How to center table on page?. Center and centering not working

Question

I am trying to center the following table. I have tried using \center and \centering after \begin{table} but it do not work. This is my code:

\documentclass{article}
\usepackage[utf8]{inputenc}

\begin{document}
\section{table of model and predictions}

\begin{table}[h]
\centering    
\begin{tabular}{lllll}
\hline
                              &  &                                            &  &                                                      \\
\multicolumn{5}{c}{Hidden Variable}                                                                                                     \\
\multicolumn{1}{c}{}          &  &                                            &  &                                                      \\ \hline
                              &  &                                            &  &                                                      \\
\textbf{Equations of motions} &  & Correct                                    &  & Rediscovered                                         \\
\textbf{}                     &  &                                            &  &                                                      \\ \hline
Saddle-Node                   &  & t                                          &  & $0.8*t + 2e-10*t^2 + 10e-4*t^3$                      \\
                              &  &                                            &  &                                                      \\
                              &  & $4\sin(t) + 9.42$                          &  & $0.17*t -2*10^{-2}*t^2+8*10^{-3} + 3.89 sin(t) + 12$ \\
Hopf                          &  & $-t+t^2-t^3$                               &  & $12.99t   -0.8t^2 +   1.06t^3$ cualitatively good    \\
\end{tabular}
\end{table}

\end{document}

Answer 1

This is because your table is too wide to put in the line, so it spans to the margin. You can see:

So you need to make adjustments to the table or change the page settings.

BTW, your empty line and column are also not recommendable which should be replaced by setting row and column separation.

EDIT

If you do want to keep this wide table, you can use \centerline,

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{lipsum}
\usepackage{graphicx}

\begin{document}
\section{table of model and predictions}

\centerline{
    \begin{tabular}{lllll}
    \hline
                                  &  &                                            &  &                                                      \\
    \multicolumn{5}{c}{Hidden Variable}                                                                                                     \\
    \multicolumn{1}{c}{}          &  &                                            &  &                                                      \\ \hline
                                  &  &                                            &  &                                                      \\
    \textbf{Equations of motions} &  & Correct                                    &  & Rediscovered                                         \\
    \textbf{}                     &  &                                            &  &                                                      \\ \hline
    Saddle-Node                   &  & t                                          &  & $0.8*t + 2e-10*t^2 + 10e-4*t^3$                      \\
                                  &  &                                            &  &                                                      \\
                                  &  & $4\sin(t) + 9.42$                          &  & $0.17*t -2*10^{-2}*t^2+8*10^{-3} + 3.89 sin(t) + 12$ \\
    Hopf                          &  & $-t+t^2-t^3$                               &  & $12.99t   -0.8t^2 +   1.06t^3$ cualitatively good    \\
    \hline
    \end{tabular}
    \vspace{1em}
}

\lipsum[1]

\end{document}

which yields