# Physics‐Based Inverse Modeling of Battery Degradation with Bayesian Methods

## TL;DR

This paper uses Bayesian methods to improve the understanding of battery degradation processes, enabling better parameterization and uncertainty quantification.

## Contribution

The paper introduces Bayesian methods like EP-BOLFI and BASQ to efficiently parameterize and validate complex battery degradation models.

## Key findings

- EP-BOLFI successfully parameterizes SEI growth models with synthetic and real data.
- Bayesian methods provide uncertainty quantification with less computational effort than traditional methods.
- Electron diffusion is identified as the best model for SEI growth during battery storage.

## Abstract

To further improve lithium‐ion batteries, a profound understanding of complex battery processes is crucial. Physical models offer understanding but are difficult to validate and parameterize. Therefore, automated machine‐learning methods are necessary to evaluate models with experimental data. Bayesian methods, e.g., Expectation Propagation + Bayesian Optimization for Likelihood‐Free Inference (EP‐BOLFI), stand out as they capture uncertainties in models and data while granting meaningful parameterization. An important topic is prolonging battery lifetime, which is limited by degradation, such as the solid‐electrolyte interphase (SEI) growth. As a case study, EP‐BOLFI is applied to parametrize SEI growth models with synthetic and real degradation data. EP‐BOLFI allows for incorporating human expertise in the form of suitable feature selection, which improves the parametrization. It is shown that even under impeded conditions, correct parameterization is achieved with reasonable uncertainty quantification, needing less computational effort than standard Markov Chain Monte Carlo methods. Additionally, the physically reliable summary statistics show if parameters are strongly correlated and not unambiguously identifiable. Further, Bayesian Alternately Subsampled Quadrature (BASQ) is investigated, which calculates model probabilities, to confirm electron diffusion as the best theoretical model to describe SEI growth during battery storage.

Active parameterization of physics‐based models is essential to drive battery science. However, due to the model's complexity, parameterization is an ill‐posed problem with uncertainties in models and data. In this article, Bayesian methods are applied to physical degradation models to show sample‐efficient parameterization with uncertainty quantification. Physical conclusions, parameter dependencies, and model selection are derived using Bayesian statistics.© 2025 WILEY‐VCH GmbH