## Additive Manufacturing: A New Approach with Knowledge Graphs Additive manufacturing relies heavily on understanding the relationships between process and material properties. A new study proposes an ontology-guided, equation-centric framework, integrating large language models (LLMs) with an additive manufacturing mathematical knowledge graph (AM-MKG). This approach aims to enable more reliable knowledge extraction and more rigorous extrapolative modeling, especially in limited data conditions. The framework transforms unstructured literature into machine-interpretable representations, supporting structured queries and reasoning. ## Equation Generation and Reliability Assessment LLM-based equation generation is conditioned on subgraphs derived from the AM-MKG, ensuring physically meaningful functional forms and mitigating non-physical or unstable extrapolations. To assess reliability, a metric is introduced that integrates extrapolation distance, statistical stability, and knowledge-graph-based physical consistency. Results demonstrate that ontology-guided extraction significantly improves the structural coherence and quantitative reliability of the extracted knowledge. Conditioned equation generation produces stable and physically consistent extrapolations compared to unguided LLM outputs. This work establishes a unified pipeline for ontology-driven knowledge representation, equation-centered reasoning, and confidence-based extrapolation assessment, highlighting the potential of knowledge-graph-augmented LLMs as reliable tools for extrapolative modeling in additive manufacturing.