A note on the use of Dynamic Mode Decomposition in mechanics

We advocate for the use of Dynamic Mode Decomposition (DMD) in mechanics. Snapshots of the temperature or displacement fields are obtained; and the DMD algorithm, which, remarkably, requires a few lines of code, is applied to matrices obtained by time shifting the snapshots. Only the higher-order modes are retained to obtain a lower-rank matrix and used for analysis. We show that DMD can be used to: predict temperature fields during transient heat conduction, estimate natural frequency of a linear elastic structure; identify the onset of plasticity in an elastic-plastic plate with a hole; and obtain a reduced-order model that describes the large deformation of a non-linear elastic structure.

Automated summary

We advocate for the use of Dynamic Mode Decomposition (DMD) in mechanics, which allows for the prediction of temperature fields, estimation of natural frequency, identification of plasticity onset, and generation of reduced-order models for nonlinear elastic structures.