Trustworthy Machine Learning and Mathematical Modelling for Lithium-Ion Battery State-of-Health Estimation

Accurate estimation of lithium-ion battery state of health (SOH) is essential for reliable battery management, although SOH cannot be measured directly during normal operation. This review considers machine-learning methods for SOH estimation from a mathematical and trustworthiness-oriented perspective. The literature is organised by learning the formulation, including supervised regression, sequence learning, multi-task prediction, and weakly physics-guided methods. Attention is given to data representation, evaluation methods, uncertainty estimation, calibration, robustness under distribution shifts, and physical validity of predictions. The reviewed studies indicate that the feature-based models remain effective in small-data settings, whereas deep sequence models show stronger performance when more informative temporal data and stricter evaluation settings are available. Reported results are strongly affected by split design, preprocessing, and differences between training and test conditions, and may be overstated under same-cell evaluation, leakage, or limited cross-condition testing. The reviewed evidence indicates that reliable SOH estimation requires suitable cross-cell or cross-condition evaluation, uncertainty estimates supported by calibration analysis, robustness under operating variation, clear reporting, and agreement with physical battery behaviour. On this basis, benchmark design principles, reporting recommendations, method-selection guidance, and open research problems are presented.