A Primer on Bayesian Parameter Estimation and Model Selection for Battery Simulators

TL;DR

The paper tackles the challenge of aligning physics-based battery simulators with experimental data by advancing Bayesian parameter estimation and model selection. It introduces SOBER (Bayesian optimisation for parameter estimation) and BASQ (Bayesian quadrature) as a paired framework to perform efficient inference and principled model comparison, even when the likelihood is intractable. Through six diverse battery-focused examples—ranging from sizing and voltage relaxation to degradation knee points, inverse surrogates, electrolyte identifiability, and impedance model selection—it demonstrates data-informed model development and quantified uncertainty. The work provides a practical toolbox integrated with PyBOP that can accelerate discovery of new battery materials and model structures, leveraging Bayesian evidence to balance model fit and complexity and enabling scalable, parallelised inference.

Abstract

Physics-based battery modelling has emerged to accelerate battery materials discovery and performance assessment. Its success, however, is still hindered by difficulties in aligning models to experimental data. Bayesian approaches are a valuable tool to overcome these challenges, since they enable prior assumptions and observations to be combined in a principled manner that improves numerical conditioning. Here we introduce two new algorithms to the battery community, SOBER and BASQ, that greatly speed up Bayesian inference for parameterisation and model comparison. We showcase how Bayesian model selection allows us to tackle data observability, model identifiability, and data-informed model development together. We propose this approach for the search for battery models of novel materials.

Figures (19)

• Figure 1: Illustration of the relation between model and LFI likelihood surrogate, which here is calculated via SOBER.
• Figure 2: Extra lifetime of a solar panel battery oversized to avoid high charge states. Time to end-of-life (blue, solid) increases with extra capacity, but there is an optimum lifetime gain per extra capacity (orange) at around 10% extra. Bayesian optimisation estimates a posterior (blue, dashed) that encodes the most relevant part of the gain function.
• Figure 3: Parameterisation posterior for a silicon electrode voltage relaxation model. We employ a visualisation suitable for several dimensions: the diagonal shows marginal distributions of each individual parameter; off-diagonals show joint distributions of parameter pairs. Joint distributions are visualised as contour plots, with each contour denoting one shared probability value.
• Figure 4: Correlation matrix of multivariate normal approximation of fig:parameterisation_posterior. To emphasise parameter interchangeability, we show off-diagonal covariances divided by square-root of the corresponding variances on the diagonal.
• Figure 5: Measurement of silicon electrode voltage relaxation, alongside representative model evaluations from the parameterised model. These are coloured according to the posterior probability density function.