Dynamic mode decomposition with core sketch

With the increase in collected data volumes, there is an ever-growing need to develop computationally efficient tools to process these data sets. Modal analysis techniques have gained significant interest due to their ability to identify patterns in the data. Dynamic mode decomposition (DMD) relies on elements of Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and decay/growth rate. Extracting these details from large data sets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and co-range of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods. The shallow water equations data is used as a prototypical model in the context of geophysical flows. We show that the proposed SketchyDMD is superior to existing randomized DMD methods based on capturing only the range of the input data.