Battery Degradation Modeling

Updated 1 January 2026

Battery degradation modeling is the quantitative study of lithium-ion battery aging, leveraging detailed electrochemical, multiphysics, and data-driven approaches.
Models range from high-fidelity DFN frameworks and reduced-order surrogates to empirical and machine learning techniques for accurate lifetime forecasting.
These methods inform design and operational control while addressing challenges in parameter estimation, model uniqueness, and real-world implementation.

Battery degradation modeling concerns the quantitative and mechanistic description of the processes by which lithium-ion batteries (LiBs) lose capacity, power, and reliability over time and usage. It encompasses physics-based, data-driven, and hybrid paradigms, spanning detailed electrochemical-thermal models, reduced-order surrogates, empirical mapping, and machine learning approaches. The field is central to lifetime forecasting, warranty analytics, design-for-reliability, energy storage business models, and the development of battery management systems (BMS).

1. Mechanistic Foundations: Electrochemical and Multiphysics Models

Physics-based degradation modeling is rooted in the multiscale, multiphysics Doyle–Fuller–Newman (DFN) pseudo-2D framework, which models solid-phase Li transport, electrochemical kinetics, electrolyte transport, charge conservation, and temperature dynamics as coupled PDE–DAE systems. Degradation mechanisms are incorporated by adding submodels that describe the evolution of state variables representing side-reactions and failure modes.

Key degradation mechanisms include:

Solid-Electrolyte Interphase (SEI) growth: Modeled as an interstitial-diffusion-limited side reaction at the negative electrode, leading to cyclable lithium consumption and increased impedance via a growing resistive layer. SEI thickness evolution typically follows a square-root-of-time law under diffusion limitation; see equations for growth flux and coupling to overpotentials in (O'Kane et al., 2021, Nazeeruddin et al., 17 Dec 2025, Pozzato et al., 2021, Li et al., 2023).
Lithium plating and stripping: Formulated via Butler–Volmer kinetics with overpotential thresholds for Li deposition. A portion of plated Li becomes “dead Li” through slow SEI-assisted reincorporation or isolation, directly contributing to irreversible capacity loss (O'Kane et al., 2021, Li et al., 2023, Nazeeruddin et al., 17 Dec 2025).
Particle cracking and mechanical Loss of Active Material (LAM): Mechanical damage, modeled using Paris–law or stress-based models, exposes new surface area for SEI formation and can disconnect active material, leading to sudden capacity or power-loss pathways (O'Kane et al., 2021, Li et al., 2023).
Electrolyte dry-out and solvent reservoir depletion: Consumption of electrolyte solvent during SEI formation and dry-out failure modes, reducing ionic conductivity and accelerating crack-induced LAM (Nazeeruddin et al., 17 Dec 2025, Li et al., 2023).

Models are implemented in modular simulation environments such as PyBaMM (O'Kane et al., 2021), supporting the composition of degradation submodels and enabling pathway analysis across a range of operating regimes. Parameterization relies on ex situ and operando measurements (e.g., atomic force microscopy, impedance spectroscopy, neutron imaging), but uncertainty in rate constants and transport/kinetic properties remains a critical challenge (O'Kane et al., 2021, Philipp et al., 2024).

2. Reduced-Order and Surrogate Models

While DFN-based models achieve high fidelity, their dimensionality limits real-time use. Reduced-order models are derived through asymptotic and physical simplifications:

Single Particle Models with electrolyte and Side Reactions (SPMe+SR): These are formally reduced from DFN equations, replacing detailed electrode-resolved descriptions with single-particle domains for each electrode, augmented by side-reaction layers to capture SEI and lithium plating. Validation against full DFN shows close agreement for capacity fade and impedance growth in regimes dominated by SEI or plating, but at a much lower computational cost (Planella et al., 2022).
Enhanced SPM (ESPM) for second-life scenarios: The ESPM accounts for SEI, plating, and LAM, with coupled equations for active surface area evolution. This model is parameterized against mid- and late-life data (0, 1000, 3300 cycles) and can reproduce both linear SEI-dominated and nonlinear LAM/plating-dominated capacity fade (Pozzato et al., 2021).
Universal Battery Performance and Degradation Model (UBDM): Combines mechanistic submodels for SEI, plating, and LAM with neural-ODE residuals within a lumped electrochemical–thermal framework, delivering efficient, physics-informed cycle-life forecasting for high-rate eVTOL missions (Bills et al., 2020).

Example: Table of Mechanistic Submodels for SEI and Plating

Model Framework	SEI Growth Law	Li Plating Law	Coupling Features
DFN/PyBaMM	Diffusion-limited flux	Butler–Volmer kinetics	Crack area, LAM, shared area
SPMe+SR (asymp.)	Reduced Fickian ODEs	Reduced BV/ODE system	Electrolyte ODE, film layer
ESPM	Butler–Volmer at surface	Threshold BV expression	Active area dynamics (LAM)

3. Empirical and Data-Driven Approaches

Empirical and machine learning models abstract degradation as a mapping from observed cycling or control-action features to capacity or SOH loss:

Degradation maps: Construct piecewise-affine (PWA) convex maps over discrete SoC × current (or SoE × power) grids, capturing incremental capacity loss per action. The convexity enables inclusion in energy system optimization and arbitrage (Fortenbacher et al., 2017).
Cycle-based Rainflow models: Represent degradation as a convex sum of depth-of-discharge cycle stress functions Φ(d), counted by the Rainflow algorithm. This yields a convex operational cost function, supporting subgradient optimization and guaranteeing tractable integration in battery dispatch (Shi et al., 2017).
Multivariable Fractional Polynomial (MFP) regression: Trains flexible, interpretable regression models on engineered features (historical capacities, temperature, C-rate, rest times), delivering competitive SoH prediction accuracy under stochastic loading (Salucci et al., 2021).
BatteryML platform: Provides standardized data handling, feature extraction, and benchmarking pipelines for statistical and deep models, ensuring comparability and reproducibility of RUL/SOH/SOC prediction performance (Zhang et al., 2023).
Neural-network-based per-cycle degradation models: Input features include ambient temperature, C-rate, starting SOC, DOD, and current SOH, delivering high-accuracy predictions of SOH loss per operational segment in scheduling or optimal control frameworks (Zhao et al., 2022).

4. Hybrid and Physics-Informed ML Models

Recent developments fuse physics-based structure with data-driven flexibility:

Hybrid ODE–ML models: Mechanistic ODEs for electrochemistry and basic degradation are augmented by residual terms learned via neural networks or Gaussian processes, compensating for model–data mismatch and improving generalizability and uncertainty calibration. Ensemble Kalman filtering supports real-time SOH for online BMS applications (Lin et al., 2021, Bills et al., 2020).
Contrastive and diffusion models: ACCEPT employs contrastive learning between simulated degradation curves (parameterized by LAM, SEI, plating, etc.) and observed time-series, enabling zero-shot, diagnostic capacity and mode-of-failure forecasting across chemistries (Sadler et al., 17 Jan 2025). DiffBatt introduces conditional diffusion models with transformer embedding of early-cycle features for probabilistic, generative RUL/SOH prediction and data augmentation, achieving best-in-class accuracy on standardized BatteryML benchmarks (Eivazi et al., 2024).
Chemistry-aware ML prediction: Integrates HMM-based real-world cycling protocol generation, high-throughput electrochemical measurement, polynomial-scale feature engineering, and ML for early-cycle prediction of lifetime, knee-points, and even inference of SEI chemistry clusters, thus connecting electrical observables to mechanistic failure pathways (Li et al., 25 Mar 2025).

5. Model Validation, Parameterization, and Uniqueness

A critical contemporary insight is the identification of non-uniqueness in degradation model validation. Many combinations of coupled degradation mechanisms can fit capacity and resistance fade data, but only models validated against explicit degradation modes—loss of lithium inventory (LLI), loss of active material (LAM) at both electrodes, and electrode slippage—are physically trustworthy. Degradation-mode analysis (DMA), enabled by advanced ex situ (DVA, XPS) and operando diagnostics, has emerged as the state-of-the-art requirement for model validation (Li et al., 2023, Li et al., 25 Mar 2025).

Multi-mechanism models (capturing SEI, plating, cracking, LAM, dry-out) uniquely fit DMA-extracted variables across temperature and cycling regimes, whereas “simpler” models—e.g., SEI-only or SEI+solvent—fail to match LAM differences and LLI: LAM ratios (Li et al., 2023).
Bayesian parameter estimation (EP-BOLFI, BASQ) affords credible intervals for kinetic parameters and identifies identifiability via feature correlation structure, with model selection confirming the electron-diffusion plus solvent-diffusion as the dominant mechanism for long-term SEI growth (Philipp et al., 2024).
Sigmoidal (five-parameter) regression models offer interpretable parameters for threshold/acceleration effects (knee points), with proven transferability to second-life and short-term/missing data scenarios (Johnen et al., 2019).

6. Practical Implications, Design, and Operational Guidance

Mechanistic and data-driven models support both design (cell architecture, choice of reservoir sizes, materials) and operational policies (charge/discharge profiles, temperature control, BMS algorithms):

Reservoir-based design: Framing degradation as solvation, lithium, and porosity “reservoirs” (finite and coupled) enables actionable co-optimization of electrolyte overfill, porosity gradients, and stoichiometry windows, yielding linear or super-additive increases in service life at minimal energy density penalty. Design rules emerge directly from the coupled ODEs for reservoir depletion rates (Nazeeruddin et al., 17 Dec 2025).
Optimal control and scheduling: Embedding convex or neural-network models of capacity loss in energy market arbitrage yields measurable profit and lifetime benefits over naïve or power-based cost models, shifting dispatch from “bang-bang” cycling to smooth, mid-SoC regimes (Fortenbacher et al., 2017, Shi et al., 2017, Reniers et al., 2017, Zhao et al., 2022).
Functional and longitudinal analysis: Two-step functional regression, incorporating usage covariates (temperature, current, voltage, rest time), reconstructs future voltage–discharge curves and offers improved prediction and coverage for non-stationary, heterogeneous data (Cho et al., 2022).

7. Open Challenges and Research Directions

Despite significant progress, battery degradation modeling faces challenges:

Precise parameter estimation for multiphysics, multi-mechanism models remains experimentally intensive and uncertain (O'Kane et al., 2021, Philipp et al., 2024).
Robust transfer across chemistries and dynamic protocols is nontrivial, requiring either generalized model libraries or zero-shot/transfer learning architectures (Sadler et al., 17 Jan 2025, Eivazi et al., 2024).
Real-world deployment (on-board BMS) constrains available computational resources and measurement frequency (Lin et al., 2021, Salucci et al., 2021).
Model uniqueness necessitates continued joint development of experimental DMA, cross-validatory protocols, and systematic uncertainty quantification (Li et al., 2023).
Incorporation of positive electrode degradation, calendar aging, pack-level thermal/electrical coupling, and multiscale heterogeneity is a current frontier (O'Kane et al., 2021, Nazeeruddin et al., 17 Dec 2025).

Future research emphasizes automated hybrid model-structure discovery, pretraining on foundation datasets, inversion with calibrated uncertainty, and coupling with lifetime-aware cell and pack design.