Inverse Cosmography: testing the effectiveness of cosmographic
  polynomials using machine learning
  Cosmography has been referred to as a solution to the inverse scattering
problem, which is reasonable since it allows us to calculate cosmological
bounds from data samplers by performing an expansion of the cosmological
observables around present time. Nevertheless, this approach is not properly an
inverse scattering solution since the method only circumvents the problem to
fit the equation of state (EoS) parameters (model-dependent) by replacing it
with their fit of its cosmographic parameters (with a polynomial
series-dependence). Therefore, can we construct a new cosmography approach
where the cosmodynamical parameters can be fitted and then employ them to
analyse the kinematics via its generic cosmographic parameters? By all means,
without experimenting the problem of truncation of the series that all
cosmography proposals in the literature argue. In this work we present a
generic EoS depending solely on the form of $f_i(z)$ and its derivative is
found, where this function can be any polynomial (mimicking a dark energy-like
term) that allow the dynamics of a specific cosmological density. We test our
generic EoS with standard cosmological models and with polynomials proposals as
Pad\'e and Chebyshev approximants. Interesting enough, a Pad\'e (2,2)
approximant has been considered inside a $f(z)$CDM-like model showing a
transition in $z=1$. Also, we found that this is not assured since models with
these characteristics have degeneracy and truncation problems that experiment a
divergence at this redshift limit. To explore our results, also we present a
new supernovae sample trained via a deep learning tool called
Recurrent-Bayesian (RNN+BNN) network that can solve problems as overfitting at
lower redshifts and increase the density of data points in this region, which
can help to discern between cosmographies at 2-$\sigma$ of precision.
