建立应用数学模型和算法的知识图谱

Björn Schembera, Frank Wübbeling, Hendrik Kleikamp, Burkhard Schmidt, Aurela Shehu, Marco Reidelbach, Christine Biedinger, Jochen Fiedler, Thomas Koprucki, Dorothea Iglezakis, Dominik Göddeke
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引用次数: 0

摘要

数学模型和算法是数学研究数据的重要组成部分,因为它们是认识论基础的数字数据。为了从语义上表示模型和算法以及它们之间的关系,使这些研究数据成为 FAIR,我们合并并扩展了两个以前不同的本体,使之成为一个活的知识图谱。这两个本体之间的联系是通过引入计算任务建立起来的,因为它们出现在建模中,与算法任务相对应。此外,还纳入了受控词汇表,并引入了一个新的类别,以区分基础量和特定用例量。现在,模型和算法都可以用元数据来充实。在这里,特定主题的元数据尤为重要,例如矩阵的对称性或数学模型的线性。这是用具体模型和算法表达特定工作流的唯一方法,因为只有知道模型的数学属性,才能确定可行的求解算法。我们将通过应用数学不同应用领域的两个实例来证明这一点。此外,我们已经将 250 多项应用数学研究成果整合到了我们的知识图谱中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics
Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this research data FAIR, two previously distinct ontologies were merged and extended, becoming a living knowledge graph. The link between the two ontologies is established by introducing computational tasks, as they occur in modeling, corresponding to algorithmic tasks. Moreover, controlled vocabularies are incorporated and a new class, distinguishing base quantities from specific use case quantities, was introduced. Also, both models and algorithms can now be enriched with metadata. Subject-specific metadata is particularly relevant here, such as the symmetry of a matrix or the linearity of a mathematical model. This is the only way to express specific workflows with concrete models and algorithms, as the feasible solution algorithm can only be determined if the mathematical properties of a model are known. We demonstrate this using two examples from different application areas of applied mathematics. In addition, we have already integrated over 250 research assets from applied mathematics into our knowledge graph.
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