Celestial Machine Learning: Discovering the Planarity, Heliocentricity,
  and Orbital Equation of Mars with AI Feynman
Zi-Yu Khoo Gokul Rajiv Abel Yang Jonathan Sze Choong Low Stéphane Bressan
Can a machine or algorithm discover or learn the elliptical orbit of Mars
from astronomical sightings alone? Johannes Kepler required two paradigm shifts
to discover his First Law regarding the elliptical orbit of Mars. Firstly, a
shift from the geocentric to the heliocentric frame of reference. Secondly, the
reduction of the orbit of Mars from a three- to a two-dimensional space. We
extend AI Feynman, a physics-inspired tool for symbolic regression, to discover
the heliocentricity and planarity of Mars' orbit and emulate his discovery of
Kepler's first law.