NOCE-Net: Representation Learning for Battery Operational Context via Nested Sequence Modelling

The gist: NOCE-Net is a deep nested sequence model that learns control-enabling representations directly from raw cyclic operational or telemetric data to predict arbitrarily long voltage responses, achieving 13.7% MAPE in zero-shot evaluation and showing transferable degradation dynamics through its learned hidden states.

Data Pipeline and Representation Learning

The paper introduces re-BatteryData to standardize heterogeneous aging datasets into semantically equivalent Full Equivalent Cycles (FECs) defined by absolute charge throughput, which enables end-to-end learning across diverse operational regimes. This standardization enforces four preprocessing steps: uniform feature dimension, adaptive temporal resampling, battery task features (η), and full equivalent cycle-based segmentation. The re-BatteryData defines a full equivalent battery cycle (FEC) as the period during which the battery undergoes an accumulated charge throughput, Qacc = R Idt, of twice its nominal capacity. This results in a bi-level sequence representation comprising an outer sequence over full-length FECs and an inner sequence containing the variable-length intra-cycle time series of operational inputs.

NOCE-Net Architecture

NOCE-Net is a taskconditioned deep learning framework for control-enabling representation learning from nested battery operational context. It combines multi-patch transformer encoders for intra-cycle dynamics with a GRU backbone for inter-cycle state evolution. The Patch Encoder uses multi-kernel convolutional layers to extract multi-resolution features from intra-cycle inputs, followed by a stacked Transformer encoder. The Gated Recurrent Network backbone models inter-cycle dynamics using aggregated intra-cycle embeddings as input. The Patch Decoder reconstructs variable-length intra-cycle voltage responses from the attended patch embeddings and the inter-cycle state.

Performance and Transferability

NOCE-Net achieves 13.7% MAPE in zero-shot evaluation on unseen battery chemistries and usage patterns, outperforming strong long-sequence baselines by over 43% while using 40× fewer parameters. The recurrent hidden states learned from voltage supervision encode battery degradation structure without capacity labels, and the principal component of the hidden state trajectory achieves Spearman ρ ≥ 0.95 with the capacity fade trajectory on average across all datasets with monotone degradation profiles. These findings suggest that the representations encode degradation dynamics transferable to downstream tasks beyond battery response modelling.

SOH Estimation via PID-R Features

The recurrent hidden states encode battery degradation structure without capacity supervision, transferring to SOH estimation with near-affine residual error and strong gains from light per-dataset calibration. The PID-R feature vector is constructed by concatenating four components: Proportional (Pc), Derivative (Dc), Integral (Ic), and Relative (Rc) hidden state summaries. These features provide a compact, fixed-dimensional summary of the battery’s degradation trajectory that is computed entirely from the frozen NOCE-Net hidden states without any additional model training. The shape decomposition analysis confirms that the latent representations encode capacity fade shape without any capacity supervision, with the dominant error being affine.

Limitations and Future Work

A limitation is that voltage supervision encodes degradation direction but not absolute scale, requiring per-dataset calibration. Furthermore, evTOL-style partial-discharge profiles produce non-monotone capacity trajectories for which scalar SOH is ill-defined. The sequential GRU backbone is also a computational bottleneck relative to fully parallel architectures. Future extensions include developing solutions addressing these challenges and probing NOCE-Net as a surrogate for data-driven battery optimisation in vehicular and grid applications.

Experimental Baselines

NOCE-Net is compared against TimerXL, AutoTimes, MAMBA, and TinyTimeMixers (TTM), evaluating three modes: M1 (nested context with binary controls), M2 (flat context), and Indep. (per cycle). The comparison highlights the value of preserving the nested structure, as NOCE-Net outperforms baselines in the aggregate setting by 42.5% over MAMBA + Method 2. The Transformer-based models like AutoTimes and TimerXL generalize poorly to irregular sequences, while MAMBA and TTM configurations with multi-patch embeddings handle variable-length inputs best among baselines. The M2 mode sees a single unbroken flattened sequence of length L1 + L2 + L3 and discards the nested boundary information entirely.

SOH Prediction Head Calibration

The per-dataset MLP head is trained on a fraction of in-domain batteries using the frozen PID-R features as input to correct residual affine error. For instance, Stanford-EV achieves 5–9% MAPE across training fractions of 10–50% of training batteries. The HUST dataset plateaus at 31–33% regardless of training fraction, indicating the remaining error reflects genuine battery-to-battery capacity variability within the HUST dataset. The model’s failure is not structural but affine, as shape correlations r ≥ 0.80 on all non-evTOL datasets indicate the trajectory shape is correctly learned from the frozen recurrent state trajectory alone. The scale ratio σSOH/σSOHˆ reveals two qualitatively distinct failure modes, with under-prediction of fade amplitude occurring in partial-cycling datasets like ISU ILCC.

Conclusion

This work introduced NOCE-Net, a control-enabling, non-invasive framework for long-horizon battery voltage forecasting that couples intra-cycle operational inputs with inter-cycle latent dynamics to capture degradation-driven changes in battery behaviour without RPTs. Extensive zero-shot and few-shot evaluations across diverse chemistries demonstrate consistent outperformance of strong baselines at substantially lower parameter cost. Ablation studies confirm that task and FEC conditioning and the recurrent backbone are each critical for learning the long-term dynamics that govern voltage response over battery life<ref:2610.

1. The NOCE-Net architecture can be improved by incorporating a joint training objective that explicitly minimizes both voltage response prediction error and a degradation-aware auxiliary loss, such as a soft monotone penalty. This would allow the model to learn representations that are not only predictive but also structurally aligned with capacity fade, addressing the limitation where Voltage supervision encodes degradation direction, shape but not absolute scale.

2. The system can be enhanced by implementing a per-dataset MLP head trained on varying fractions of in-domain batteries to correct residual affine errors. This allows for dataset-specific calibration, as shown by the finding that Stanford-EV achieves 5–9% MAPE across these fractions, which mitigates the issue where the scale and offset of the predicted fade curve varies significantly between datasets.

3. The representation learning can be further generalized by explicitly incorporating task and FEC conditioning embeddings into a more expressive manner. This addresses the finding that Removing task, FEC, and learnable-token embeddings degrades aggregate zero-shot MAE by ∼ 50%, suggesting that richer conditioning mechanisms are necessary for robust generalization across diverse battery chemistries.

4. The system can be made more computationally efficient by exploring alternatives to the GRU backbone for inter-cycle dynamics, given its role as a computational bottleneck. Replacing it with a more parallelizable recurrent structure could improve scalability when dealing with extremely long sequences in future applications.

5. The downstream State-of-Health (SOH) estimation can be made more robust by utilizing the full set of PID-R features, including the integral term that acts as a learnable exponential moving average. This provides a signal that is robust to individual cycle noise and sensitive to long-term drift, leading to more accurate SOH tracking than relying on raw hidden states alone.

Learning effective representations from battery operational history is essential for predictive health management and control-oriented applications. Existing approaches rely on response-dependent engineered features or short early-life windows, limiting generalisability and precluding use in prospective settings where future responses are unavailable. We propose NOCE-Net, a deep nested sequence model that learns control-enabling representations directly from raw cyclic operational or telemetric data. Our data pipeline, re-BatteryData, standardises heterogeneous aging datasets into semantically equivalent Full Equivalent Cycles (FECs) defined by absolute charge throughput, enabling end-to-end learning across diverse operational regimes. NOCE-Net combines multi-patch transformer encoders for intra-cycle dynamics with a GRU backbone for inter-cycle state evolution, operating on approximately 700 batteries across ten public datasets spanning over 300 operational profiles. In zero-shot evaluation on unseen battery chemistries and usage patterns, NOCE-Net achieves 13.7% MAPE in voltage response prediction, outperforming strong long-sequence baselines by over 43% while using 40 times fewer parameters. Shape and component diagnostics of the learned hidden states reveal that the GRU's principal direction of evolution achieves Spearman ρ at least 0.95 with the capacity fade trajectory on average across all datasets with monotone degradation profiles, including zero-shot test batteries, providing evidence that the representations encode degradation dynamics transferable to downstream tasks beyond battery response modelling. Code is available at https://github.com/BeArnab96/NOCE-Net.