  We introduce the "ACTIONFINDER", a deep learning algorithm designed to
transform a sample of phase-space measurements along orbits in a static
potential into action and angle coordinates. The algorithm finds the mapping
from positions and velocities to actions and angles in an unsupervised way, by
using the fact that points along the same orbit have identical actions. Here we
present the workings of the method, and test it on simple axisymmetric models,
comparing the derived actions to those generated with the Torus Mapping
technique. We show that it recovers the Torus actions for halo-type orbits in a
realistic model of the Milky Way to $\sim 0.6$% accuracy with as few as 1024
input phase-space measurements. These actions are much better conserved along
orbits than those estimated with the St\"ackel fudge. In our case, the
reciprocal mapping from actions and angles to positions and velocities can also
be learned. One of the advantages of the ACTIONFINDER is that it does not
require the underlying potential to be known in advance, indeed it is designed
to return the acceleration field. We expect the algorithm to be useful for
analysing the properties of dynamical systems in numerical simulations.
However, our ultimate goal with this effort will be to apply it to real stellar
streams to recover the Galactic acceleration field in a way that is relatively
agnostic about the underlying dark matter properties or the behavior of
gravity.
