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

Abstract

Reliable process models are a valuable asset in polymer extrusion to reduce downtimes and rejects, to improve process efficiency, and to accelerate the development 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 attractive option for process engineers, since it provides information 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, integrating domain knowledge into the regression data is already known to support the search for accurate prediction models. To assess this benefit systematically and quantitatively, 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 preprocessing: 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 equation. 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.