When performing machine learning predictions within the fields of materials mechanics and processing, considering fundamental physical laws can reduce errors and enhance generalization. On the one hand, physics-based models contain assumptions and simplifications; thus, produce errors. On the other hand, data-driven models can require large data sets to represent fundamental relationships. Via the synergistic combination of both model approaches, these respective disadvantages can be compensated. In hybrid modeling, a physics-based model (either analytical or numerical) is data-mined and corrected via a data-driven discrepancy model to achieve the desired reference solution, in this work provided by either high-fidelity simulations or experimental measurements. Application examples for three different materials processing techniques are presented: Laser-Shock-Peening, a technique used for the modification of residual stresses in metallic materials; Friction Surfacing, a solid-state processing technique of metallic materials used for additive manufacturing; as well as Hot Rolling, whereby metal strips with specific geometries and mechanical properties are produced. For all examples, physics-based feature engineering is implemented via dimensionless formulations of inputs and outputs based on a dimensionality analysis according to the Buckingham Pi theorem, which reduces prediction scatter and allows for physical extrapolation. In summary, it is demonstrated that integrating physics into the data science workflow can enhance prediction performance and generalization especially in scarce data settings and to the extent that physical extrapolation can be achieved.