<p>Tetrahedral mesh simplification represents a key technique for optimizing the storage space and improving computational efficiency in finite element analysis. However, traditional mesh simplification methods typically rely on geometric fidelity and fail to incorporate the practical requirements of physical analysis. This yields simplified mesh accuracy that can satisfy geometric constraints but cannot meet analysis requirements. To solve these problems, this study proposes a tetrahedral mesh simplification model based on a graph convolutional neural network (GCN) and a graph attention mechanism (GAT) named TetSimNet. The proposed TetSimNet realizes physical information-driven mesh simplification by integrating geometrical, topological, quality, spatial, and physical information and identifying and deleting edges that have a small impact on the accuracy of the analysis. The TetSimNet adopts a graph structure with mesh edges as nodes, combining the GCN and GAT with a tetrahedral mesh structure to create a multi-scale feature adaptive fusion module that can effectively capture local edge features, ensuring the accuracy of simulation analysis. The experimental results demonstrate that the TetSimNet can reduce the number of mesh elements by approximately 30% while ensuring analysis accuracy.</p>