  We investigate the use of machine learning for solving analytic problems in
theoretical physics. In particular, symbolic regression (SR) is making rapid
progress in recent years as a tool to fit data using functions whose overall
form is not known in advance. Assuming that we have a mathematical problem that
is posed analytically, e.g.~through equations, but allows easy numerical
evaluation of the solution for any given set of input variable values, one can
generate data numerically and then use SR to identify the closed-form function
that describes the data, assuming that such a function exists. In addition to
providing a concise way to represent the solution of the problem, such an
obtained function can play a key role in providing insight and allow us to find
an intuitive explanation for the studied phenomenon. We use a state-of-the-art
SR package to demonstrate how an exact solution can be found and make an
attempt at solving an unsolved physics problem. We use the Landau-Zener problem
and a few of its generalizations as examples to motivate our approach and
illustrate how the calculations become increasingly complicated with increasing
problem difficulty. Our results highlight the capabilities and limitations of
the presently available SR packages, and they point to possible modifications
of these packages to make them better suited for the purpose of finding exact
solutions as opposed to good approximations. Our results also demonstrate the
potential for machine learning to tackle analytically posed problems in
theoretical physics.
