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Towards a FAIR Documentation of Workflows and Models in Applied Mathematics

Marco Reidelbach, Björn Schembera, Marcus Weber

TL;DR

The paper addresses the need for FAIR, machine-interpretable documentation of Model-Simulation-Optimization workflows in applied mathematics. It presents MaRDMO, a plugin for RDMO, and MathModDB, an ontology for mathematical models, and demonstrates their integration via a Digital Humanities algebraic modeling workflow. The approach enables automatic capture, semantic encoding, and publication of comprehensive workflow knowledge in the MaRDI Portal Knowledge Graph, enhancing reproducibility and interdisciplinarity. The demonstrated cross-domain transfer from numerical MSO workflows to algebraic modeling shows the versatility and potential for broader adoption in mathematics and beyond.

Abstract

Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.

Towards a FAIR Documentation of Workflows and Models in Applied Mathematics

TL;DR

The paper addresses the need for FAIR, machine-interpretable documentation of Model-Simulation-Optimization workflows in applied mathematics. It presents MaRDMO, a plugin for RDMO, and MathModDB, an ontology for mathematical models, and demonstrates their integration via a Digital Humanities algebraic modeling workflow. The approach enables automatic capture, semantic encoding, and publication of comprehensive workflow knowledge in the MaRDI Portal Knowledge Graph, enhancing reproducibility and interdisciplinarity. The demonstrated cross-domain transfer from numerical MSO workflows to algebraic modeling shows the versatility and potential for broader adoption in mathematics and beyond.

Abstract

Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain.
Paper Structure (12 sections, 1 figure)

This paper contains 12 sections, 1 figure.

Table of Contents

  1. Introduction
  2. MaRDMO, MathModDB and their Connection
  3. MaRDMO
  4. MathModDB
  5. MaRDMO and MathModDB
  6. A semantic Representation of an Algebraic Modeling Workflow
  7. Introduction
  8. Object Data and Encoding
  9. Interdisciplinary Collaboration
  10. Interpretation and Validation
  11. Reproducibility and Future Applications
  12. Conclusion and Outlook

Figures (1)

  • Figure 1: Schematic representation of the object comparison model within the field of Egyptology, designed to identify destruction rules. Developed by Weber et al. (2022) Weber2022, the model employs a boolean ring as its formulation, with object properties serving as quantities, represented as booleans. The model is associated with a task, featuring its own formulation, input, and output quantities.