Physics-Informed DeepONet With Ensemble Pretraining and Dynamic Loss Weighting for Lithium-Ion Battery State-of-Health Estimation

Abstract

Accurate state-of-health (SOH) estimation is critical for the safe operation and predictive maintenance of lithium-ion batteries. Existing data-driven methods lack physical interpretability, while physics-informed neural networks (PINNs) often suffer from gradient conflicts and training instability. This article proposes a physics-informed deep operator network (PI-DeepONet) framework that integrates operator learning with degradation physics for robust SOH estimation. The architecture decouples sensor features and temporal coordinates through a Branch–Trunk structure and incorporates a neural ODE-based physics discovery module to learn latent degradation dynamics. A monotonicity constraint is enforced to prevent physically inconsistent capacity regeneration. To address optimization challenges, a two-stage training strategy is designed: ensemble-based data-driven initialization followed by physics-regularized fine-tuning with dynamic loss weighting. The proposed method is evaluated on three publicly available battery aging datasets (XJTU, TJU, and MIT) covering diverse chemistries, temperatures, and cycling protocols. Experimental results demonstrate that PI-DeepONet achieves state-of-the-art prediction accuracy, with up to 29.8% root-mean-squared error (RMSE) reduction compared to the best data-driven baseline and 40.6% compared to the standard PINN. Ablation studies confirm the contribution of each component, and convergence analysis validates the effectiveness of the dynamic weighting strategy in mitigating gradient conflicts.