On the importance of scaling in equation-based modelling

Equation-based modelling languages adopt a declarative modelling approach, focused on writing the model equations in a clear way and leaving the task of deriving efficient simulation code to the tool. One aspect of declarative modelling is that the use of dimensionally consistent SI units for the physical variables is preferrable; however, in many application areas this can lead to implicit nonlinear systems of equations which are badly scaled from a numerical point of view. This paper shows the negative impact of not dealing with this aspect on a benchmark test case, and then shows how the same performance of manually scaled models can be recovered by suitably exploiting information about the scaling of variables that can be declared by the modeller.