comparisonstudybetweenhybridnelder-mead particleswarmoptimizationandopencircuitvoltage—recursiveleastsquareforthebatteryparametersestimation. Journal of Energy Storage, 50:104424, 2022

work page 2022

[7] [6]

Gandoman, Joris Jaguemont, Shovon Goutam, Rahul Gopalakrishnan, Yousef Firouz, Theodoros Kalogiannis, Noshin Omar, and Joeri Van Mierlo

Foad H. Gandoman, Joris Jaguemont, Shovon Goutam, Rahul Gopalakrishnan, Yousef Firouz, Theodoros Kalogiannis, Noshin Omar, and Joeri Van Mierlo. Concept of reliability and safety assessment of lithium-ion batteries in electric vehicles: Basics, progress, and challenges. Applied Energy, 251:113343, 2019

work page 2019

[8] [7]

Areviewofthestateofhealthforlithium-ionbatteries:Researchstatusandsuggestions

HuixinTian,PengliangQin,KunLi,andZhenZhao. Areviewofthestateofhealthforlithium-ionbatteries:Researchstatusandsuggestions. Journal of Cleaner Production, 261:120813, 2020

work page 2020