Automated Battery Model Selection with Bayesian Quadrature and Bayesian Optimization

In the process of constructing physics-based battery models, there are usually several candidate submodels for any mechanism of interest, as seen in the modular battery model software PyBaMM [1]. Parameterizing such varied model sets is a challenging task, since developing a specialized routine for each combination of submodels is unfeasible. Aitio et al. have shown that Metropolis-Hastings can di- rectly fit a model to measured voltage [2]. Kuhn et al. have shown that Metropolis-Hastings scales poorly when the models or measurements get more involved [3]. Hence, they propose EP-BOLFI as an alter- native, which can parameterize a wide variety of models reliably, and do it faster as well. But, a well parameterized model does not imply that the data supports that model. Adachi, Kuhn et al. have shown that the closeness of the fitted model to the data is not a reliable measure [4]. Hence, EP-BOLFI does not help in selecting a model. Instead, they propose a Bayesian Quadrature approach for model selection, BASQ [5]. The caveat is that BASQ needs to perform a successful parameterization to then give good measures for model quality. And the result of BASQ depends on the randomly chosen model evaluations it is initialized with. In contrast, if the optimal parameter set is within the prior bounds, Metropolis-Hastings and EP-BOLFI have a much higher chance to eventually reach that optimum. In this work, we investigate if the stability of EP-BOLFI can supplement BASQ. We showcase this on the example used in Ref. 4, the selection of the number of RC-pairs in a R-RC-RC-etc. equivalent circuit model. We find that preconditioning the prior probability distribution with EP-BOLFI before giving it to BASQ can improve the parameterization, and hence, the model selection success rate