  A method for machine learning and serving of discrete field theories in
physics is developed. The learning algorithm trains a discrete field theory
from a set of observational data on a spacetime lattice, and the serving
algorithm uses the learned discrete field theory to predict new observations of
the field for new boundary and initial conditions. The approach to learn
discrete field theories overcomes the difficulties associated with learning
continuous theories by artificial intelligence. The serving algorithm of
discrete field theories belongs to the family of structure-preserving geometric
algorithms, which have been proven to be superior to the conventional
algorithms based on discretization of differential equations. The effectiveness
of the method and algorithms developed is demonstrated using the examples of
nonlinear oscillations and the Kepler problem. In particular, the learning
algorithm learns a discrete field theory from a set of data of planetary orbits
similar to what Kepler inherited from Tycho Brahe in 1601, and the serving
algorithm correctly predicts other planetary orbits, including parabolic and
hyperbolic escaping orbits, of the solar system without learning or knowing
Newton's laws of motion and universal gravitation. The proposed algorithms are
also applicable when effects of special relativity and general relativity are
important. The illustrated advantages of discrete field theories relative to
continuous theories in terms of machine learning compatibility are consistent
with Bostrom's simulation hypothesis.
