data matrices $X$ and $\dot{X}$, see Eq. , . $$\begin{aligned}
\label{eq:dataMatricesX}
    X &= \begin{bmatrix}
        x^T(t_1) \\ 
        x^T(t_2) \\
        \vdots \\
        x^T(t_m)
    \end{bmatrix}
    =   \newcommand{\mymatrix}[1]{\ensuremath{\overset{\xrightarrow[\hphantom{#1}]{\text{\scriptsize States}}}{#1}\left\downarrow\vphantom{#1}\right.}}
    \mymatrix{\begin{bmatrix}
        x_1(t_1)    &   x_2(t_1)    & \dots &   x_n(t_1) \\
        x_1(t_2)    &   x_2(t_2)    & \dots &   x_n(t_2) \\
        \vdots      &   \vdots      & \ddots&   \vdots   \\
        x_1(t_m)    &   x_2(t_m)    & \dots &   x_n(t_m) \\
        \end{bmatrix}}
        \text{\scriptsize Time}
\\
\dot{X} &=
\begin{bmatrix}
\dot{x}^T (t_1) \\ 
\dot{x}^T (t_2) \\
\vdots \\
\dot{x}^T (t_m)
\end{bmatrix}
= \begin{bmatrix}
    \dot{x}_1(t_1)  &   \dot{x}_2(t_1)  & \dots &   \dot{x}_n(t_1) \\
    \dot{x}_1(t_2)  &   \dot{x}_2(t_2)  & \dots &   \dot{x}_n(t_2) \\
    \vdots      &   \vdots      & \ddots&   \vdots   \\
    \dot{x}_1(t_m)  &   \dot{x}_2(t_m)  & \dots &   \dot{x}_n(t_m) 
    \end{bmatrix}
    \label{eq:dataMatricesXdot}\end{aligned}$$

As a next step, a library $\Theta(X)$ is built from candidate functions, in which $X$ is evaluated. Typical candidates are polynomials, trigonometric functions and constants, but arbitrary functions can be included as well. An example is given in Eq. . $$\begin{aligned}
\Theta(X)\!= \!
\begin{bmatrix}
\vline  &\vline & \vline    &\vline     &       &   \vline  & \vline  &         & \\
1       &   X   & X^{P_2}   & X^{P_3}   & \!\dots\! & \sin(X)   & \cos(X) & \!\dots\!   & e^X  \\
\vline  &\vline & \vline    &\vline     &       &   \vline  & \vline  &         &
\end{bmatrix}
\label{eq:bibliothekStruktur}\end{aligned}$$

The terms 