Conventional predictive modeling of parametric relationships in manufacturing processes is limited by the subjectivity of human expertise and intuition on the one hand and by the cost and time of experimental data generation on the other hand. This work addresses this issue by establishing a new Large Language Model (LLM) framework. The novelty lies in combining automatic extraction of process-relevant knowledge embedded in the literature with iterative model refinement based on a small amount of experimental data. This approach is evaluated on three distinct manufacturing processes that are based on machining, deformation, and additive principles. The results show that for the same small experimental data budget the models derived by our framework have unexpectedly high extrapolative performance, often surpassing the capabilities of conventional Machine Learning. Further, our approach eliminates manual generation of initial models or expertise-dependent interpretation of the literature. The results also reveal the importance of the nature of the knowledge extracted from the literature and the significance of both the knowledge extraction and model refinement components.