  Elastic topological states have been receiving increased intention in
numerous scientific and engineering fields due to their defect-immune nature,
resulting in applications of vibration control and information processing.
Here, we present the data-driven discovery of elastic topological states using
dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved
from the propagation of the relevant states along the topological boundary,
where their nature is learned by DMD. Applications such as classification and
prediction can be achieved by the underlying characteristics from DMD. We
demonstrate the classification between topological and traditional
metamaterials using DMD modes. Moreover, the model enabled by the DMD modes
realizes the prediction of topological state propagation along the given
interface. Our approach to characterizing topological states using DMD can pave
the way towards data-driven discovery of topological phenomena in material
physics and more broadly lattice systems.
