analyze the effect of delay.

The simulation is implemented in Simulink^^. For this example, 20 different settings were processed, whereof 16 served as training- and four as validation set. The dynamics of the tank system is given in Eq. . $$\begin{aligned}
\begin{split}
\label{eq:tank_dynamics}
    h(t+1) = h(t) + u(t-l_p) + Q_{out} \text{, with } \\
    u(t) =  \begin{cases}
    Q_{in}, & \text{if pump on.} \\
    0, & \text{if pump off.}
    \end{cases}
\end{split}\end{aligned}$$ As a result, the pump works in rectangular pulses and the water level changes in a saw-tooth curve.

Influence of polynomial degree
------------------------------

The library prepared for SINDy consists of polynomials and hysterons. In a first experiment, we vary the degree of the polynomials. Figure \[fig:exp2\_sim\_h\] contains the simulated prediction of the filling level. Apparently, polynomials of low degree lead to the best results. For polynomials of degree one, the identified model is shown in Eq. . It consists of 4 out of 55 functions of the library, meaning a high degree of sparsity. Due to the hybrid form of hysteron $H_1$, it has the same structure as the correct model in Eq. . The models of higher degree manage to reproduce state transitions at the correct critical points, but 