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NOCE-Net: Representation Learning for Battery Operational Context via Nested Sequence Modelling
Arnab Bhattacharjee, Wayes Tushar, Tapan Kumar Saha
TL;DR
Learning battery-type-aware, generalizable representations from real-world data remains an open challenge for predictive optimization and degradation monitoring. NOCE-Net models nested operational context from telemetric inputs using FEC segmentation. It outperforms strong baselines at lower parameter cost, and its hidden states also encode degradation structure without capacity labels.
Problem
Learning battery-type-aware, generalizable representations from real-world battery data remains an open challenge for predictive optimization and degradation monitoring.
Source: §1 · p. 2Method
NOCE-Net predicts long-horizon voltage responses from telemetric operational inputs segmented into variable-length FECs, coupling intra-cycle response dynamics with inter-cycle degradation dynamics.
Source: §1 · p. 2Results
NOCE-Net consistently outperforms strong baselines at substantially lower parameter cost in zero-shot and few-shot voltage forecasting.
Source: §5 · p. 13Takeaways & Limitations
Its recurrent hidden states encode degradation structure without capacity supervision and transfer to SOH estimation with near-affine residual error and gains from light per-dataset calibration.
Source: §1 · p. 3, §5 · p. 13Voltage-supervised degradation states capture direction and shape, not absolute scale, so SOH estimation requires per-dataset calibration.
Source: §5 · pp. 13–14
Abstract
from arXiv · showhide
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 $|\rho| \geq 0.95$ 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.
1 Introduction
The paper targets battery representations that generalize across changing usage histories without relying on response-dependent features or short early-life windows. It introduces a unified data pipeline and nested sequence model, reporting improved zero-shot voltage prediction and degradation structure in learned hidden states.
1 Introduction
- The paper identifies response-dependent engineered features, short early-life windows, heterogeneous datasets, and RPT-dependent analytic models as bottlenecks to generalizable battery representation learning.It motivates representations that encode long-horizon changes in battery dynamics across battery types and usage histories.Source: §1 · pp. 1–2
- NOCE-Net predicts long-horizon voltage responses from telemetric operational inputs, using nested full equivalent cycles to couple intra-cycle response dynamics with inter-cycle degradation dynamics.This nested context also compresses the temporal dimension for computationally efficient long-horizon supervised learning.Source: §1 · pp. 2–3
- re-BatteryData standardizes heterogeneous aging datasets into nested operational contexts with uniform feature dimensions and temporal resolution for end-to-end learning from raw cyclic data.The curated data spans approximately 700 batteries, around 300 operational profiles, and 10 public datasets, including variable profiles such as EV drive cycles and aircraft operations.Source: §1 · pp. 2–3
- NOCE-Net achieves 13–14% MAPE in zero-shot response prediction and a 43% improvement over the strongest baseline; ablations show it captures long-range, degradation-induced changes in battery dynamics.Source: §1 · p. 3
- The principal component of recurrent hidden-state trajectories achieves near-perfect rank correlation with capacity fade across splits, including zero-shot batteries.Shape analysis finds residual SOH prediction errors are affine rather than structural, and the representations are proposed as a foundation for downstream degradation monitoring.Source: §1 · p. 3
2 Proposed Methodology
The methodology standardizes raw aging records into nested cycle-level operational context, then predicts voltage responses with NOCE-Net to learn representations that retain intra-cycle and long-term inter-cycle information.
2 Proposed Methodology
- NOCE-Net predicts intra-cycle voltage responses from nested operational inputs using multi-patch encoding and segment-level recurrence to preserve local semantics and global battery context.Its patch decoder reconstructs variable-length responses aligned with each FEC’s intra-cycle resolution.Source: §2 · p. 3, §2.2 · p. 5, §2.2.3 · p. 7
2.1 re-BatteryData
- re-BatteryData standardizes heterogeneous datasets with six operational features and adaptive resampling, using time-weighted averages for continuous features and sums for accumulated features.The six features are charge and discharge current, temperature, time, and charge and discharge throughput.Source: §2.1 · p. 4
- Each FEC spans accumulated absolute-current throughput of twice nominal capacity, creating semantically comparable operational segments despite different conditions.The boundary is a segmentation criterion, not a claim that degradation conditions are identical; each segment retains current, temperature, and time information.Source: §2.1 · p. 5
2.2.1 Patch Encoder
- The Patch Encoder uses multi-kernel convolutions to extract multi-resolution features across patch lengths, with task and FEC embeddings included in its input.The encoder operates in parallel across FECs.Source: §2.2.1 · p. 6
2.2.2 Gated Recurrent Network Backbone
- A GRU processes fixed-dimensional cycle aggregators into states encoding cumulative operational context, while expensive intra-cycle transformer operations run in parallel.Task-conditioned initialization supports generalization across battery types.Source: §2.2.2 · pp. 6–7
2.2.3 Patch Decoder: Voltage Response Prediction
- The Patch Decoder reconstructs variable-length intra-cycle voltage responses from attended patch embeddings and the inter-cycle state, preserving temporal alignment.Residual-fusion upsampling across patch scales restores each FEC’s original intra-cycle length.Source: §2.2.3 · p. 7
3 Experimental Details
The experiments combine a large, diverse battery-aging collection with held-out dataset-level tests and baseline configurations designed to examine nested context and inter-cycle memory.
3.1 Dataset and Training
- Ten public datasets contribute 700 batteries and around 300 operational profiles; five datasets are held out entirely for cross-chemistry and cross-regime zero-shot and few-shot evaluation.The remaining training datasets are split 6:2:2 for training, validation, and in-sample testing.Source: §3.1 · pp. 7–8
3.2 Baselines
- Baseline modes compare nested M1 sequences, flattened M2 sequences, and independent per-cycle samples to isolate nested-structure and inter-cycle-memory contributions.M1-versus-M2 comparisons use the same architecture; some configurations were omitted because of out-of-memory errors.Source: §3.2 · pp. 8–9
4 Results and Discussions
NOCE-Net outperforms baselines in zero-shot and few-shot voltage forecasting, while ablations show the contribution of conditioning and recurrence. Its recurrent hidden states track degradation patterns and support downstream SOH prediction.
4.1 Zero-shot and Few-shot Response Forecasting
- 13.7% MAPE and MAE of 0.0656 in aggregate zero-shot evaluation, improving over TTM + Indep. and MAMBA + M2 by 43.8% and 34.5%, respectively.The models are evaluated on lifetime voltage responses of test batteries.Source: §4.1 · pp. 9–10
- 42.5% lower MAE than MAMBA + M2 in few-shot forecasting, after fine-tuning only final MLP heads on the first 50 FECs per test cell.NOCE-Net retains the best aggregate few-shot performance.Source: §4.1 · p. 10
4.2 Ablation Studies
- Removing task, FEC, and learnable-token embeddings degrades aggregate zero-shot MAE by about 50%, while removing recurrence causes a larger collapse.The recurrent-backbone ablation reaches MAE 0.16 and MAPE 36.84%.Source: §4.2 · p. 11
- Without recurrence, intra-cycle prediction error accumulates with FEC index at nearly 3× the full model’s rate, limiting tracking of aging-driven voltage shifts across battery life.Figure 4 plots MAE across cycle percentage to end of life.Source: §4.2 · p. 11, Figure 4 · p. 11
4.3 Transferability of Learned Representations to SOH Prediction
- PC1(H) achieves mean |ρ| = 1.000 against FEC index and |ρ| ≥ 0.83 against normalized capacity fade across datasets with monotone degradation, except evTOL and NASA-PCoE.The reported correlations include zero-shot test batteries.Source: §4.3 · p. 11
- Relativized states H−h0 evolve monotonically and share degradation directions across chemistries, whereas raw-state PCA arcs have inconsistent orientations.The PCA trajectories include training and zero-shot batteries.Source: Figure 5 · p. 12, §4.3 · p. 12
- Hidden-state SOH shape correlation averages r = 0.856 (range 0.69–0.99, evTOL excluded); per-dataset heads reach 5–33% MAPE on four datasets at 30% training fraction.ISU ILCC and NASA Rand remain hardest at 72% and 77% MAPE, respectively.Source: §4.3 · pp. 12–13
- On zero-shot batteries, PID-R achieves 52.7% and 90.5% lower aggregate MAPE than FEC-only Linear and MLP baselines, respectively.FEC-only baselines edge out PID-R on some batteries where the SOH head has known affine miscalibration.Source: §4.3 · p. 13
5 Conclusion and Limitations
NOCE-Net couples intra-cycle operational inputs with inter-cycle latent dynamics for long-horizon voltage forecasting and reports transfer of degradation structure to SOH estimation. The authors identify limits in absolute-scale recovery, non-monotone capacity trajectories, data requirements, computational cost, and real-world validation.
5 Conclusion and Limitations
- NOCE-Net couples intra-cycle operational inputs with inter-cycle latent dynamics for long-horizon voltage forecasting without RPTs.The authors report consistent outperformance of strong baselines in zero-shot and few-shot evaluations across diverse chemistries, at substantially lower parameter cost.Source: §5 · p. 13
- In voltage forecasting, recurrent hidden states encode battery degradation structure without capacity supervision and transfer to SOH estimation, yielding near-affine residual error and strong gains from light per-dataset calibration.Source: §5 · p. 13
- Voltage supervision captures degradation direction and shape but not absolute scale, requiring per-dataset calibration; non-monotone capacity trajectories can make scalar SOH ill-defined.The authors suggest a joint SOH auxiliary loss as a natural remedy.Source: §5 · p. 14
- Re-BatteryData requires current, temperature, and time signals, while sequential GRU processing is a computational bottleneck and real-world closed-loop validation remains open.Datasets lacking temperature records require imputation; closed-loop deployment requires controllable or reliably forecasted temperature.Source: §5 · p. 14
A Related Work
Prior battery modeling approaches face limitations in prospective control-oriented prediction, operational diversity, scalability, and nested sequence handling. The related work reviews feature-based, hybrid, transfer-learning, dataset-standardization, and time-series-model approaches, as well as uniform feature construction.
A.1 Feature-Based Data-Driven Battery Modeling
- Response-dependent engineered features require voltage trajectories unavailable for unseen future operations, while short repeatable segments discard operational history and leave path-dependent effects unmodeled.Early-life formulations also assume stationary operating conditions and remain retrospective or static rather than control-enabling.Source: §A.1 · p. 15
A.2 Hybrid Physics–Data-Driven Battery Models
- Hybrid models offer physical grounding but are typically validated on few batteries and narrow regimes; computational overhead and periodic RPT requirements constrain lifetime-scale learning.RPTs take batteries offline and disrupt normal operation.Source: §A.2 · pp. 15–16
A.3 Generalization, Transfer Learning, and Domain Adaptation in Battery Modeling
- Transfer and domain-adaptation gains often remain within narrow gaps, while response-dependent features preserve limitations for control-enabling tasks and evolving conditions.The reviewed methods do not resolve the challenge of universal representations across diverse datasets.Source: §A.3 · p. 16
A.4 Large-Scale Battery Datasets and Data Standardization
- Large-scale battery pipelines mainly target retrospective prediction and use early-life data, fixed resampling, semantically non-identical cycles, or flat sequences rather than raw nested operational context.BatteryLife and BatteryML expand standardization and scale, but the described pipelines remain limited for end-to-end operational-context learning.Source: §A.4 · p. 16
A.5 Foundational Time-Series Models and Structural Limitations
- Time-series models commonly assume uniform sampling, fixed-length contexts, or one temporal dimension, while classical recurrent models do not scale well to extremely long sequences or explicitly model nesting.Padding, truncation, interpolation, or flattening can lose information when each battery cycle is itself a variable-length time series.Source: §A.5 · p. 17
B.1.1 Uniform Feature Dimension
- Uniform feature construction computes charge and discharge throughput by integrating absolute current over time and resetting accumulation at each current sign change.The described raw records include current, temperature, and time; charge and discharge throughputs are retained as separate features.Source: §B.1.1 · p. 17
B.1.2 Battery Specific Task Features
Battery-specific task features encode metadata about capacity, voltage range, form factor, and electrode composition. Full Equivalent Cycle segmentation instead uses absolute charge throughput to create operation-agnostic periods.
B.1.2 Battery Specific Task Features
- Task features encode nominal capacity, manufacturer voltage limits, form factor, and electrode composition, with categorical metadata including an Unknown class.Form factor, anode, and cathode composition use categorical features; nominal capacity and voltage limits are continuous features.Source: §B.1.2 · pp. 17–18, Table 5 · p. 18
B.1.3 Full Equivalent Cycle based Segmentation
- Full Equivalent Cycles use absolute charge throughput to group operational periods with equivalent normalized throughput, rather than counting charge–discharge events as equivalent cycles.In Figure 6, cycles A, (B,C), and (D,E) form three FECs; an FEC boundary is a segmentation criterion, not a claim of identical degradation conditions.Source: §B.1.3 · pp. 18–19, Figure 6 · p. 19
C Datasets
The datasets cover varied battery chemistries, cycling regimes, and profile complexity. The section lists training datasets and identifies five additional datasets for out-of-distribution evaluation.
C Datasets
- Other listed training datasets include 155 variable-profile ISU-ILCC batteries, NASA-Rand randomized-discharge cells, MATR full-cycle cells, XJTU-Partial cells, TJU batteries, and UMICH pouch batteries.The passage describes variation in chemistry, cycling profile, temperature, and mechanical stress across these datasets.Source: C Datasets · p. 19
- Five additional datasets were used for out-of-distribution evaluation, and Figure 7 compares distributions of current, throughput, and voltage across datasets.The supplied dataset passage does not name the five additional datasets.Source: C Datasets · p. 19, Figure 7 · p. 20
- The listed training datasets include eVTOL aircraft discharge profiles, NASA PCoE full-cycle NMC–Graphite cells, Stanford EV dynamic operation, HUST LFP–Graphite cells, and XJTU Full dynamic cycles.Together, the datasets span NMC, LFP, and hybrid chemistries, partial and full cycling, and varied profile complexity.Source: C Datasets · p. 20
D Baselines
The section compares sequence-model baselines and their input-representation modes for battery forecasting. It also identifies the architectural trade-offs motivating the comparison.
D Baselines
- TimerXL handles flattened time series but lacks explicit variable-length sequence support and incurs substantial compute overhead on long battery lifecycles.MAMBA uses selective scanning for variable-length sequences with linear complexity, while AutoTimes is computationally expensive and can overfit small datasets without strong inductive biases.Source: D Baselines · p. 21
- MAMBA combines recurrence efficiency with input-dependent parameterization, while TTM uses lightweight MLP mixers to trade attention-heavy computation for temporal modeling.The baselines span transformer, state-space, pretrained language-model, and MLP-based approaches.Source: D Baselines · pp. 21–22
- Tables 6 and 7 provide parameter-count and structural comparisons between baseline input-representation modes and NOCE-Net.Their captions identify comparison scope but do not provide the underlying values here.Source: Table 6 · p. 22, Table 7 · p. 23
- Three modes test baseline adaptability: nested operations, flattened nested context, and independent mapping of each intra-cycle input to its output.Nested Operations includes MPATCH and VARSEQ controls, yielding four sub-experiments per baseline.Source: D Baselines · pp. 22–23
E Experimental Details
Experimental details cover a composite training loss, model configuration, and memory-conscious training over long battery histories.
E.1 Loss Function
- For a particular FEC c, the training loss is defined, with q75 denoting the 75%-ile absolute error value and α and β being fixed constants.Source: §E.1 · p. 23
E.2 Architectural Configurations
- NOCE-Net transformer blocks use query-key normalization, prenormalization with SwiGLU, xPoS embeddings, and multi-query attention.Task-Emb combines categorical embeddings and continuous-variable projections, while FEC-Emb uses a single linear projection; training uses Adam with a step scheduler.Source: §E.2 · p. 23, Table 8 · p. 24
E.3 Training Configurations
- Training divides each battery’s life into non-overlapping groups of 100 cycles, detaching recurrent states between groups to fit memory constraints.Stateless baselines treat each 100-cycle segment as an independent sample; MAMBA carries recurrent states with the same detachment interval.Source: §E.3 · p. 24
F.1 In-sample Prediction
Few-shot results favor NOCE-Net in aggregate, and the extended analysis examines how recurrent hidden states track and predict capacity fade. It also identifies where transferred SOH predictions need calibration or fail under particular data conditions.
G.1 Spearman Rank Correlation Diagnostics
- Capacity fade is strictly monotone at the FEC timescale for well-behaved datasets except NASA and evTOL, while PC1(H) retains |ρ| = 1.000 where raw hidden-state norm correlations fall.For MATR validation and HUST test, raw norm correlations are 0.333 and 0.612, respectively; high inter-battery variance in initial-state magnitude can disrupt aggregate ranking.Source: §G.1 · pp. 25–26, Figure 10 · p. 27
F.2 Few Shot Forecasting
- 42.5% lower MAE than MAMBA + Method 2 and 30% lower MAE than TTM + Method-1(False, True) are achieved by NOCE-Net in aggregate few-shot forecasting.MAMBA + Method 2 performs best on three individual datasets, while NOCE-Net fine-tuned with 100 cycles performs worse than with 50.Source: §F.2 · p. 25, Table 10 · p. 26
G.2 PID-R Feature Extraction from GRU Hidden States
- PID-R features concatenate four hidden-state summaries: current state, local change, smoothed history, and displacement from battery initialization.They form a fixed-dimensional summary computed from frozen NOCE-Net hidden states without additional model training; relative features reach |ρ| = 0.997 on test versus 0.750 for raw norm.Source: §G.2 · pp. 26, 28
G.3 Direct SOH Prediction Head
- The direct SOH head predicts normalized capacity trajectory from frozen-state PID-R features using a three-layer MLP and a composite loss.UMICH is excluded for missing capacity measurements, and evTOL is excluded from capacity metrics because its aircraft discharge profiles produce non-monotone capacity trajectories; its PC1 representation correlation remains 0.997.Source: §G.3 · p. 28
G.4 Shape Diagnostic
- Shape correlations r ≥ 0.7 on non-evTOL datasets indicate that frozen recurrent states capture trajectory shape, while residual SOH errors are primarily scale and offset differences.Stanford-EV’s chemically distinct profiles yield an over-compressed trajectory, and per-dataset MLP calibration corrects the described scale-related failure modes.Source: §G.4 · p. 29
G.5 Per-Battery GP Baseline
- On slow-degrading ISU ILCC batteries, the per-battery Gaussian Process reaches 338% MAPE at k = 5 because the initial observations span negligible SOH range.The one-dimensional PC1 input leaves the scale parameter unconstrained when early targets are flat; the per-dataset MLP instead uses the full 4dh-dimensional PID feature vector.Source: §G.5 · p. 29
G.6 Full Per-Dataset MLP Sweep
The per-dataset MLP sweep shows that calibration data needs vary by dataset, with some error levels persisting despite increased training fractions.
G.6 Full Per-Dataset MLP Sweep
- Stanford-EV achieves 5–9% MAPE across training fractions and changes little with added data, while XJTU-Full improves from 33% to 24% as the fraction rises from 10% to 50%.The reported patterns suggest Stanford-EV is homogeneous, whereas XJTU-Full may benefit from more batteries.Source: §G.6 · p. 30
- HUST plateaus at 31–33% MAPE across training fractions, with the remaining error attributed to battery-to-battery capacity variability absent from voltage-forecasting hidden states.TJU peaks at a 20% training fraction before degrading slightly at higher fractions, which the passage describes as suggestive of mild MLP-head overfitting.Source: §G.6 · p. 30
- NASA Rand shows variance up to ±47% at a 50% training fraction, and the authors state that reliable conclusions require more batteries.The dataset is small and uses highly non-stationary random discharge protocols.Source: §G.6 · p. 30
- ISU ILCC’s deep degradation and potentially largest within-dataset variability are associated with high SOH-modeling errors.The authors suggest examining other recurrent-state features for per-dataset SOH heads.Source: §G.6 · p. 30