  \texttt{SpaceMath v.2.0} with Machine Learning is an extension of the
previous version which we implement observables related with LHC Higgs boson
data and their projections for the High Luminosity and High Energy Large Hadron
Collider. In this version we implemented processes with Flavor-Changing Neutral
Currents at tree and one-loop level, namely, i) Radiative decays
$\ell_i\to\ell_j \gamma$, ii) $\ell_i\to \ell_j \ell_k \bar{\ell}_k$ decays
($\ell_i=\tau,\,\mu$, $\ell_{j,\,k}=\mu,\,e$, with $\ell_i \neq\ell_j
\neq\ell_k$) and iii) anomalous magnetic dipole moment of the muon $\delta
a_\mu$. \texttt{SpaceMath v.2.0} is able to find allowed regions for free
parameters of models with both real and complex singlets and real and complex
doublets using the processes previously mentioned within a friendly interface
and an intuitive environment in which the user enters the couplings
symbolically, sets parameters and execute \texttt{Mathematica} in the
traditional way. As result, both tables as plots with values and areas agree
with experimental data are generated. We present examples using
\texttt{SpaceMath v.2.0} to analyze the free \textit{Two-Higgs Doublet Model of
type III} parameter space, step by step, in order to start new users in a fast
and efficient way. Finally, we have implemented in this version of
\texttt{SpaceMath} algorithms of Machine Learning to generate specific
Benchmark Points to be used directly in numerical evaluations of calculations
of physical observables.
