  An extremely challenging problem of significant interest is to predict
catastrophes in advance of their occurrences. We present a general approach to
predicting catastrophes in nonlinear dynamical systems under the assumption
that the system equations are completely unknown and only time series
reflecting the evolution of the dynamical variables of the system are
available. Our idea is to expand the vector field or map of the underlying
system into a suitable function series and then to use the compressive-sensing
technique to accurately estimate the various terms in the expansion. Examples
using paradigmatic chaotic systems are provided to demonstrate our idea.
