Abstract: Classical matrix completion methods focus on data with stationary latent structure and hence are not effective in missing value imputation when the latent structure changes with time. This paper proposes a dynamic nonlinear matrix completion (D-NLMC) method, which is able to recover the missing values of streaming data when the low-dimensional nonlinear latent structure of the data changes with time. We provide an efficient method to update the nonlinear model dynamically. It incorporates the information of the new data and remove the information of the earlier data recursively. We show that the missing data can be estimated if the change of latent structure is slow enough. Different from existing online or adaptive low-rank matrix completion methods, our method does not require the local low-rank assumption and is able to adaptively recover high-rank matrices with low-dimensional latent structures. Note that existing high-rank matrix completion methods have high-computational costs and are not applicable to streaming data with varying latent structures, which fortunately can be handled by our D-NLMC efficiently and accurately. Numerical results show that D-NLMC is more effective than the baselines.