DeepONet-Based Learning of Time-Varying Observer Gains for Lithium-Ion Battery State-of-Charge Estimation

This paper develops a Deep Operator Network (DeepONet) approach to accelerate observer-gain computation for thermal single-particle battery state-of-charge (SOC) estimation. The offline network maps complete sampled diffusion trajectories to a continuous-time, boundary-constrained backstepping kernel; observer gains follow by differentiating the same kernel. Lipschitz continuity is established on a uniformly analytic input class. A perturbed Volterra transformation proves exponential observer and SOC error decay under uniform residual bounds and a positive decay margin.After all six models had completed training and their weights had been fixed, we evaluated the three independently trained full-feature models and their corresponding feature-ablation models on a newly generated common test set of 72 trajectories. Complete-feature models attain mean gain relative RMSE of 0.3936%, versus 0.6070% after masking. Across 500 public-parameter inversion and perturbation tests, paired SOC RMSE remains below 0.000229 percentage points. After training, DeepONet computes 10,100 gains per trajectory in 2.70–3.11 ms on CPU (0.54–0.63 ms on GPU), versus 4.93–5.18 s for the CPU implementation of the six-term numerical solver, giving approximately 7871–9645-fold speedups. The results demonstrate accurate offline gain replacement and reduced gain-generation cost relative to the specified numerical implementation.