Organizations: Laboratoire de Réactivité et de Chimie des Solides (LRCS), UMR CNRS 7314-Université de Picardie Jules Verne, 15 Rue Baudelocque, 80000, Amiens, France · Réseau sur le Stockage Electrochimique de l’Energie (RS2E), CNRS FR 3459, Hub de l’Energie, 15 Rue Baudelocque, 80000, Amiens, France · Predeeption (INRIA Startup Studio / CNRS Innovation), Hub de l’energie, 80000, Amiens, France · Mathematics Institute, University of Warwick, Gibbet Hill Road, CV4 7AL, Coventry, UK · The Faraday Institution, Quad One, Becquerel Avenue, Harwell Campus, OX11 0RA, Didcot, UK
Abstract
Long-horizon physics-based simulations of battery degradation provide mechanistic insight but remain computationally expensive, limiting their use for dense exploration of operating conditions over extended cycle life. Here, we propose a hybrid physics-probabilistic learning framework for surrogate modeling of lithium-ion battery degradation trajectories at unseen charging rates. Cycle-resolved degradation data generated with a DFN/P2D electrochemical model in PyBaMM are first transformed into capacity-aligned voltage and derivative features and encoded using a Variational Autoencoder (VAE). The resulting two-dimensional latent space organizes degradation trajectories according to both cycle progression and charging protocol. A sparse multitask Gaussian process (GP) is then trained in this latent space using cycle number and C-rate as input variables, providing continuous interpolation of latent degradation dynamics together with posterior uncertainty estimates. Under protocol-level holdout evaluation, the latent-space GP accurately recovers unseen C-rate trajectories and exhibits uncertainty behavior consistent with the support of the training data. When queried at unseen interior C-rates, the model generates latent trajectories that remain coherently positioned between neighboring simulated protocols. Decoding the GP-predicted latent states through the frozen VAE decoder yields smooth voltage-capacity evolution, while Monte Carlo propagation of the GP latent posterior through an auxiliary latent to State of Health (SOH) predictor provides uncertainty-aware SOH estimates. The proposed BattVAE-GP framework therefore offers a computationally efficient and uncertainty-aware surrogate for long-horizon degradation modeling, providing a structured basis for extending battery health prediction toward richer operating conditions and future simulation-experiment fusion.
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.
Accurate prediction of lithium-ion battery state of health (SOH) is essential for reliable energy storage operation. However, purely data-driven models may generalize poorly across cycling protocols and produce physically implausible behavior during long-term extrapolation. We developed a physics-informed differentiable degradation modeling framework (PiDDM) for battery SOH prediction. PiDDM incorporates empirical Arrhenius degradation kinetics associated with solid electrolyte interphase growth and loss of lithium inventory into the training objective, encouraging physically consistent capacity fade under diverse operating conditions. The framework was evaluated using a public dataset of 55 batteries cycled under six operating protocols. PiDDM achieved the lowest average prediction error among the evaluated models and substantially reduced mean squared error relative to a multilayer perceptron and a baseline physics-informed neural network. For extrapolation, the models were trained on the first 90% of each battery's cycle life and evaluated on the unseen final 10%. PiDDM captured accelerated end-of-life degradation while avoiding the nonphysical capacity regeneration produced by the baseline models. These results show that incorporating degradation physics into neural network training improves predictive accuracy and physical consistency, providing a promising approach for practical battery health monitoring.
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.