  We address the problem of predicting the zero-temperature dynamical stability
(DS) of a periodic crystal without computing its full phonon band structure.
Here we report the evidence that DS can be inferred with good reliability from
the phonon frequencies at the center and boundary of the Brillouin zone (BZ).
This analysis represents a validation of the DS test employed by the
Computational 2D Materials Database (C2DB). For 137 dynamically unstable 2D
crystals, we displace the atoms along an unstable mode and relax the structure.
This procedure yields a dynamically stable crystal in 49 cases. The elementary
properties of these new structures are characterised using the C2DB workflow,
and it is found that their properties can differ significantly from those of
the original unstable crystals, e.g. band gaps are opened by 0.3 eV on average.
All the crystal structures and properties are available in the C2DB. Finally,
we train a classification model on the DS data for 3295 2D materials in the
C2DB using a representation encoding the electronic structure of the crystal.
We obtain an excellent receiver operating characteristic (ROC) curve with an
area under the curve (AUC) of 0.90, showing that the classification model can
drastically reduce computational efforts in high-throughput studies.
