Physics-based and empirical degradation modeling approaches offer distinct advantages and challenges in predicting battery aging. The choice between these methods depends on computational resources, available data, and required accuracy. Three prominent techniques—pseudo-two-dimensional (P2D) models, equivalent circuit models (ECMs), and data-driven fits—serve different purposes across cell-to-pack scales. Hybrid approaches combine their strengths to improve predictive capabilities.

Physics-based models, such as P2D models, derive from first principles of electrochemistry and transport phenomena. These models solve coupled partial differential equations to describe lithium-ion concentration, potential distribution, and reaction kinetics across electrodes and electrolytes. Computational complexity is high, often requiring hours to days for full-cycle simulations on high-performance systems. Parameterization demands are stringent, needing detailed material properties like diffusion coefficients, kinetic rate constants, and electrode porosity. However, their accuracy in capturing degradation mechanisms—such as solid-electrolyte interphase (SEI) growth, lithium plating, and active material loss—is well-documented. P2D models excel at isolating root causes of aging but are impractical for large-scale systems due to computational overhead.

Equivalent circuit models simplify battery behavior using electrical components like resistors, capacitors, and voltage sources. ECMs parameterize these components from experimental data, such as impedance spectra or discharge curves. Computational requirements are minimal, enabling real-time or faster-than-real-time simulations on embedded systems. Parameterization relies on fitting to voltage-current responses, requiring fewer inputs than P2D models. However, ECMs lack intrinsic degradation mechanisms; aging effects are often incorporated via empirical adjustments to component values. For example, resistance increase over cycles may represent SEI growth, but this correlation is indirect. While ECMs are scalable to pack-level simulations, their predictive accuracy diminishes without frequent recalibration.

Data-driven fits use statistical or machine learning techniques to correlate aging with operational variables like temperature, depth of discharge, and charge rates. These models require no prior knowledge of battery physics but depend heavily on large, high-quality datasets. Computational complexity varies: linear regressions are lightweight, while neural networks demand more resources. Parameterization involves training on historical degradation data, making predictions sensitive to dataset representativeness. Data-driven models perform well in interpolating within observed conditions but struggle with extrapolation to unseen scenarios. Their black-box nature also limits interpretability of underlying degradation processes.

Hybrid approaches merge physics-based and empirical methods to balance accuracy and efficiency. One common strategy embeds reduced-order physical models within data-driven frameworks. For instance, a P2D model might simulate electrode-level degradation, while a surrogate model approximates its outputs for faster pack-level predictions. Another approach augments ECMs with physics-inspired degradation terms, such as Arrhenius-based aging rates for temperature effects. Hybrid models are particularly effective at bridging cell-to-pack scales. At the cell level, physical mechanisms guide degradation predictions; at the pack level, empirical approximations reduce computational load. However, hybrid models inherit some complexity from their physics-based components and require careful validation across scales.

The table below summarizes key attributes of each approach:

Approach Computational Complexity Parameterization Needs Prediction Accuracy
P2D Models High Extensive material data High (mechanistic)
ECMs Low Fitted circuit parameters Medium (empirical)
Data-Driven Fits Variable Large degradation datasets High (interpolation)
Hybrid Models Moderate Mixed physical/empirical High (balanced)

Application scales further differentiate these methods. P2D models are typically confined to single-cell analysis due to computational constraints. ECMs extend to modules and packs by replicating circuit networks, though homogenization errors may arise. Data-driven fits scale efficiently if training data covers diverse pack conditions. Hybrid models are most versatile, applying mechanistic insights at the cell level while leveraging empirical simplifications for larger systems.

In practice, the selection between physics-based and empirical modeling depends on the use case. P2D models suit detailed degradation studies in research or materials development. ECMs are preferred for battery management systems requiring real-time updates. Data-driven fits work well when historical data is abundant and conditions are stable. Hybrid approaches offer a middle ground for applications like pack lifetime estimation or warranty forecasting.

Tradeoffs between interpretability and computational cost persist across all methods. Physics-based models provide clear mechanistic insights but are resource-intensive. Empirical models are lightweight but less transparent. Hybrid solutions aim to mitigate these tradeoffs but require careful integration. Future advancements may further blur the lines between these approaches, enabling more accurate and scalable degradation predictions.