Impact of domain knowledge on developing pumping models for single-screw extruders using symbolic regression

Reliable process models are a valuable asset in
polymer extrusion to reduce downtimes and rejects, to
improve process efficiency, and to accelerate the develop-
ment of new screw designs. With ongoing progress in
computational capabilities, increasing attention is paid to
modeling techniques that infer predictions directly from the
process data. Out of these, symbolic regression is an attrac-
tive option for process engineers, since it provides infor-
mation as ready-to-use analytical mathematical expressions.
However, extensive workload for data curation and model
generation impedes obtaining regression models of high
precision and general validity. In polymer extrusion, inte-
grating domain knowledge into the regression data is
already known to support the search for accurate prediction
models. To assess this benefit systematically and quantita-
tively, we developed symbolic regression models for the
pumping characteristics of single-screw extruders from
three-dimensional fluid dynamics simulations, including
different modules of domain knowledge at data pre-
processing: Initially, models are created (i) using theory of
similarity only, followed by models that further (ii) accept
derived physical parameters as additional input features,
(iii) combine additional input features with logarithmic
scaling, and (iv) correct a theoretical approximation equa-
tion. For each case of data preprocessing, the regression
models are evaluated in terms of their interpolation and
extrapolation capabilities, their structural complexities, and
their required training times. This study demonstrates that
symbolic regression is most efficient on the original
dimensionless data if nonlinear trends in dimensionless
space remain below second order or within one decade.
Once stronger nonlinearities occur, however, capturing
these nonlinearities with prior theoretical approximations
substantially enhances extrapolation capability and
computational efficiency, albeit at the price of larger models.