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arxiv: 2603.09103 · v1 · submitted 2026-03-10 · 💻 cs.LG · eess.SP

Recognition: 1 theorem link

· Lean Theorem

Probabilistic Hysteresis Factor Prediction for Electric Vehicle Batteries with Graphite Anodes Containing Silicon

Runyao Yu , Viviana Kleine , Philipp Gromotka , Thomas Rudolf , Adrian Eisenmann , Gautham Ram Chandra Mouli , Peter Palensky , Jochen L. Cremer
Authors on Pith no claims yet

Pith reviewed 2026-05-15 13:54 UTC · model grok-4.3

classification 💻 cs.LG eess.SP
keywords hysteresis factorsilicon-graphite anodesprobabilistic predictionelectric vehicle batteriesstate-of-charge estimationdata harmonizationmachine learninggeneralizability
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The pith

A data-driven probabilistic model predicts hysteresis factors in silicon-graphite EV batteries with uncertainty estimates.

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

This paper develops a machine learning method to predict the hysteresis factor in batteries using silicon-graphite anodes, which is key for accurate state-of-charge estimation in electric vehicles. It proposes a data harmonization framework to standardize varied driving cycles and applies statistical and deep learning models to deliver predictions that include uncertainty while remaining computationally efficient. The work then tests how well the best model setup transfers to entirely new vehicle models through retraining, zero-shot prediction, fine-tuning, and joint training. If the approach holds, it would cut the need for lengthy high-fidelity lab tests when introducing these higher-energy-density batteries into production vehicles.

Core claim

The central claim is that statistical learning and deep learning models, after data harmonization of heterogeneous driving cycles, can predict the hysteresis factor probabilistically for silicon-graphite anode batteries, with the optimal configuration showing good generalizability to unseen vehicle models via retraining, zero-shot prediction, fine-tuning, or joint training.

What carries the argument

A data harmonization framework that standardizes heterogeneous driving cycles across operating conditions, combined with statistical and deep learning models that output probabilistic hysteresis factor predictions while tracking computational cost.

Load-bearing premise

That a data harmonization framework can standardize heterogeneous driving cycles across varying operating conditions without losing critical information needed for accurate hysteresis prediction in silicon-graphite batteries.

What would settle it

A controlled test in which harmonized data from one set of driving cycles and vehicles produces large errors or overconfident uncertainty bounds when applied to a distinctly different unseen cycle or vehicle model.

Figures

Figures reproduced from arXiv: 2603.09103 by Adrian Eisenmann, Gautham Ram Chandra Mouli, Jochen L. Cremer, Peter Palensky, Philipp Gromotka, Runyao Yu, Thomas Rudolf, Viviana Kleine.

Figure 1
Figure 1. Figure 1: Illustration of OCV-SoC curves. a The OCV-SoC relationship provided by the cell manufacturer. b The OCV-SoC relationship with voltage hysteresis, which is particularly significant for silicon–graphite anode-based batteries. consumer acceptance. In addition to estimation accuracy, BMS is often memory- and computation-constrained in highly com￾petitive cost structures as in the automotive industry, requiring… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of harmonization framework and exemplary driving cycles of two vehicle models. ˜˜ [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example illustration of segmentation. A valid segment starts at the 4th [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: a Filtering Statistical feature extraction Filtering Resampling to Steps b [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of model performance and computational efficiency for different modeling strategies on sequence-level and subsequence-level prediction [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Batteries with silicon-graphite-based anodes, which offer higher energy density and improved charging performance, introduce pronounced voltage hysteresis, making state-of-charge (SoC) estimation particularly challenging. Existing approaches to modeling hysteresis rely on exhaustive high-fidelity tests or focus on conventional graphite-based lithium-ion batteries, without considering uncertainty quantification or computational constraints. This work introduces a data-driven approach for probabilistic hysteresis factor prediction, with a particular emphasis on applications involving silicon-graphite anode-based batteries. A data harmonization framework is proposed to standardize heterogeneous driving cycles across varying operating conditions. Statistical learning and deep learning models are applied to assess performance in predicting the hysteresis factor with uncertainties while considering computational efficiency. Extensive experiments are conducted to evaluate the generalizability of the optimal model configuration in unseen vehicle models through retraining, zero-shot prediction, fine-tuning, and joint training. By addressing key challenges in SoC estimation, this research facilitates the adoption of advanced battery technologies. A summary page is available at: https://runyao-yu.github.io/Porsche_Hysteresis_Factor_Prediction/

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

2 major / 2 minor

Summary. The manuscript introduces a data-driven probabilistic framework for predicting the hysteresis factor in EV batteries using silicon-graphite anodes. It proposes a data harmonization step to standardize heterogeneous driving cycles from varying operating conditions, applies statistical learning and deep learning models to generate predictions with uncertainty quantification while considering computational efficiency, and evaluates the optimal model's generalizability on unseen vehicle models via retraining, zero-shot prediction, fine-tuning, and joint training regimes.

Significance. If validated with quantitative results, the work could meaningfully improve SoC estimation accuracy for high-energy-density batteries by providing efficient probabilistic hysteresis predictions that account for uncertainty, directly supporting adoption of silicon-graphite anode technologies. The multi-regime generalizability evaluation and emphasis on computational constraints represent practical strengths for real-world EV battery management systems.

major comments (2)
  1. [Data harmonization framework] Data harmonization framework (described in the methods and experiments sections): the central claim that this step standardizes driving cycles while preserving information for accurate hysteresis prediction is load-bearing, yet the description provides no explicit validation that path-dependent voltage hysteresis loops specific to silicon-graphite anodes (varying with C-rate, temperature, and SoC trajectory) are retained after resampling, normalization, or alignment. If these features are smoothed or averaged, the downstream statistical and DL models would be trained on degraded targets, directly undermining the reported generalizability results under zero-shot and joint-training regimes.
  2. [Abstract and results] Abstract and results sections: no quantitative error metrics, uncertainty calibration scores, or baseline comparisons are reported, making it impossible to evaluate whether the probabilistic predictions support the claimed accuracy and generalizability. This absence is particularly problematic given the emphasis on uncertainty quantification as a core contribution.
minor comments (2)
  1. [Conclusion] The summary page link is a positive addition for accessibility, but the manuscript should include a brief reproducibility statement detailing data availability and code release.
  2. [Methods] Notation for the hysteresis factor and uncertainty bounds should be defined consistently in the first use within the methods section to improve clarity for readers unfamiliar with battery modeling conventions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and indicate the planned revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Data harmonization framework] Data harmonization framework (described in the methods and experiments sections): the central claim that this step standardizes driving cycles while preserving information for accurate hysteresis prediction is load-bearing, yet the description provides no explicit validation that path-dependent voltage hysteresis loops specific to silicon-graphite anodes (varying with C-rate, temperature, and SoC trajectory) are retained after resampling, normalization, or alignment. If these features are smoothed or averaged, the downstream statistical and DL models would be trained on degraded targets, directly undermining the reported generalizability results under zero-shot and joint-training regimes.

    Authors: We agree that explicit validation is required to confirm that path-dependent hysteresis features are preserved. The manuscript describes the harmonization steps (resampling, normalization, and alignment) but does not include direct pre/post comparisons of hysteresis loop characteristics. In the revision we will add a dedicated validation subsection with quantitative metrics (hysteresis loop area retention, voltage trajectory correlation coefficients stratified by C-rate and temperature) and supporting figures. These additions will be placed in the Methods section and will directly support the generalizability claims under the zero-shot and joint-training regimes. revision: yes

  2. Referee: [Abstract and results] Abstract and results sections: no quantitative error metrics, uncertainty calibration scores, or baseline comparisons are reported, making it impossible to evaluate whether the probabilistic predictions support the claimed accuracy and generalizability. This absence is particularly problematic given the emphasis on uncertainty quantification as a core contribution.

    Authors: We acknowledge the absence of explicit numerical results in the abstract and the need for clearer quantitative reporting in the results section. While the manuscript describes the experimental setup and generalizability regimes, specific error metrics, calibration scores, and baseline comparisons are not presented. In the revised version we will (i) update the abstract to report key quantitative outcomes (prediction error and calibration metrics) and (ii) expand the results section with tables containing MAE/RMSE, expected calibration error, and comparisons against statistical and deep-learning baselines. These changes will enable direct evaluation of the claimed accuracy and uncertainty quantification. revision: yes

Circularity Check

0 steps flagged

No circularity in data-driven modeling framework

full rationale

The paper describes an empirical data-driven pipeline: a harmonization step standardizes driving cycles, followed by statistical and deep learning models trained to predict a hysteresis factor with uncertainty estimates. Generalizability is assessed via standard ML protocols (retraining, zero-shot, fine-tuning, joint training) on unseen vehicle data. No equations, derivations, or self-referential definitions appear in the abstract or description that would reduce any claimed prediction to a fitted parameter or prior result by construction. No self-citation chains or uniqueness theorems are invoked as load-bearing steps. The work is self-contained as an applied modeling study whose claims rest on empirical performance metrics rather than tautological reductions.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit parameters, axioms, or invented entities; the approach implicitly assumes standard machine-learning data representativeness and that hysteresis can be treated as a learnable statistical quantity without physical first-principles modeling.

free parameters (1)
  • model hyperparameters
    Deep learning and statistical models require numerous tunable parameters fitted to training data.

pith-pipeline@v0.9.0 · 5518 in / 1110 out tokens · 38350 ms · 2026-05-15T13:54:16.544744+00:00 · methodology

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Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages · 2 internal anchors

  1. [1]

    A data-driven energy estimation based on the mixture of experts method for battery electric vehicles.,

    P. Petersen, T. Rudolf, and E. Sax, “A data-driven energy estimation based on the mixture of experts method for battery electric vehicles.,” inVEHITS, 2022, pp. 384–390

    work page 2022

  2. [2]

    A fully automated methodol- ogy for the selection and extraction of energy-relevant features for the energy consumption of battery electric vehicles,

    P. Petersen and E. Sax, “A fully automated methodol- ogy for the selection and extraction of energy-relevant features for the energy consumption of battery electric vehicles,”SN Computer Science, vol. 3, no. 5, p. 342, 2022

    work page 2022

  3. [3]

    EY Mobility Consumer Index 2022 study,

    M. Samant, A. Khatri, G. Batra, and A. Goel, “EY Mobility Consumer Index 2022 study,” EY, Tech. Rep., 2022. IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION 10

    work page 2022

  4. [4]

    Graphite as anode materials: Fundamental mechanism, recent progress and advances,

    H. Zhang, Y . Yang, D. Ren, L. Wang, and X. He, “Graphite as anode materials: Fundamental mechanism, recent progress and advances,”Energy Storage Materi- als, vol. 36, pp. 147–170, 2021

    work page 2021

  5. [5]

    Automotive Li-Ion Batteries: Cur- rent Status and Future Perspectives,

    Y .-L. Ding et al., “Automotive Li-Ion Batteries: Cur- rent Status and Future Perspectives,”Electrochemical Energy Reviews, vol. 2, no. 1, pp. 1–28, 2019.DOI: 10.1007/s41918-018-0022-z

    work page doi:10.1007/s41918-018-0022-z 2019

  6. [6]

    Global EV Out- look 2023: Catching up with climate ambitions,

    International Energy Agency (IEA), “Global EV Out- look 2023: Catching up with climate ambitions,” Tech. Rep., 2023

    work page 2023

  7. [7]

    Evers,Why Porsche, Mercedes and GM are betting on silicon-anode batteries, 2022

    A. Evers,Why Porsche, Mercedes and GM are betting on silicon-anode batteries, 2022

    work page 2022

  8. [8]

    G. L. Plett, “Extended kalman filtering for battery man- agement systems of lipb-based hev battery packs: Part

    work page

  9. [9]

    state and parameter estimation,”Journal of Power sources, vol. 134, no. 2, pp. 277–292, 2004

    work page 2004

  10. [10]

    A study of the open circuit voltage characterization technique and hysteresis assessment of lithium-ion cells,

    A. Barai, W. D. Widanage, J. Marco, A. McGordon, and P. Jennings, “A study of the open circuit voltage characterization technique and hysteresis assessment of lithium-ion cells,”Journal of Power Sources, vol. 295, pp. 99–107, 2015

    work page 2015

  11. [11]

    Full battery pack modelling: An electrical sub-model using an eecm for hev applications,

    R. Rolt, R. Douglas, P. Nockemann, and R. Best, “Full battery pack modelling: An electrical sub-model using an eecm for hev applications,” SAE Technical Paper, Tech. Rep., 2019

    work page 2019

  12. [12]

    Y . Xie, S. Wang, G. Zhang, Y . Fan, C. Fernandez, and J. M. Guerrero, “Improved lumped electrical charac- teristic modeling and adaptive forgetting factor recur- sive least squares-linearized particle swarm optimiza- tion full-parameter identification strategy for lithium-ion batteries considering the hysteresis component effect,” Journal of Energy Stora...

    work page 2023

  13. [13]

    State-of-charge estimation of lithium-ion battery based on an improved dual-polarization model,

    S. Xie, X. Zhang, W. Bai, A. Guo, W. Li, and R. Wang, “State-of-charge estimation of lithium-ion battery based on an improved dual-polarization model,”Energy Tech- nology, vol. 11, no. 4, p. 2 201 364, 2023

    work page 2023

  14. [14]

    Estimating the state-of-charge of lithium-ion batteries using an H- infinity observer with consideration of the hysteresis characteristic,

    J. Xie, J. Ma, Y . Sun, and Z. Li, “Estimating the state-of-charge of lithium-ion batteries using an H- infinity observer with consideration of the hysteresis characteristic,”Journal of Power Electronics, vol. 16, no. 2, pp. 643–653, Mar. 2016.DOI: 10 . 6113 / JPE . 2016.16.2.643

    work page 2016

  15. [15]

    Parameter Identification and SOC Estimation of a Bat- tery under the Hysteresis Effect,

    M. Kwak, B. Lkhagvasuren, J. Park, and J. H. You, “Parameter Identification and SOC Estimation of a Bat- tery under the Hysteresis Effect,”IEEE Transactions on Industrial Electronics, vol. 67, no. 11, pp. 9758–9767, Nov. 2020.DOI: 10.1109/TIE.2019.2956394

    work page doi:10.1109/tie.2019.2956394 2020

  16. [16]

    A new soc estimation for lfp batteries: Application in a 10 ah cell (hw 38120 l/s) as a hysteresis case study,

    Y . Ko and W. Choi, “A new soc estimation for lfp batteries: Application in a 10 ah cell (hw 38120 l/s) as a hysteresis case study,”Electronics (Switzerland), vol. 10, no. 6, pp. 1–14, Mar. 2021.DOI: 10 . 3390 / electronics10060705

    work page 2021

  17. [17]

    Experimental analysis of open-circuit voltage hysteresis in lithium-iron-phosphate batteries,

    F. Baronti, W. Zamboni, N. Femia, R. Roncella, and R. Saletti, “Experimental analysis of open-circuit voltage hysteresis in lithium-iron-phosphate batteries,” IECON Proceedings (Industrial Electronics Confer- ence), pp. 6728–6733, 2013.DOI: 10 . 1109 / IECON . 2013.6700246

    work page arXiv 2013

  18. [18]

    Online state of charge estimation and open circuit voltage hysteresis modeling of LiFePO4 battery using invariant imbedding method,

    G. Dong, J. Wei, C. Zhang, and Z. Chen, “Online state of charge estimation and open circuit voltage hysteresis modeling of LiFePO4 battery using invariant imbedding method,”Applied Energy, vol. 162, pp. 163–171, Jan. 2016.DOI: 10.1016/j.apenergy.2015.10.092

    work page doi:10.1016/j.apenergy.2015.10.092 2016

  19. [19]

    A comparative per- formance analysis of electrical equivalent circuit models with the hysteresis effect of lithium iron phosphate batteries,

    A. J. Antony and K. Selvajyothi, “A comparative per- formance analysis of electrical equivalent circuit models with the hysteresis effect of lithium iron phosphate batteries,”International Journal of Green Energy, 2023. DOI: 10.1080/15435075.2023.2258216

    work page doi:10.1080/15435075.2023.2258216 2023

  20. [20]

    OCV Hysteresis Effect-based SOC Estimation in Extended Kalman Filter Algorithm for a LiFePO 4 /C Cell,

    J. Kim, G.-S. Seo, C. Chun, B.-H. Cho, S. Lee, and R. Center, “OCV Hysteresis Effect-based SOC Estimation in Extended Kalman Filter Algorithm for a LiFePO 4 /C Cell,” in2012 IEEE International Electric Vehicle Conference, IEVC 2012, 2012, pp. 1–5.DOI: 10.1109/ IEVC.2012.6183174

    work page arXiv 2012

  21. [21]

    Dynamic electric behavior and open-circuit-voltage modeling of LiFePO 4-based lithium ion secondary batteries,

    M. A. Roscher and D. U. Sauer, “Dynamic electric behavior and open-circuit-voltage modeling of LiFePO 4-based lithium ion secondary batteries,”Journal of Power Sources, vol. 196, no. 1, pp. 331–336, Jan. 2011. DOI: 10.1016/j.jpowsour.2010.06.098

    work page doi:10.1016/j.jpowsour.2010.06.098 2011

  22. [22]

    SOC Esti- mation Based on Hysteresis Characteristics of Lithium Iron Phosphate Battery,

    W. Zhou, X. Ma, H. Wang, and Y . Zheng, “SOC Esti- mation Based on Hysteresis Characteristics of Lithium Iron Phosphate Battery,”Machines, vol. 10, no. 8, Aug. 2022.DOI: 10.3390/machines10080658

    work page doi:10.3390/machines10080658 2022

  23. [23]

    Study of hysteresis voltage state dependence in lithium-ion battery and a novel asymmetric hysteresis modeling,

    P. Yu, S. Wang, C. Yu, W. Shi, and B. Li, “Study of hysteresis voltage state dependence in lithium-ion battery and a novel asymmetric hysteresis modeling,” Journal of Energy Storage, vol. 51, Jul. 2022.DOI: 10. 1016/j.est.2022.104492

    work page arXiv 2022

  24. [24]

    Determination of half-cell open-circuit potential curve of silicon-graphite in a physics-based model for lithium- ion batteries,

    Y . Gao, Z. Sun, D. Zhang, D. Shi, and X. Zhang, “Determination of half-cell open-circuit potential curve of silicon-graphite in a physics-based model for lithium- ion batteries,”Applied Energy, vol. 349, Nov. 2023. DOI: 10.1016/j.apenergy.2023.121621

    work page doi:10.1016/j.apenergy.2023.121621 2023

  25. [25]

    Improving the state of charge estimation of reused lithium-ion batteries by abating hysteresis using ma- chine learning technique,

    Z. Xu, J. Wang, Q. Fan, P. D. Lund, and J. Hong, “Improving the state of charge estimation of reused lithium-ion batteries by abating hysteresis using ma- chine learning technique,”Journal of Energy Storage, vol. 32, Dec. 2020.DOI: 10.1016/j.est.2020.101678

    work page doi:10.1016/j.est.2020.101678 2020

  26. [26]

    Exploring the Hysteresis Effect in SOC Estimation of Li-ion Batteries,

    W. Li, S. Ruan, A. Bahitbek, Z. Gao, N. Turak, and H. Li, “Exploring the Hysteresis Effect in SOC Estimation of Li-ion Batteries,” inJournal of Physics: Conference Series, vol. 2456, Institute of Physics, 2023.DOI: 10. 1088/1742-6596/2456/1/012023

    work page 2023

  27. [27]

    Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs - Part 2. Modeling and identification,

    G. L. Plett, “Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs - Part 2. Modeling and identification,”Journal of Power Sources, vol. 134, no. 2, pp. 262–276, Aug. 2004.DOI: 10.1016/j.jpowsour.2004.02.032

    work page doi:10.1016/j.jpowsour.2004.02.032 2004

  28. [28]

    Open-Circuit V oltage Measurement of Lithium-Iron-Phosphate Batteries,

    F. Baronti, W. Zamboni, R. Roncella, R. Saletti, and G. Spagnuolo, “Open-Circuit V oltage Measurement of Lithium-Iron-Phosphate Batteries,”Conference Record - IEEE Instrumentation and Measurement Technology Conference, vol. 2015-July, pp. 1711–1716, 2015. IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION 11

    work page 2015

  29. [29]

    Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

    S. Ioffe and C. Szegedy, “Batch Normalization: Accel- erating Deep Network Training by Reducing Internal Covariate Shift,”ArXiv, vol. abs/1502.03167, Feb. 2015. DOI: https://doi.org/10.48550/arXiv.1502.03167

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1502.03167 2015

  30. [30]

    The potential of data-driven engineer- ing models: An analysis across domains in the automo- tive development process,

    J. Kn ¨odler et al., “The potential of data-driven engineer- ing models: An analysis across domains in the automo- tive development process,” SAE Technical Paper, Tech. Rep., 2023

    work page 2023

  31. [31]

    Regression quantiles,

    R. Koenker and G. Bassett Jr, “Regression quantiles,” Econometrica: journal of the Econometric Society, pp. 33–50, 1978

    work page 1978

  32. [32]

    Xgboost: A scalable tree boosting system,

    T. Chen and C. Guestrin, “Xgboost: A scalable tree boosting system,” inProceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining, 2016, pp. 785–794

    work page 2016

  33. [33]

    Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling

    J. Chung, C. Gulcehre, K. Cho, and Y . Bengio, “Em- pirical evaluation of gated recurrent neural networks on sequence modeling,”arXiv preprint arXiv:1412.3555, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  34. [34]

    Koenker,Quantile regression

    R. Koenker,Quantile regression. Cambridge university press, 2005, vol. 38

    work page 2005