# Bayesian Model Selection of Lithium-Ion Battery Models via Bayesian Quadrature

arXiv: https://arxiv.org/abs/2210.17299 · HTML: https://mlsanity.com/paper/2210.17299/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature](https://mlsanity.com/paper/1411.0439/) (2014)
- [Positively Weighted Kernel Quadrature via Subsampling](https://mlsanity.com/paper/2107.09597/) (2021)
- [Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination](https://mlsanity.com/paper/2206.04734/) (2022)
- [Improving Quadrature for Constrained Integrands](https://mlsanity.com/paper/1802.04782/) (2018)
- [Bayesian Parameter Estimation Applied to the Li-ion Battery Single Particle Model with Electrolyte Dynamics](https://mlsanity.com/paper/2001.09890/) (2020)
- [Identifiability and parameter estimation of the single particle lithium-ion battery model](https://mlsanity.com/paper/1702.02471/) (2017)

## Built on by (most cited first, 8 of 8)

- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spaces](https://mlsanity.com/paper/2301.11832/) (2023)
- [Machine Learning Benchmarks for the Classification of Equivalent Circuit Models from Electrochemical Impedance Spectra](https://mlsanity.com/paper/2302.03362/) (2023)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [Principled Bayesian Optimisation in Collaboration with Human Experts](https://mlsanity.com/paper/2410.10452/) (2024)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [Neural-ANOVA: Analytical Model Decomposition using Automatic Integration](https://mlsanity.com/paper/2408.12319/) (2024)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)

## Abstract (arXiv)

A wide variety of battery models are available, and it is not always obvious which model `best' describes a dataset. This paper presents a Bayesian model selection approach using Bayesian quadrature. The model evidence is adopted as the selection metric, choosing the simplest model that describes the data, in the spirit of Occam's razor. However, estimating this requires integral computations over parameter space, which is usually prohibitively expensive. Bayesian quadrature offers sample-efficient integration via model-based inference that minimises the number of battery model evaluations. The posterior distribution of model parameters can also be inferred as a byproduct without further computation. Here, the simplest lithium-ion battery models, equivalent circuit models, were used to analyse the sensitivity of the selection criterion to given different datasets and model configurations. We show that popular model selection criteria, such as root-mean-square error and Bayesian information criterion, can fail to select a parsimonious model in the case of a multimodal posterior. The model evidence can spot the optimal model in such cases, simultaneously providing the variance of the evidence inference itself as an indication of confidence. We also show that Bayesian quadrature can compute the evidence faster than popular Monte Carlo based solvers.