PiDDM: Physics-Informed Differentiable Degradation Modeling for Lithium-Ion Battery State-of-Health Prediction

Technical Summary: PiDDM for Lithium-Ion Battery SOH Prediction

Problem Statement
Accurate prediction of the State-of-Health (SOH) for lithium-ion batteries is critical for the reliability of modern energy storage systems. While data-driven machine learning models have shown promise, they often suffer from poor generalization across different cycling protocols and may generate physically implausible predictions, such as non-physical capacity regeneration, during long-term extrapolation. Conversely, purely physics-based models (e.g., porous electrode models) offer mechanistic insights but require extensive parameterization and calibration, making them difficult to deploy in practical settings where routine measurements lack the necessary observability. The challenge lies in developing a model that retains physical grounding to ensure robustness across diverse operating conditions without sacrificing the flexibility of data-driven learning.

Methodology: Physics-Informed Differentiable Degradation Modeling (PiDDM)
The authors propose PiDDM, a framework that integrates empirical degradation kinetics directly into the training objective of a neural network. Unlike standard Physics-Informed Neural Networks (PINNs) that impose generic residual penalties, PiDDM embeds a specific, differentiable degradation-rate prior derived from battery aging mechanisms.

• Degradation Mechanism: The model focuses on two primary aging modes: Solid Electrolyte Interphase (SEI) growth and Loss of Lithium Inventory (LLI). The degradation rate is formulated using an Arrhenius–power-law relation (Eq. 1) that accounts for:
  • Thermal acceleration: Modeled via an Arrhenius term dependent on absolute temperature ($T$).
  • Cycling severity: Modeled via power-law terms dependent on Depth of Discharge (DoD) and accumulated ampere-hour throughput ($Ah$).
  • Time dependence: A power-law term for time ($t$) representing SEI growth.
• Network Architecture:
  • Input: A 16-dimensional vector of statistical features extracted from the constant-current (CC) and constant-voltage (CV) charging phases (e.g., voltage response, current decay, entropy descriptors).
  • Neural Network: A fully connected network maps these features to five effective, cycle-dependent kinetic parameters ($\hat{E}_{SEI}, \hat{\alpha}, \hat{E}_{LLI}, \hat{b}_1, \hat{b}_2$).
  • Differentiable Module: These parameters, combined with global trainable pre-exponential factors ($k_{SEI}, k_{LLI}$) and known operating variables, are fed into the degradation rate equation.
  • Output: The predicted capacity trajectory is generated by numerically integrating the degradation rate over time using a forward-Euler scheme, starting from an initial measured capacity.
• Training Objective: The model minimizes the mean squared error between predicted and observed SOH while enforcing the physics-based degradation structure. This acts as an inductive bias, constraining the learned trajectory to be monotonic and thermally consistent.

Key Contributions

1. Novel Framework: Introduction of PiDDM, which treats empirical degradation kinetics as a differentiable constraint within the neural network training loop, rather than as a rigid forward model or a generic penalty.
2. Physical Consistency: The formulation explicitly enforces the physically expected direction of capacity fade (monotonic decrease) and incorporates thermal and cycling severity dependencies, preventing non-physical artifacts like capacity regeneration.
3. Generalization: The approach is designed to generalize across diverse operating protocols (constant current, random walk, satellite mission profiles) without extensive retraining for each new condition.

Results
The framework was evaluated on a public dataset containing 55 NCM batteries cycled under six distinct protocols. Performance was compared against a standard Multilayer Perceptron (MLP) and a baseline PINN.

• Standard Prediction: PiDDM achieved the lowest average prediction error across all metrics (MAPE, RMSE, MAE, MSE) compared to the MLP and baseline PINN. The improvement was particularly notable in dynamic protocols (Random Walk and Satellite), where PiDDM better captured temporal degradation trends.
• Extrapolation: In tests where models were trained on only the first 90% of a battery's life and evaluated on the remaining 10%, PiDDM demonstrated superior stability.
  • The MLP exhibited unstable oscillatory behavior and noise in long-horizon predictions.
  • The baseline PINN occasionally produced non-physical upward fluctuations (capacity regeneration).
  • PiDDM successfully captured the accelerated end-of-life degradation knee while maintaining a smooth, monotonic trajectory.
• Trade-off: The authors note that for the R2.5 protocol, where ground-truth data contained localized upward fluctuations (likely noise or artifacts), PiDDM's strict adherence to monotonic degradation resulted in slightly higher absolute mean error compared to the baseline PINN. However, PiDDM maintained lower RMSE and MSE, indicating better robustness against outliers.

Significance and Claims
The paper claims that incorporating degradation physics into neural network training significantly improves both predictive accuracy and physical consistency, particularly in extrapolation scenarios. The authors posit that PiDDM offers a promising framework for practical battery health monitoring by balancing the flexibility of data-driven learning with the stability of physical laws. The study suggests that while the model may not perfectly track every local fluctuation in noisy experimental data, its ability to avoid non-physical predictions makes it more reliable for real-world applications where robustness is paramount. Future work is identified as extending the framework to include additional variables like time-varying temperature and internal resistance, and testing across broader battery chemistries.