Phase Transitions in the Dynamic Mode Decomposition Algorithm

We analyze the Dynamic Mode Decomposition (DMD) algorithm in the noisy data setting. Previous work has shown that DMD is a source separation algorithm in disguise, i.e., that it is capable of unmixing linearly mixed time series. In this work, we analyze the performance of DMD when the mixed time series are corrupted by noise. We demonstrate that a preprocessing step of the truncated SVD before applying DMD yields significant benefits, and quantify the performance of the truncated-SVD-plus-DMD (tSVD-DMD) algorithm using tools from random matrix theory. We validate our findings with numerical simulations.