Cosmological informed neural networks to solve the background dynamics
  of the Universe
  The field of machine learning has drawn increasing interest from various
other fields due to the success of its methods at solving a plethora of
different problems. An application of these has been to train artificial neural
networks to solve differential equations without the need of a numerical
solver. This particular application offers an alternative to conventional
numerical methods, with advantages such as lower memory required to store the
solutions, parallelization, and in some cases less overall computational cost
than its numerical counterparts. In this work, we train artificial neural
networks to represent a bundle of solutions of the differential equations that
govern the background dynamics of the Universe for four different models. The
models we have chosen are $\Lambda \mathrm{CDM}$, the
Chevallier-Polarski-Linder parametric dark energy model, a quintessence model
with an exponential potential, and the Hu-Sawicki $f\left(R\right)$ model. We
used the solutions that the networks provide to perform statistical analyses to
estimate the values of each model's parameters with observational data; namely,
estimates of the Hubble parameter from Cosmic Chronometers, the Supernovae type
Ia data from the Pantheon compilation, and measurements from Baryon Acoustic
Oscillations. The results we obtain for all models match similar estimations
done in the literature using numerical solvers. In addition, we estimated the
error of the solutions by comparing them to the analytical solution when there
is one, or to a high-precision numerical solution when there is not. Through
those estimations we found that the error of the solutions was at most
$\sim1\%$ in the region of the parameter space that concerns the $95\%$
confidence regions that we found using the data, for all models and all
statistical analyses performed in this work.
