  Equation discovery methods enable modelers to combine domain-specific
knowledge and system identification to construct models most suitable for a
selected modeling task. The method described and evaluated in this paper can be
used as a nonlinear system identification method for gray-box modeling. It
consists of two interlaced parts of modeling that are computer-aided. The first
performs computer-aided identification of a model structure composed of
elements selected from user-specified domain-specific modeling knowledge, while
the second part performs parameter estimation. In this paper, recent
developments of the equation discovery method called process-based modeling,
suited for nonlinear system identification, are elaborated and illustrated on
two continuous-time case studies. The first case study illustrates the use of
the process-based modeling on synthetic data while the second case-study
evaluates on measured data for a standard system-identification benchmark. The
experimental results clearly demonstrate the ability of process-based modeling
to reconstruct both model structure and parameters from measured data.
