Dynamic Mode Decomposition

Dynamic Mode Decomposition

Physical systems, such as fluid flow or mechanical vibrations, behave in characteristic patterns, known as modes. In a recirculating flow, for example, one may think of a hierarchy of vortices, a big main vortex driving smaller secondary ones and so on. Most of the motion of such a system can be faithfully described using only a few of those patterns. In a purely mathematical setting similar modes can be extracted form the governing equations using an eigenvalue decomposition. But in many cases the mathematical model is very complicated or not available at all. In an experiment, the mathematical description is not at hand and one has to rely on the measured data only. The dynamic mode decomposition (DMD) is a mathematical method to extract the relevant modes from experimental data, without any recurrence to the governing equations. It can thus be applied to any dynamic phenomenon where appropriate data is available. It is similar, but different from proper orthogonal decomposition which has similar features but lacks dynamical information about the data.