Abstract
Additive manufacturing (AM) relies critically on understanding and extrapolating process-property relationships; however, existing data-driven approaches remain limited by fragmented knowledge representations and unreliable extrapolation under sparse data conditions. In this study, we propose an ontology-guided, equation-centric framework that tightly integrates large language models (LLMs) with an additive manufacturing mathematical knowledge graph (AM-MKG) to enable reliable knowledge extraction and principled extrapolative modeling. By explicitly encoding equations, variables, assumptions, and their semantic relationships within a formal ontology, unstructured literature is transformed into machine-interpretable representations that support structured querying and reasoning. LLM-based equation generation is further conditioned on MKG-derived subgraphs, enforcing physically meaningful functional forms and mitigating non-physical or unstable extrapolation trends. To assess reliability beyond conventional predictive uncertainty, a confidence-aware extrapolation assessment is introduced, integrating extrapolation distance, statistical stability, and knowledge-graph-based physical consistency into a unified confidence score. Results demonstrate that ontology-guided extraction significantly improves the structural coherence and quantitative reliability of extracted knowledge, while subgraph-conditioned equation generation yields stable and physically consistent extrapolations compared to unguided LLM outputs. Overall, 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.
Abstract (translated)
增材制造（AM）严重依赖于对工艺-性能关系的理解和外推；然而，现有的数据驱动方法仍受限于知识表示的碎片化以及在稀疏数据条件下不可靠的外推。在这项研究中，我们提出了一种以本体论为导向、以方程为中心的框架，该框架紧密整合了大型语言模型（LLMs）与增材制造数学知识图谱（AM-MKG），以实现可靠的知识提取和原则性的外推建模。通过在一个正式的本体论内显式编码方程式、变量、假设及其语义关系，非结构化的文献被转化为支持结构化查询和推理的机器可解释表示形式。基于LLM的方程生成进一步受到从MKG导出的子图条件制约，从而强制执行物理上有意义的功能形式，并减少非物理或不稳定的外推趋势。 为了在传统预测不确定性之外评估可靠性，引入了一种基于置信度的外推评估方法，该方法将外推距离、统计稳定性以及基于知识图谱的物理一致性综合为统一的置信分数。结果表明，本体论引导的知识提取显著改善了所提取知识的结构一致性和定量可靠性，而子图条件制约下的方程生成与未指导的LLM输出相比，产生了稳定且物理上一致的外推。 总体而言，这项工作建立了一个统一的工作流程，用于基于本体论的知识表示、以方程式为中心的推理以及基于置信度的外推评估，突显了增强型知识图谱在增材制造领域作为可靠工具进行外推建模的巨大潜力。
URL
https://arxiv.org/abs/2601.05298
