STEK: Structural-Terrain-Enhanced Koopman-Inspired Cross-Channel Regularization for Retrospective Battery Multi-Target Estimation

Transition-metal-based batteries rely on critical elements such as lithium, cobalt, and nickel. Their extraction creates environmental and supply-chain challenges. Organic electrode materials (OEMs) reduce this reliance and provide broad molecular tunability. However, OEM-based batteries still show limited long-term cycling stability. Their design also requires the joint optimization of coupled metrics such as voltage, specific capacity, capacity retention, and energy density. These metrics depend on the full battery stack and on the interactions among its components rather than on the active material alone. In our previous work, we developed a data-fusion multi-task framework for average discharge voltage and first-cycle specific capacity. Both targets are single-valued. Here, we extend that framework to multi-horizon prediction by predicting a property at every cycle of a discharge trajectory rather than at a single cycle. Our multi-fidelity and Multi-horizon Deep Operator Network learns DFT redox potentials and cycle-dependent specific-capacity trajectories within one model. We train it on complete battery-stack representations and usage conditions, so it learns battery-stack interactions rather than cathode-only effects. This framework supports long-term property prediction, inverse design, and process optimization for organic battery systems.

Accurate assessment of lithium-ion battery ageing is challenged by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven models across datasets. In particular, robust identification of degradation transitions, such as the knee point, and reliable early-life prediction of remaining useful life (RUL) remain open problems. This study proposes a unified framework for battery ageing analysis based on continuous representations of voltage-capacity and capacity-cycle trajectories learned from heterogeneous public datasets (NASA, CALCE, ISU-ILCC). The continuous formulation enables consistent extraction of degradation descriptors, including curvature, plateau length and knee-related metrics, while reducing sensitivity to dataset-specific discretisation. Across more than 250 cells, statistically significant correlations between knee onset and end-of-life (Pearson 0.75-0.84) are observed. Additional early-life analysis confirms that knee-related features retain predictive value when estimated from partial trajectories. Early-life models provide increasingly stable RUL predictions as the number of observed cycles increases, with meaningful predictive performance emerging within the first 5-20 cycles and remain robust under cross-dataset domain shift. The framework integrates continuous modelling, feature extraction and uncertainty-aware prediction, providing an interpretable and dataset-consistent approach demonstrating robustness across heterogeneous dataset types. Compared with conventional discrete or feature-based methods, the proposed representation reduces sensitivity to sampling resolution and improves cross-dataset consistency. The study is limited to laboratory-scale datasets and capacity-based end-of-life definitions.

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.