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We introduce the "ACTIONFINDER", a deep learning algorithm designed totransform a sample of phase-space measurements along orbits in a staticpotential into action and angle coordinates. The algorithm finds the mappingfrom positions and velocities to actions and angles in an unsupervised way, byusing the fact that points along the same orbit have identical actions. Here wepresent the workings of the method, and test it on simple axisymmetric models,comparing the derived actions to those generated with the Torus Mappingtechnique. We show that it recovers the Torus actions for halo-type orbits in arealistic model of the Milky Way to $\sim 0.6$% accuracy with as few as 1024input phase-space measurements. These actions are much better conserved alongorbits than those estimated with the St\"ackel fudge. In our case, thereciprocal mapping from actions and angles to positions and velocities can alsobe learned. One of the advantages of the ACTIONFINDER is that it does notrequire the underlying potential to be known in advance, indeed it is designedto return the acceleration field. We expect the algorithm to be useful foranalysing the properties of dynamical systems in numerical simulations.However, our ultimate goal with this effort will be to apply it to real stellarstreams to recover the Galactic acceleration field in a way that is relativelyagnostic about the underlying dark matter properties or the behavior ofgravity.

The ACTIONFINDER: An unsupervised deep learning algorithm for calculating actions and the acceleration field from a set of orbit segments