The convergence of the Newton Solver during initialization is a key challenge when modelling complex system. Several strategies have been developed, such as the *homotopy* method.

In addition to this method, a slightly different approach is proposed in ThermoCycle: the system is initialized on a simplified system of equations, and the more complex non-linear equations, such as the computation of the heat transfer coefficients as a function of mass flow, are activated one by one during integration using an initialization component developed for that purpose. Note that this approach can also solve some issues linked to numerical oscillations at the beginning of the simulation, and that can lead the system to exceed acceptable boundaries.

The simplified signal should be connected to the lower connector, while the more non-linear signal should be connected to the upper connector. The model uses a smooth interpolation function that switches the value of the output signal from the lower connector to the upper connector.