# Augmented Physics-Based Li-ion Battery Model via Adaptive Ensemble Sparse Learning and Conformal Prediction

arXiv: https://arxiv.org/abs/2507.00353 · HTML: https://mlsanity.com/paper/2507.00353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression](https://mlsanity.com/paper/2307.08107/) (2023)
- [Integrating Physics-Based Modeling with Machine Learning for Lithium-Ion Batteries](https://mlsanity.com/paper/2112.12979/) (2021)
- [Improving Low-Fidelity Models of Li-ion Batteries via Hybrid Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2411.12935/) (2024)
- [Combining physics-based and machine learning methods to accelerate innovation in sustainable transportation and beyond: a control perspective](https://mlsanity.com/paper/2305.04840/) (2023)
- [Real-Time Optimal Design of Experiment for Parameter Identification of Li-Ion Cell Electrochemical Model](https://mlsanity.com/paper/2504.15578/) (2025)

## Abstract (arXiv)

Accurate electrochemical models are essential for the safe and efficient operation of lithium-ion batteries in real-world applications such as electrified vehicles and grid storage. Reduced-order models (ROM) offer a balance between fidelity and computational efficiency but often struggle to capture complex and nonlinear behaviors, such as the dynamics in the cell voltage response under high C-rate conditions. To address these limitations, this study proposes an Adaptive Ensemble Sparse Identification (AESI) framework that enhances the accuracy of reduced-order li-ion battery models by compensating for unpredictable dynamics. The approach integrates an Extended Single Particle Model (ESPM) with an evolutionary ensemble sparse learning strategy to construct a robust hybrid model. In addition, the AESI framework incorporates a conformal prediction method to provide theoretically guaranteed uncertainty quantification for voltage error dynamics, thereby improving the reliability of the model's predictions. Evaluation across diverse operating conditions shows that the hybrid model (ESPM + AESI) improves the voltage prediction accuracy, achieving mean squared error reductions of up to 46% on unseen data. Prediction reliability is further supported by conformal prediction, yielding statistically valid prediction intervals with coverage ratios of 96.85% and 97.41% for the ensemble models based on bagging and stability selection, respectively.