Machine Learning for Lithium-Ion Battery Voltage Modeling: Insights from NARX-RNN, Deep Koopman, and LSTM-NARX

As global energy demand surges, lithium-ion batteries play a pivotal role in enabling renewable energy integration and advancing electrified transportation—both essential for energy independence and environmental sustainability. Their widespread adoption hinges on ensuring long-term reliability, operational resilience, and functional safety. Battery Management Systems (BMS) are central to this mission, requiring accurate internal models for control, monitoring, and diagnostics. Although physics-based models offer interpretability, their computational complexity limits flexibility. Reduced-order models mitigate this, but often lack generalization under dynamic loading. With the growing availability of high-resolution sensor data, data-driven modeling techniques provide a scalable and accurate alternative. This work investigates learning-based approaches to model battery terminal voltage dynamics using current and historical voltage inputs. We evaluated and compared three architectures: Nonlinear AutoRegressive models with eXogenous inputs (NARX-RNN), Deep Koopman Operator networks that embed nonlinear behavior into latent linear dynamics, and LSTM-based NARX models for temporal pattern learning. The models are trained on experimental datasets and assessed in both steady-state and transient scenarios. Results demonstrate high predictive accuracy and robustness, highlighting their value in BMS development, offline diagnostics, and accelerated testing for safer and more intelligent energy storage systems.