The steady growth of the plastics industry has driven development in polymer processing as well as recycling. To meet the ever-increasing demands on polymer materials and plastics machinery, polymer processing requires further optimization using most modern techniques. Therefore, this work presents hybrid modeling concepts combining both numerically and experimentally driven modeling by data mining techniques. This hybrid modeling approach enables knowledge discovery from data as well as the development of several regression models that can serve as a basis for modern control concepts and predictive modeling. Numerically driven modeling is applied to describe the throughput-pressure gradient relationship of non-Newtonian polymer melt flows through woven screens used in mechanical recycling. Based on characteristic elementary cells for woven screens, extensive numerical parameter studies were performed varying the influencing variables and numerically solving the set of coupled, non-linear, partial differential equations. We first analyzed and simplified the governing equations and then transformed them into dimensionless form applying the theory of similarity. By applying the theory of similarity, the number of influencing parameters was reduced significantly in dimensionless representation. Considering these findings, a set of independent design points was created by varying the dimensionless input quantities and numerically solved. These data served as a basis for symbolic regression based on genetic programming to develop novel heuristic models estimating the initial pressure drop of woven screens without the need for further numerical calculations. Extensive experimental design studies were performed to proof the high accuracy of the developed mathematical models. Due to the algebraic structure, the approximation relationships can be easily implemented in expert systems, removing the need for computationally expensive and time-consuming numerical techniques.