Exploring a Graph Theoretic Approach for the Quantitative Comparison of Digital Twin Designs

Abstract A graph theoretic approach for quantitatively comparing digital twin designs is explored in this paper, with a novel methodology being offered to evaluate the structural and functional similarities between these complex systems. Graph theory is leveraged to represent digital twins as mathematical graphs in our approach, with nodes represented by function-flow pairs and the interactions between the functions depicted by edges. The application of graph-based similarity measures, such as NetSimile and DeltaCon distance, for quantitatively assessing the resemblance between digital twin designs is allowed by this representation. Our method addresses the limitations of conventional vector-based metrics of design comparison, which focuses on the connectivity and interactions within these systems, offering a more nuanced and comprehensive analysis. The designs of six digital twins were collected, and functional models were created using the Functional Basis. The functional models were then converted to graphs to perform design similarity analysis. At the end of the study, it was concluded that graph similarity measures such as NetSimile and DeltaCon can be used as quantitative tools for comparing digital twins. However, further investigation is needed to test the effectiveness of such measures for complex designs such as digital twins. The limitations inherent in the current methodology are highlighted, such as challenges in capturing dynamic interactions and the evolving nature of digital twins. Finally, graph neural networks (GNN) are proposed for multiple feature-based similarity analysis and large language models (LLMs) to automate functional model generation.