# DTL-GNN: Digital Twin Lightweight Method Based on Graph Neural Network
## 3 Virtual Model Lightweight Approach
### Method Main Process
This approach is more flexible and practical when handling real-world data, particularly in the presence of noise or missing data, where it demonstrates greater robustness. In practice, the subgraph matching problem can be approached using various filtering strategies to reduce the search space. For instance, one might construct index structures such as VS-tree indices [53], Tree Structures [54], or Adjacency Lists [55] to index candidate vertices. Static and dynamic vertex equivalence [56], Topological Node Features (TNF) [57], and path decomposition-based indexing, which build a similarity set for the query graph through k-partition intersections [58], are also used to filter the search space. Moreover, graph structure information and the newly proposed LOOKUP-TABLE-GRAPH data structure have been employed for dynamic filtering [59]. However, when performing graph matching in the DTL database, searching for the target graph within the multi-layered, large graphs in the database is necessary. Since the DTL database is continuously updated during use, frequently constructing index structures for large data sets is not feasible in a lightweight digital twin system. Due to the way DTL-GNN constructs data, the nodes in the DTL graph data contain attribute information, and the generated attribute information can, to some extent, reflect the graph structure. Therefore, this chapter employs an affinity matrix and a threshold-based approach to achieve approximate graph matching. Specifically, based on the Euclidean distance between the attributes of the database and the target graph, an affinity matrix is constructed for the two, and chains of nodes with high affinity are filtered out. In addition, simgnn [60] is introduced to evaluate the results. If the similarity is higher than a threshold, the data analysis session is skipped to extract the classification in the database directly. The graph matching method for the DTL database is as follows. An affinity matrix with \(\text{N}_{\text{DL}}\times\text{N}_{\text{Target}}\) dimensions is generated based on the Euclidean distance between the attributes, where \(\text{N}_{\text{DL}}\) and \(\text{N}_{\text{Target}}\) represent the number of nodes in the database graph and the number of nodes in the target graph, respectively. After visualization, two node chains with the highest affinity can be found, corresponding to the same robotic arm on two pipelines in the database model, as shown in Figure 4:0 Next, score the similarity between the matched chain and the target model in virtual space. The similarity obtained is higher than the threshold, and the corresponding classification simplification method inthe database is transmitted to DTL-GNN to simplify the virtual model. The construction of lightweight digital twins is completed through the establishment of information exchange between physical entities and simplified virtual entities. ## 5 Experimental Results

In order to verify the impact of the DTL-GNN approach on different types of digital twin systems, this paper conducted experiments using independent and overall models as examples, which contain 4834 and 60 rows of data, respectively, to evaluate their classification accuracy, feature retention, and file size changes under the DTL-GNN method. The two datasets were extracted from factory and robotic arm models, including part information and graph connectivity data of assemblies. For the selection of baseline models, this study compares and analyzes Graph Attention Networks [61] (GAT), Graph Convolutional Networks [62] (GCN), and their variants. GAT employs a multi-head self-attention mechanism, effectively capturing the local structural characteristics of nodes while considering the influence of multiple neighboring nodes on the core node. Conversely, GCN utilizes graph convolution operations to propagate and aggregate node information via adjacency and feature matrices. GAT and GCN and their variants have demonstrated excellent performance in graph data classification tasks.