Compressive Sampling and Dynamic Mode Decomposition
These results rely on a number of theoretical advances. First, we establish connections between the full-state and projected DMD. Next, we demonstrate the invariance of the DMD algorithm to left and right unitary transformations. When data and modes are sparse in some transform basis, we show a similar invariance of DMD to measurement matrices that satisfy the so-called restricted isometry principle from compressive sampling. We demonstrate the success of this architecture on two model systems. In the first example, we construct a spatial signal from a sparse vector of Fourier coefficients with a linear dynamical system driving the coefficients. In the second example, we consider the double gyre flow field, which is a model for chaotic mixing in the ocean.