  We use Topological Data Analysis to study the post buckling behavior of
laboratory scale cylindrical silos under gravity driven granular discharges.
Thin walled silos buckle during the discharge if the initial height of the
granular column is large enough. The deformation of the silo is reversible as
long as the filling height does not exceed a critical value, $L_c$. Beyond this
threshold the deformation becomes permanent and the silo often collapses. We
study the dynamics of reversible and irreversible deformation processes,
varying the initial filling height around $L_c$. We find that all reversible
processes exhibit striking similarities and they alternate between regimes of
slow and fast dynamics. The patterns that occur at the beginning of
irreversible deformation processes are topologically very similar to those that
arise during reversible processes. However, the dynamics of reversible and
irreversible processes is significantly different. In particular, the evolution
of irreversible processes is much faster. This allows us to make an early
prediction of the collapse of the silo based solely on observations of the
deformation patterns.
