## 2 Related Works
### Knowledge Graph Completion  
In recent years, knowledge graph completion technology has received extensive attention and achieved in-depth development. At present, knowledge graph completion technology is abstracted as a link prediction problem which predicts the missing parts of the triple, such as head entity prediction \((7,r,t)\), tail entity prediction \((h,r,?)\) and relation prediction \((h,?,t)\), where? indicates the part that needs to be predicted and the other two parts are known.  
Among all knowledge completion methods, those based on knowledge representation learning have emerged as the most effective and widely adopted approaches and use linear or neural network models to predict the missing information in knowledge triples by learning low-dimensional vector representations of entities and relations on the basis of preserving the internal structure of the KG [26]. These methods can be roughly divided into three categories: triple-embedding-based methods, path-based methods, and graph-structure-based methods.  
Triple-embedding-based methods map the entities and relations in the KG to a low-dimensional vector space and use the relations between the vectors to predict the associations between the entities [27]. For example, in the relational rotation model proposed by [PERSON] et al. [28], each relation is represented as a rotation angle on the complex plane, and the association information between entities is captured by the rotation operation. Similarly, in the box-embedding model proposed by [PERSON] et al. [29], entities are embedded as points and relations are embedded as box-like hyperrectangles to capture relation rules and represent logical properties on KGs.  
Path-based methods predict the relation by analyzing the path information between entities. [PERSON] et al. [30] proposed a path representation method that combines semantic and data-driven approaches, which can integrate information from multiple paths to generate a more interpretable and generalized path representation. The reasoning method based on Graph Neural Networks (GNNs) learns the information of entities and their neighbors to predict the relation between entities by performing message passing and aggregation operations on the KG [31].  
In the sequence relation Graph Convolutional Network method proposed by [PERSON] et al. [32], the set of paths between entity pairs is constructed as a path graph, which is serialized into a series of subgraphs, and the reasoning task is performed by the GNN algorithm [33]. [PERSON] et al. [34] proposed Relational Reasoning Networks (R2N), a neuro-symbolic model that integrates knowledge graph embeddings with logical reasoning. It can perform multi-hop relational reasoning in latent space, enhancing relational representation and reasoning capabilities under uncertainty.  
However, the existing methods have limitations. Methods based on triple embedding mainly capture local semantic relations and lack a global understanding of complex graph structure [35]. Path-based methods consider path information, but their reasoning performance may be limited in the case of missing paths or incomplete information. Methods based on GNNs can aggregate the information of neighbor nodes, but they often ignore the differences in the characteristics of different relations in the KG.  
In order to solve the problem that the existing knowledge graph completion methods cannot balance the reasoning accuracy of all relations, this paper proposes a knowledge graph reasoning model based on a two-branch reasoning network in the continuous casting domain.  
KGTBRN classifies the triples in the C2Q-KG according to the number distribution of the head and tail entities and introduces a two-branch reasoning network structure following the GAT layer to select a more appropriate method for the knowledge graph completion task according to different entity distribution types, so as to improve the analysis accuracy of KGTBRN in the root cause analysis of cast product defects.