  A technique to forecast spatiotemporal time series is presented. it uses a
Proper Ortogonal or Karhunen-Lo\`{e}ve Decomposition to encode large
spatiotemporal data sets in a few time-series, and Genetic Algorithms to
efficiently extract dynamical rules from the data. The method works very well
for confined systems displaying spatiotemporal chaos, as exemplified here by
forecasting the evolution of the onedimensional complex Ginzburg-Landau
equation in a finite domain.
