The ACTIONFINDER: An Unsupervised Deep Learning Algorithm for Calculating Actions and the Acceleration Field from a Set of Orbit Segments

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