Accurate capacity estimation is essential in a board range of battery applications. Because of the highly nonlinearity in the battery aging mechanism, recent works employ many supervised learning methods, which assume training and testing battery samples are generated from the same sample distribution. However, it is common for different battery data sets to have some extent of distribution shifts caused by different battery sizes, testing environments and historical load patterns.

In this work, we consider the scenario when only a few of labeled samples from the testing data set are available and formulate the battery estimation problem as a semi-supervised transfer learning problem. Inspired by JDOT, an unsupervised joint distribution domain adaptation algorithm based on optimal transport, we propose Semi-JDOT for regression problems where the source and the target label distributions have unequal supports. Our approach incorporates prior information of the labeled target samples as additional constraints and can be solved analytically. We conduct comprehensive experiments on a number of distinct battery data sets. The results show that the proposed approach outperforms existing supervised and semi-supervised methods by 10-30% under various few-shot experiment settings.