Abstract
Battery monitoring requires high accuracy and robustness throughout the entire lifespan to ensure safe and optimal operations. Here we introduce mechanistic leading residual learners to enhance the monitoring of battery charge and health states, as well as guide safety warnings, targeting large-scale applications. Leveraging prior knowledge from real-time filtering as primary guidance, complemented by mechanistic and statistical features, our approach significantly improves accuracy and robustness. We propose and validate two general residual learning pipelines, namely the correction model and compensation model, across various scenarios, encompassing different battery types, loading profiles, aging conditions, and environmental conditions, using three aging datasets under …
Abstract
Battery monitoring requires high accuracy and robustness throughout the entire lifespan to ensure safe and optimal operations. Here we introduce mechanistic leading residual learners to enhance the monitoring of battery charge and health states, as well as guide safety warnings, targeting large-scale applications. Leveraging prior knowledge from real-time filtering as primary guidance, complemented by mechanistic and statistical features, our approach significantly improves accuracy and robustness. We propose and validate two general residual learning pipelines, namely the correction model and compensation model, across various scenarios, encompassing different battery types, loading profiles, aging conditions, and environmental conditions, using three aging datasets under dynamic cycling. Our method achieves a relative root mean square error reduction of over 50% from the results observed in prior estimations. The extrapolation capability under unseen conditions, along with interpretability, enhances both accuracy and trustworthiness. The models remain effective even with reduced training data and sampling frequency, maintaining the potential for practical electric vehicle applications. Application demonstrations confirm the efficacy in providing continuous monitoring across lifespan without the need for offline testing and model calibration during operation.
Data availability
Source data for the figures in the main text, including the reproduction code, are provided with this paper in the Source Data file. All data including cycling data and OCV data from the pouch and prismatic cells are (https://doi.org/10.5281/zenodo.15606246) for results generation. The cylindrical cell dataset is available from Stanford University at (https://purl.stanford.edu/td676xr4322). Source data are provided with this paper.
Code availability
Code for the main text figures reproduction is provided together with the Source Data file. All codes for modeling and results generation are available at https://doi.org/10.5281/zenodo.1560624648.
References
Pozzato, G. et al. Analysis and key findings from real-world electric vehicle field data. Joule 7, 2035–2053 (2023).
Zhang, H., Hu, X., Hu, Z. & Moura, S. J. Sustainable plug-in electric vehicle integration into power systems. Nat. Rev. Electr. Eng. 1, 35–52 (2024).
Wang, Y. et al. A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems. Renew. Sustain. Energy Rev. 131, 110015 (2020).
Jones, P., Stimming, U. & Lee, A. A. Impedance-based forecasting of battery performance amid uneven usage. Nat. Commun. 13, 4806 (2022).
Ng, M. F., Zhao, J., Yan, Q., Conduit, G. J. & Seh, Z. W. Predicting the state of charge and health of batteries using data-driven machine learning. Nat. Mach. Intell. 2, 161–170 (2020).
Sulzer, V. et al. The challenge and opportunity of battery lifetime prediction from field data. Joule 5, 1934–1955 (2021).
Mc Carthy, K., Gullapalli, H., Ryan, K. M. & Kennedy, T. Review—Use of Impedance Spectroscopy for the Estimation of Li-ion Battery State of Charge, State of Health and Internal Temperature. J. Electrochem Soc. 168, 080517 (2021).
Zhao, P. et al. Challenges and opportunities in truck electrification revealed by big operational data. Nat. Energy 9, 1427–1437 (2024).
Rahimi-Eichi, H., Ojha, U., Baronti, F. & Chow, M. Y. Battery management system: An overview of its application in the smart grid and electric vehicles. IEEE Ind. Electron. Mag. 7, 4–16 (2013).
Palacín, M. R. & De Guibert, A. Batteries: Why do batteries fail? Science (1979) 351, 1253292 (2016).
Che, Y., Hu, X., Lin, X., Guo, J. & Teodorescu, R. Health prognostics for lithium-ion batteries: mechanisms, methods, and prospects. Energy Environ. Sci. 16, 338–371 (2023).
Thelen, A. et al. Integrating physics-based modeling and machine learning for degradation diagnostics of lithium-ion batteries. Energy Storage Mater. 50, 668–695 (2022).
Nascimento, R. G., Corbetta, M., Kulkarni, C. S. & Viana, F. A. C. Hybrid physics-informed neural networks for lithium-ion battery modeling and prognosis. J. Power Sources 513, 230526 (2021).
Hu, X., Xu, L., Lin, X. & Pecht, M. Battery lifetime prognostics. Joule 4, 310–346 (2020).
Aykol, M. et al. Perspective—combining physics and machine learning to predict battery lifetime. J. Electrochem Soc. 168, 030525 (2021).
Li, Y., Ye, M., Wang, Q., Lian, G. & Xia, B. An improved model combining machine learning and Kalman filtering architecture for state of charge estimation of lithium-ion batteries. Green. Energy Intell. Transp. 3, 100163 (2024).
Yu, H., Lu, H., Zhang, Z. & Yang, L. A generic fusion framework integrating deep learning and Kalman filter for state of charge estimation of lithium-ion batteries: analysis and comparison. J. Power Sources 623, 235493 (2024).
Tian, J., Xiong, R., Lu, J., Chen, C. & Shen, W. Battery state-of-charge estimation amid dynamic usage with physics-informed deep learning. Energy Storage Mater. 50, 718–729 (2022).
Qi, W., Qin, W. & Yun, Z. Closed-loop state of charge estimation of Li-ion batteries based on deep learning and robust adaptive Kalman filter. Energy 307, 132805 (2024).
Tian, Y., Lai, R., Li, X., Xiang, L. & Tian, J. A combined method for state-of-charge estimation for lithium-ion batteries using a long short-term memory network and an adaptive cubature Kalman filter. Appl Energy 265, 114789 (2020).
Tu, H., Moura, S., Wang, Y. & Fang, H. Integrating physics-based modeling with machine learning for lithium-ion batteries. Appl Energy 329, 120289 (2023).
Pozzato, G., Li, X., Lee, D., Ko, J. & Onori, S. Accelerating the transition to cobalt-free batteries: a hybrid model for LiFePO4/graphite chemistry. NPJ Comput Mater. 10, 14 (2024).
Surya, S., Samanta, A., Marcis, V. & Williamson, S. Hybrid electrical circuit model and deep learning-based core temperature estimation of lithium-ion battery cell. IEEE Trans. Transp. Electr. 8, 3816–3824 (2022).
Zheng, Y., Che, Y., Hu, X., Sui, X. & Teodorescu, R. Sensorless temperature monitoring of lithium-ion batteries by integrating physics with machine learning. IEEE Trans. Transp. Electr. 10, 2643–2652 (2023).
Liu, X., Li, K., Wu, J., He, Y. & Liu, X. An extended Kalman filter based data-driven method for state of charge estimation of Li-ion batteries. J. Energy Storage 40, 102655 (2021).
Singh, S., Ebongue, Y. E., Rezaei, S. & Birke, K. P. Hybrid modeling of lithium-ion battery: physics-informed neural network for battery state estimation. Batteries 9, 301 (2023).
Wang, F., Zhai, Z., Zhao, Z., Di, Y. & Chen, X. Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis. Nat. Commun. 15, 4332 (2024).
Zhu, J. et al. Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation. Nat. Commun. 13, 1–10 (2022).
Severson, K. A. et al. Data-driven prediction of battery cycle life before capacity degradation. Nat. Energy 4, 383–391 (2019).
Geslin, A. et al. Selecting the appropriate features in battery lifetime predictions. Joule 7, 1956–1965 (2023).
Li, T., Zhou, Z., Thelen, A., Howey, D. A. & Hu, C. Predicting battery lifetime under varying usage conditions from early aging data. Cell Rep. Phys. Sci. 5, 101891 (2024).
Li, M. et al. Lithium inventory tracking as a non-destructive battery evaluation and monitoring method. Nat. Energy 9, 612–621 (2024).
Lu, J. et al. Deep learning to estimate battery state of health without additional degradation experiments. Nat. Commun. 14, 2760 (2023).
Che, Y., Zheng, Y., Onori, S. & Hu, X. Increasing generalization capability of battery health estimation using continual learning. Cell Rep. Phys. Sci. 4, 101743 (2023).
Kim, S. et al. Accelerated battery life predictions through synergistic combination of physics-based models and machine learning. Cell Rep. Phys. Sci. 3, 101023 (2022).
Kim, M., Kim, I., Kim, J. & Choi, J. W. Lifetime prediction of lithium ion batteries by using the heterogeneity of graphite anodes. ACS Energy Lett. 8, 2946–2953 (2023).
Murdoch, W. J., Singh, C., Kumbier, K., Abbasi-Asl, R. & Yu, B. Definitions, methods, and applications in interpretable machine learning. Proc. Natl. Acad. Sci. USA 116, 22071–22080 (2019).
Rudin, C. et al. Interpretable machine learning: Fundamental principles and 10 grand challenges. Stat. Survevs 16, 1–85 (2022).
Gilpin, L. H. et al. Explaining Explanations: An Overview Of Interpretability Of Machine Learning. Proceedings - 2018 IEEE 5th International Conference on Data Science and Advanced Analytics (DSAA), 80–89 (2018). 1.
Galuppini, G. et al. Improving diagnostics and prognostics of implantable cardioverter defibrillator batteries with interpretable machine learning models. J. Power Sources 610, 234668 (2024).
Geslin, A. et al. Dynamic cycling enhances battery lifetime. Nat. Energy 10, 172–180 (2025).
Nielsen, R. L. et al. Data-driven identification of predictive risk biomarkers for subgroups of osteoarthritis using interpretable machine learning. Nat. Commun. 15, 2817 (2024).
Yang, J., Tao, L., He, J., McCutcheon, J. R. & Li, Y. Machine learning enables interpretable discovery of innovative polymers for gas separation membranes. Sci. Adv. 8, 9545 (2022).
Linardatos, P., Papastefanopoulos, V. & Kotsiantis, S. Explainable AI: a review of machine learning interpretability methods. Entropy 23, 18 (2021).
Samek, W., Montavon, G., Lapuschkin, S., Anders, C. J. & Müller, K. R. Explaining deep neural networks and beyond: A review of methods and applications. Proc. IEEE 109, 247–278 (2021).
Lundberg, S. M., Allen, P. G. & Lee, S.-I. A unified approach to interpreting model predictions. NIPS’17: Proc. 31st Int. Conf. Adv. Neural Inf. Process. Syst. 30, 4768–4777 (2017).
Sun, W. & Braatz, R. D. Smart process analytics for predictive modeling. Comput Chem. Eng. 144, 107134 (2021).
Che, Y. et al. Mechanistic leading residual learning for battery state monitoring entire full life. Zenodo https://doi.org/10.5281/zenodo.15606246 (2025).
Acknowledgements
This work is funded by the Novo Nordisk Foundation (Y. Che and R.D. Braatz), Independent Research Foundation Denmark (Y. Che), and Villum Foundation (R. Teodorescu, Y. Che, and Y. Zheng). We would like to thank Wenxue Liu for the OCV test of the pouch cell and paper review.
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Authors and Affiliations
Department of Chemical Engineering, Massachusetts Institute of Technology, Massachusetts, MA, USA
Yunhong Che, Jinwook Rhyu, Shimin Wang & Richard D. Braatz 1.
Department of Energy, Aalborg University, Aalborg, Denmark
Yunhong Che, Yusheng Zheng, Jia Guo & Remus Teodorescu 1.
Department of Mechanical Engineering, Imperial College London, London, UK
Jia Guo
Authors
- Yunhong Che
- Yusheng Zheng
- Jinwook Rhyu
- Jia Guo
- Shimin Wang
- Remus Teodorescu
- Richard D. Braatz
Contributions
Y.C. Conceptualization, Methodology, Software, Investigation, Writing-Original Draft, Visualization, Funding Acquisition. Y.Z. Methodology, Investigation, Writing-Original Draft, Visualization. J.R. Validation, Writing - Review & Editing. J.G. Writing - Review & Editing. S.W. Writing - Review & Editing. R.T. Supervision, Funding Acquisition, Writing - Review & Editing. R.D.B. Conceptualization, Supervision, Funding Acquisition, Writing - Review & Editing.
Corresponding author
Correspondence to Richard D. Braatz.
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Che, Y., Zheng, Y., Rhyu, J. et al. Mechanistically guided residual learning for battery state monitoring throughout life. Nat Commun (2026). https://doi.org/10.1038/s41467-025-67565-z
Received: 23 December 2024
Accepted: 03 December 2025
Published: 15 January 2026
DOI: https://doi.org/10.1038/s41467-025-67565-z