Table 1 Comparison of deep learning and hybrid models for SoH estimation.

LSTM/BiLSTM

Sequence modeling, captures long-term dependencies, widely used in battery SoH estimation. Variants include BiLSTM and hybrid BiLSTM–KAN models

^{11,59,60,63,64,65}

GRU/BiGRU

Simplified gating structure, faster convergence compared to LSTM; used standalone or in hybrid GRU–Transformer frameworks

^59,64

Transformer

Attention-based architecture, effective in long-range dependency modeling. Applied in CNN–Transformer and BiGRU–Transformer hybrids, and cross-domain transfer learning

^{10,17,51,66,67,68}

MLP/ANN

Lightweight models, cycle-level prediction, fast convergence; includes TinyML deployment for edge devices

^{5,14,60,69,70}

TCN

Efficient parallel processing, robust gradient flow; often combined with GRU and Transformer in hybrid frameworks

^6,67

Hybrid fusion (Physics + DL)

Combines physics-based reduced-order electrochemical models with CNN/ML-based architectures; improves generalization under real-world conditions

^71,72,73,74

CNN/CNN-LSTM/CNN-GRU

Local feature extraction combined with temporal modeling; effective for SoH under varying C-rates and real-world datasets

^69,70,75,76

Ensemble/stacking

Combines multiple learners (e.g., XGBoost, RF, Kalman filter, ensemble TL); improves robustness under small or noisy datasets

^77,78,79,80

Physics-informed ML

Embeds physical constraints (electrochemical, thermal, impedance, relaxation models) into ML training for interpretability and robustness

^72,73,74,81

Advanced optimization frameworks

Incorporates evolutionary/metaheuristic optimization (WOA, ISAO, HHO, etc.) to tune deep learning models and improve SoH/RUL prediction accuracy

^81,82,83,84

Real-world data oriented models

Designed for noisy, incomplete, or real-vehicle datasets; includes vehicle-cloud collaboration, TabNet, interpretable DL, and big-data simulation

^{54,65,85,86,87,88,89}

Review/benchmark frameworks

Provide systematic comparisons, taxonomies, or real-world insights into ML-based SoH estimation

^54,55,77,90