Conditional Wasserstein barycenters to predict battery health degradation at unobserved experimental conditions

Modeling the health degradation process of batteries is a fundamental need for manufacturers. It allows one to anticipate how long the battery will be useful in application and to what performance level. Since degradation strongly depends on the operating conditions (ambient temperature, charging and discharging policy...), degradation should be modeled for a full range of conditions. However, a serious obstacle in this task is the small number of tested experimental conditions, potentially separated by strong performance differences. To handle this issue, while keeping the interesting results previously obtained for a fixed experimental condition, we propose a two-step methodology, separating the time degradation from the effect of experimental factors. Time modeling is handled by previously developed methods, and the effect of experimental factors is handled by a model-based approach, allowing the inclusion of physical prior knowledge with more robust predictions. This article focuses on this second step which requires particular developments, with a regression method over complex objects. This is handled using optimal transport theory thanks to dedicated Conditional Wasserstein barycenters models.