  We present a method for reconstructing cosmological densityn for and velocity
fields using the Lagrangian Zel'dovich formalism. . The method involves finding
the least action solution for straight line particle paths in an evolving
density field. Our starting point is the final, evolved density , so that we
are in effect carrying out the standard Zel'dovich Approximation based process
in reverse. Using a simple numerical algorithm we are able to minimise the
action for the trajectories of several million particles. We apply our method
to the evolved density taken from N-body simulations of different cold dark
matter dominated universes, testing both the prediction for the present day
velocity field and for the initial density field. The method is easy to apply,
reproduces the accuracy of the forward Zel'dovich Approximation, and also works
directly in redshift space with minimal modification.
