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BatteryMFormer: Multi-level Learning for Battery Degradation Trajectory Forecasting

Ruifeng Tan, Jintao Dong, Weixiang Hong, Jia Li, Jiaqiang Huang, Tong-Yi Zhang

arXiv:2605.27044v2cs.AI

TL;DR

Early BDTF must forecast full-life SOH trajectories from limited early operational data despite multi-level degradation structure and SOC-localized signatures. BatteryMFormer addresses this with condition-aware decoding, prototype memory, and dual-view encoding, and it consistently improves performance across four battery domains. The authors identify long redundant inputs and the mismatch between regular laboratory data and irregular noisy field data as important boundaries.

  • Problem

    Early BDTF lacks explicit modeling of aging-condition regularities, shared trajectory patterns, and SOC-localized degradation signatures that matter for forecasting full-life SOH trajectories.

  • Method

    BatteryMFormer combines an aging-condition-aware decoder, meta degradation pattern memory, and dual-view encoder for temporal and SOC perspectives.

  • Results

    BatteryMFormer consistently improves over state-of-the-art baselines across four battery domains, achieving the best performance across domains and metrics.

  • Takeaways & Limitations

    Explicitly modeling multi-level degradation structure supports consistent early BDTF improvements, with ablations indicating that the major components contribute meaningfully.

  • Takeaways & Limitations

    More than 25 early cycles can produce over 7,500 input points, while field data are often irregular and noisier than the evaluated laboratory and production tests.

Abstract

from arXiv · show

Early battery degradation trajectory forecasting (BDTF), which predicts the full-life state-of-health trajectory from early operational data, is critical for battery optimization, manufacturing, and deployment. Battery degradation data exhibit two key characteristics. First, degradation data present a multi-level structure, including regularities shared within aging conditions and trajectory patterns shared across batteries. Second, degradation-related variations in voltage-current profiles are often localized to specific state of charge (SOC) intervals. Existing approaches often fail to explicitly model these characteristics. To bridge this gap, we propose BatteryMFormer, a multi-level Transformer for early BDTF. BatteryMFormer integrates (1) an aging-condition-aware decoder that injects aging-condition priors via aging-condition-informed queries and aging-condition-aware attention, (2) a meta degradation pattern memory that learns and retrieves trajectory prototypes to guide long-horizon forecasting, and (3) a dual-view encoder that jointly captures temporal dynamics and SOC-localized variations from voltage and current time series. Extensive experiments on four battery domains show that BatteryMFormer consistently outperforms state-of-the-art baselines, marking a significant step toward reliable BDTF. Our code is available at https://github.com/Ruifeng-Tan/BatteryMFormer.

1 Introduction

Early BDTF forecasts full-life SOH trajectories from early operational data, but existing methods do not explicitly model aging-condition regularities, shared trajectory patterns, or localized degradation signatures. BatteryMFormer addresses these gaps with a multi-level architecture combining condition-aware decoding, trajectory-pattern memory, and dual-view operational encoding.

  • BDTF predicts full-life battery SOH trajectories from early operational data to support battery optimization, manufacturing, and deployment.
  • Existing methods use handcrafted features or generic forecasting mappings, but features may be protocol- or dataset-specific and early-cycle SOH can be insufficient for extrapolation.
  • Battery degradation has multi-level structure, including regularities within aging conditions and trajectory patterns shared across batteries.
  • BatteryMFormer integrates an aging-condition-aware decoder, meta degradation pattern memory, and dual-view encoder to model condition priors, trajectory prototypes, and SOC-localized variations.
  • The paper evaluates BatteryMFormer extensively across four battery domains and reports superior performance against existing approaches.

2 Preliminaries

The paper defines aging conditions, degradation trajectories, and early BDTF using operational measurements and SOH derived from discharge capacity. Early BDTF uses the first S≤100 cycles to forecast the SOH trajectory beyond the observation window, while degradation signatures may concentrate in specific SOC intervals.

  • 2.1 Aging Condition: An aging condition is the tuple of recorded battery specifications and experimental settings that determines a battery’s degradation regime.
  • 2.2 Degradation Trajectory: Discharge capacity for cycle i is computed by integrating the absolute measured current over the discharge interval.
  • 2.2 Degradation Trajectory: SOH is defined from discharge capacity relative to a reference capacity, with CALB using a protocol-specific first-cycle discharge capacity reference.
  • 2.2 Degradation Trajectory: Voltage–SOC and current–SOC profiles can show aging-induced deviations concentrated within specific SOC intervals despite smooth global evolution.
  • 2.3 Task Formulation: Early BDTF uses the first S≤100 cycles of voltage-current operational data and related variables to predict the future SOH trajectory beyond the observation window.

3 Methodology

BatteryMFormer combines temporal and SOC views of early operational data with aging-condition-aware decoding and prototype-memory retrieval for long-horizon degradation forecasting.

  • Dual-view encoder: The dual-view encoder produces complementary temporal and SOC tokens from early operational data.Temporal tokens summarize cycle-level intra-cycle dynamics, while SOC tokens model cross-cycle evolution within SOC intervals.
  • Dual-view encoder: The SOC view captures degradation signatures localized to SOC intervals by applying convolution along the SOC axis and aggregating each interval across cycles.
  • Aging-condition-aware decoder: The aging-condition-aware decoder injects metadata-derived priors into queries and conditions attention to promote aging-condition-consistent decoding.Metadata are encoded into query-specific prior vectors, and query modulation injects aging-condition priors into every attention operation.
  • Meta degradation pattern memory: The meta degradation pattern memory stores learnable trajectory prototypes and retrieves the two most similar patterns using cosine similarity.Retrieved patterns are aligned with full-life trajectory embeddings during training and can be reconstructed to preserve trajectory information.
  • Forecasting and training: Gated fusion incorporates the retrieved degradation pattern into a linear forecasting head that outputs the predicted degradation trajectory.The training objective weights alignment and recovery losses with λ1 and λ2.

4 Experiments

Experiments across four battery domains evaluate BatteryMFormer under standard, varying-early-cycle, ablation, case-study, and reduced-data settings. The model consistently outperforms baselines, while component analyses support complementary roles for SOC-localized modeling, trajectory prototypes, and aging-condition-aware decoding.

  • Overall Performance: BatteryMFormer achieves the best performance on all four domains and metrics, reducing MAPE by 11.07%, 8.49%, 17.66%, and 8.97% over second-best models.The corresponding MAE reductions are 10.94%, 10.83%, 17.65%, and 11.83% on Li-ion, CALB, Na-ion, and Zn-ion, respectively.
  • Overall Performance: The strongest baseline varies by domain, with IC2ML leading on Li-ion, CALB, and Zn-ion and TimeBridge leading on Na-ion.This variation is accompanied by substantial performance instability for some generic forecasting models.
  • Different Numbers of Usable Cycles: BatteryMFormer maintains consistent improvements across a broad range of usable early-cycle counts in all four domains.The evaluation reports MAE and MAPE for top-performing models as the amount of early degradation information changes.
  • Different Numbers of Usable Cycles: For Li-ion and Na-ion, prediction errors can increase when S>25, showing that longer inputs may introduce redundancy and optimization difficulty.At 300 points per cycle, S>25 corresponds to more than 7,500 input points.
  • Ablation Study: Removing the SOC view, MDPM, or ACDecoder consistently degrades results across domains, while their gains vary with battery domain.The SOC view helps most on Li-ion and Na-ion, whereas ACDecoder has stronger effects on CALB and Zn-ion; ACQuery and ACAttention are both important.
  • Case Study: MDPM retrieves trajectory prototypes consistent with superlinear, linear, and sublinear long-horizon degradation patterns, including slowdown beyond the observed early stage.The case study indicates that retrieved prototypes provide priors for long-range extrapolation and can support batteries from aging conditions absent during training.
  • Case Study: SOC-view attention concentrates on selected SOC intervals near major DVA peaks and shoulder regions associated with degradation-sensitive changes.The analysis links these localized patterns to electrochemical signatures associated with battery aging mechanisms.
  • Data-Efficient Learning: With only 50% of the training data, BatteryMFormer achieves the best performance across all four domains.Relative MAPE reductions over the strongest baseline are 12.45%, 2.81%, 15.23%, and 17.69% across Li-ion, CALB, Na-ion, and Zn-ion.

5 Related Work

Prior BDTF methods use either handcrafted degradation descriptors or learned representations from raw measurements. Representation-learning approaches often frame BDTF as generic time-series forecasting, but early-cycle SOH can be weakly informative.

  • Feature-engineering methods extract handcrafted descriptors from voltage, current, capacity, or relaxation signals before predicting future capacity or SOH trajectories.
  • These descriptors are commonly extracted from measurement regions where aging signatures are pronounced.
  • Representation-learning methods learn forecasting-relevant representations directly from raw or minimally processed measurements using neural networks.
  • Generic time-series approaches extrapolate future SOH from historical SOH using architectures such as LSTM or Transformer variants.
  • Handcrafted features may be protocol- or dataset-specific, while SOH-only inputs can be weakly informative during early cycles.

6 Limitations and Ethical Considerations

The paper identifies limitations involving ultra-long, redundant inputs and a mismatch between evaluated laboratory or production tests and noisier, irregular field data. It also cautions that deployment errors require validation against target operating distributions.

  • Limitations: More than 25 early cycles produce over 7,500 input points, which can compromise model performance on ultra-long inputs.
  • Limitations: Field data such as EV logs are often more irregular and noisy than the laboratory and production tests used for evaluation.
  • Limitations: Applying BatteryMFormer to field conditions may require modified representations and preprocessing for inaccurate and irregular records.
  • Ethical Considerations: Forecast errors in field deployment can induce suboptimal decisions, including premature retirement or delayed maintenance.
  • Ethical Considerations: Models should be validated against the target operating distribution before high-stakes deployment.

7 Conclusion and Future Work

The conclusion emphasizes explicitly modeling multi-level structure in early BDTF and reports consistent improvements across four battery domains. It also identifies long operational sequences and irregular, noisy field data as future challenges.

  • BatteryMFormer models trajectory patterns, aging conditions, and battery-specific dynamics in early battery degradation trajectory forecasting.
  • The model delivers consistent improvements over state-of-the-art baselines across four battery domains.
  • Ablation studies and case studies confirm that each component contributes meaningfully to the reported gains.
  • BatteryMFormer performs better in data-efficient settings with reduced training data.
  • Future work will improve modeling of long operational time series and adapt the framework to irregular, noisy field data.

8 GenAI Disclosure

The paper discloses that generative AI assisted language editing and code development, while authors reviewed the resulting manuscript and code. The supplied methodological passages define SOC-aligned preprocessing and cycle-level inputs.

  • GenAI Disclosure: Generative AI tools assisted with language editing and code development, but were not used to generate the reported experimental results.
  • GenAI Disclosure: The authors reviewed and validated all AI-assisted edits to the manuscript and code and retained responsibility for correctness, originality, and integrity.
  • Methodological Context: Each battery follows a protocol SOC interval, with charging and discharging returning to the starting SOC before the next cycle.
  • Methodological Context: Within each cycle, SOC is assumed to vary linearly with within-segment charge or discharge capacity change.
  • Methodological Context: SOC-aligned resampling places voltage, current, and capacity on a uniform SOC grid before concatenating charge and discharge sequences.

C Further Implementation Details

The implementation standardizes cycling inputs, early-cycle availability, and SOH targets across batteries and domains. It uses resampling, zero-padding, validity masking, and domain-specific EOL normalization for training and evaluation.

  • Input processing: Each cycle’s charge and discharge segments are resampled to uniformly spaced sequences and concatenated into length-L voltage, current, and capacity inputs.Current is normalized to C-rate, while voltage and capacity retain their original scales.
  • Input processing: BatteryMFormer additionally computes SOC, while all models use at most the first 100 cycles and zero-pad shorter histories.A cycle-level validity mask identifies existing cycles so attention-based models can ignore padding.
  • Target normalization and padding: Each battery trajectory is padded to a maximum horizon of 5000 cycles to cover the longest trajectories in the database.This establishes a common output length for trajectory forecasting.
  • Target normalization and padding: SOH targets are normalized using domain-specific EOL thresholds during training and transformed back to the original scale before MAE and MAPE evaluation.The threshold is defined as τ in Appendix A.

C.2 Baseline Implementation

The appendix adapts generic forecasting and battery-specific baselines to output full 5000-cycle SOH trajectories under the common early-BDTF setup. Supervised models use masked-MSE training, whereas TimesFM is evaluated zero-shot.

  • Generic time-series forecasting models: Generic time-series models reshape the early cycling inputs and replace their original forecasting heads with trajectory heads producing length-5000 SOH sequences.The trajectory head flattens the encoder representation when necessary before applying a linear projection.
  • Generic time-series forecasting models: TimesFM forecasts future SOH zero-shot from the historical univariate SOH sequence without task-specific fine-tuning.Inputs are padded to a multiple of its fixed patch length of 32 by repeating the last observed SOH value.
  • Battery-specific models: CPTransformer and CPMLP retain their official implementations while changing only the output head to produce the length-5000 trajectory.IC2ML is adapted because its fixed 3.6–3.8 V input window is unavailable or incomparable across all batteries and protocols.
  • Training objective: Supervised baselines use the same masked-MSE prediction loss as BatteryMFormer, with IC2ML also retaining its original multi-task auxiliary losses.TimesFM is evaluated without task-specific fine-tuning.
  • Hyperparameter search: Hyperparameters are selected using validation MAPE, with per-domain or per-fold searches and shared training and validation splits for fair comparison.The search spaces include model dimensions, memory size, query count, patch-encoder kernel size, learning rate, batch size, and dropout rate.

D Further Details of Data Preprocessing

The preprocessing pipeline removes isolated measurement artifacts and smooths non-standard testing regions that can create abrupt, non-protocol degradation signals. It also filters batteries lacking sufficient degradation information.

  • Preprocessing rationale: Non-standard segments such as RPTs, formation cycles, and equipment faults are smoothed to reduce abrupt SOH deviations while preserving sustained degradation trends.These segments may otherwise impair model training when treated as regular degradation signals.
  • SOH computation and battery filtering: Single-cycle SOH drops exceeding 3% of the previous cycle are clipped, while batteries not degrading below τ + 2.5% are excluded.The filtering threshold uses τ = 90% for CALB and τ = 80% for other datasets.
  • SOH trajectory smoothing: Artifact onsets are identified from RPT timestamps or dataset-specific gaps between cycle timestamps before smoothing regions.The gap threshold γ_gap is fixed for each dataset before model training.
  • SOH trajectory smoothing: For each artifact region, the recovery point is the earliest cycle returning within tolerance ε for W consecutive cycles, after which PCHIP interpolation smooths the region.M normal cycles before and after the region provide interpolation anchors.
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