Online Dynamic Mode Decomposition: An Alternative Approach for Low Rank Datasets

In this study, we provide an alternative approach for computing the dynamic mode decomposition (DMD) in real-time for streaming datasets. It is a low-storage method that updates the DMD approx­imation of a given dynamic as new data becomes available. Unlike the standard online DMD method, which is applicable only to over­constrained and full-rank datasets, the new method is applicable for both overconstrained and underconstrained datasets. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations and is entirely data-driven. Several numerical examples are presented to demonstrate the performance of the method.