$^\circ C$" and one for “temperature above 100 $^\circ C$".

### PWARX models. {#PWARX}

Piece-Wise-Affine (PWA) methods divide the state-space into discrete regions, commonly shaped as polyhedronscite[Ferrari-Trecate.2000]{}. For every region a continuous model is set up, e.g. the well known linear *autoregressive model with exogenous input* (ARX-model). This procedure is called PWARX[@pwarx_paoletti]. If the transition from one state to another is affected by hysteresis behavior, PWA models are not sufficient anymore, because they assume fixed transition borders from one discrete state to another. They are unable to include memory of the past trajectory of the system’s state. [@Fang.2015] present a data-driven approach to model sticky valves using the Preisach model for hysteresis, which originated from describing natural hysteresis in ferromagnetic materials. They succeed in modeling the state transitions, but they separate the identification of the transition model from the identification of dynamic models for the discrete states. Also, the number of discrete states must be known beforehand. This will be overcome by using SINDyHybrid.

### SARX models. {#SARX}

**S**witched **A**ffine Modelle (*SARX*) models can be used if transitions of the state are triggered by external events. It is also possible to use **p**iece**w**ise continuously differentiable **n**onlinear functions (*PWNARX*, *SNARX*). An 