Battery degradation modeling is a critical aspect of optimizing performance, safety, and longevity in energy storage systems. Traditional approaches rely on either physics-based models or purely data-driven machine learning (ML) techniques. Physics-based models, grounded in electrochemical principles such as Fick’s laws of diffusion and Butler-Volmer kinetics, provide interpretability but often struggle with computational complexity and incomplete representations of real-world conditions. On the other hand, purely data-driven ML models excel at pattern recognition but lack physical consistency and may fail outside their training domains. Physics-informed neural networks (PINNs) bridge this gap by integrating known physical laws into neural network architectures, enabling hybrid models that are both accurate and generalizable.

PINNs operate by embedding physical equations directly into the loss function of a neural network. For battery degradation modeling, this means incorporating governing equations like the diffusion equation for lithium-ion transport or the Butler-Volmer equation for charge transfer kinetics. The network is trained not only on empirical data but also on residuals of these equations, ensuring that predictions adhere to fundamental physics. This approach mitigates the need for exhaustive datasets, as the physical constraints guide learning even in data-sparse regions. For example, a PINN can predict capacity fade by combining voltage and temperature measurements with degradation mechanisms described by Arrhenius kinetics.

One key advantage of PINNs is their ability to handle multi-scale and multi-physics problems. Battery degradation involves coupled phenomena—mechanical stress, thermal effects, and electrochemical reactions—occurring across different time and length scales. Traditional models often simplify these interactions, leading to inaccuracies. PINNs, however, can simultaneously learn from particle-level diffusion data and cell-level cycling data while respecting the underlying physics. This capability is particularly valuable for predicting heterogeneous degradation, such as lithium plating or solid-electrolyte interphase (SEI) growth, where localized effects dominate.

Another benefit is robustness in extrapolation. Pure ML models may produce unphysical results when applied to conditions outside their training range, such as extreme temperatures or high C-rates. PINNs, constrained by physical laws, maintain plausible behavior even in untested scenarios. For instance, a PINN trained on moderate cycling data can still predict degradation under accelerated aging conditions by leveraging the embedded Arrhenius relationship. This property is crucial for applications like electric vehicles, where batteries operate across diverse environments.

Despite their promise, implementing PINNs for battery degradation modeling presents several challenges. The first is the selection and formulation of appropriate physical constraints. While equations like Fick’s law are well-established, their numerical implementation within a neural network requires careful discretization and scaling. Poorly chosen constraints can lead to stiff optimization problems or conflicting gradients during training. Additionally, the balance between data-driven and physics-driven terms in the loss function must be tuned to avoid overfitting or underfitting. Too much emphasis on physics may ignore valuable empirical trends, while too little may reintroduce unphysical artifacts.

Computational cost is another hurdle. Training PINNs often involves solving partial differential equations (PDEs) iteratively, which can be resource-intensive compared to standard ML models. Techniques like adaptive sampling or reduced-order modeling can alleviate this burden, but they add complexity to the implementation. Furthermore, the interpretability of PINNs, while better than pure ML, still lags behind traditional physics-based models. Extracting explicit degradation mechanisms from the network’s weights remains an open research question.

Case studies demonstrate the potential of PINNs in hybrid modeling frameworks. In one example, researchers applied a PINN to predict capacity fade in lithium-ion batteries by combining cycling data with a simplified degradation model incorporating SEI growth and lithium plating. The hybrid approach achieved higher accuracy than either physics-based or ML models alone, particularly in predicting long-term fade trajectories. Another study focused on thermal runaway prediction, where a PINN integrated heat generation equations with real-time temperature measurements to forecast failure events. The model successfully identified early warning signs missed by conventional methods.

A notable application is the use of PINNs for state of health (SOH) estimation. By encoding degradation physics into the network, PINNs can provide real-time SOH updates without requiring full electrochemical simulations. This capability is especially useful for battery management systems (BMS), where computational resources are limited. In a comparative study, PINN-based SOH estimators outperformed both equivalent circuit models and recurrent neural networks in terms of accuracy and robustness to sensor noise.

The integration of PINNs with digital twin technologies further enhances their utility. A digital twin of a battery system can leverage PINNs to continuously update degradation predictions based on operational data, enabling proactive maintenance and optimized charging strategies. For example, a PINN-informed digital twin could adjust charging protocols to minimize SEI growth while maximizing energy throughput, extending battery life without sacrificing performance.

Future directions for PINNs in battery degradation modeling include the incorporation of more complex physics, such as mechanical strain effects or multi-particle interactions. Advances in neural network architectures, like attention mechanisms or graph neural networks, may also improve the handling of spatially heterogeneous degradation. Additionally, the development of standardized benchmarks and open-source frameworks will accelerate adoption across academia and industry.

In summary, physics-informed neural networks represent a powerful paradigm for battery degradation modeling, combining the strengths of data-driven learning and physical principles. Their ability to handle multi-physics problems, robust extrapolation, and real-time applications makes them well-suited for the complexities of energy storage systems. While challenges remain in implementation and interpretability, ongoing research and case studies underscore their potential to transform battery management and design. As the demand for reliable and long-lasting batteries grows, PINNs offer a promising path toward more accurate and physically consistent degradation predictions.