Characterization of elastic topological states using dynamic mode decomposition

TL;DR

This paper introduces a data-driven method using dynamic mode decomposition to identify and predict elastic topological states, enhancing understanding and classification of topological phenomena in materials.

Contribution

The study presents a novel application of dynamic mode decomposition for characterizing and predicting elastic topological states from propagation data.

Findings

Successfully classified topological vs. traditional metamaterials using DMD modes

Enabled prediction of topological state propagation along interfaces

Demonstrated the approach's potential for data-driven discovery in material physics

Abstract

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.