Tetrahedral mesh simplification method based on graph neural network

Abstract

The invention discloses a tetrahedral mesh simplification method based on a graph neural network, and the method is characterized in that feature extraction is carried out on each mesh edge of each tetrahedral mesh unit in a tetrahedral mesh model, and the deletion probability of each mesh edge is predicted to determine a to-be-deleted mesh edge; performing deletion validity check on the to-be-deleted grid edges to obtain a to-be-deleted grid edge set; and finally, deleting the to-be-deleted grid edge set in batches until the to-be-deleted grid edge set is empty, and outputting a simplified tetrahedral grid model. The method has the advantages that feature extraction is carried out on the grid edges from multiple dimensions such as geometry, topology, quality, physics and space, the relation between the grid edge structure and simulation analysis precision can be automatically learned by introducing the graph neural network technology, the influence of the to-be-deleted grid edges on the overall grid analysis precision is predicted, and the accuracy of the whole grid analysis precision is improved. And intelligent grid simplification with analysis precision as a guide is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of finite element analysis and mesh modeling in engineering digital simulation, and particularly relates to a tetrahedral mesh simplification method based on a graph neural network. BACKGROUND

[0002] Tetrahedral mesh is one of the commonly used types in three-dimensional entity mesh partitioning, which is composed of tetrahedral elements formed by four triangular faces, and is suitable for modeling of complex geometrical shapes. In the field of finite element analysis, tetrahedral mesh is widely used in simulation analysis of complex structures due to its excellent geometric adaptability and automatic generation capability. To meet the demand for high-precision solution, high-density mesh is usually generated to fully capture local geometric details and local characteristics of physical fields. However, with the increase of product model size, such high-density mesh significantly increases the consumption of computing resources, memory occupation and solution time during simulation analysis. Therefore, it is crucial to select a reasonable mesh simplification strategy for specific analysis, that is, to significantly reduce the number of meshes while ensuring simulation accuracy, so as to obtain high-precision simulation results at a lower computational cost.

[0003] Existing tetrahedral mesh simplification techniques are mostly based on triangular mesh simplification methods, such as extending the progressive mesh algorithm, introducing various cost functions to guide the edge folding process, and preventing tetrahedral mesh intersection and inversion during folding operation. With the rapid development of deep learning, intelligent mesh generation and processing methods have gradually emerged, such as triangular mesh simplification methods based on neural networks, which use attention modules to extract geometric features and find the optimal merging point position by optimizing the Hausdorff distance to achieve mesh simplification. For example, by performing convolution operations on mesh edges to extract local features of triangular mesh, and introducing pooling operations to simplify the mesh. However, these current triangular mesh simplification methods do not consider actual physical analysis results (i.e. simulation results), and fail to find the mapping relationship between mesh precision and mesh structure, resulting in that the simplified mesh often cannot meet the accuracy requirements of actual engineering analysis. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a tetrahedral mesh simplification method based on a graph neural network that can effectively simplify the mesh while ensuring the accuracy of simulation analysis.

[0005] The technical solution adopted by the present application to solve the above technical problem is as follows: A tetrahedral mesh simplification method based on a graph neural network, comprising the following specific steps: (1) performing feature extraction on each mesh edge of each tetrahedral mesh element in the tetrahedral mesh model, including geometric features, topological features, quality features, spatial features and physical features; (2) Constructing the original feature matrix based on the grid edge multi-dimensional features, inputting the original feature matrix into the graph neural network to obtain the final feature matrix of the grid edge, and then predicting the deletion probability of each grid edge through the node prediction module, and comparing it with the pre-set deletion threshold value, if the deletion probability is greater than the deletion threshold value, the grid edge is identified as a grid edge to be deleted; (3) Geometric invalidity judgment, quality pre-judgment of the grid unit after deletion, and interference judgment of the adjacent structure of the grid edge, to realize the deletion effectiveness check of the grid edge to be deleted, and after removing the grid edge to be deleted that meets any one of the judgment conditions, the remaining grid edge to be deleted is put into the same set to obtain the grid edge to be deleted set; (4) Batch deleting the grid edge to be deleted set, and then repeating steps (1)-(4) until the grid edge to be deleted set established in step (3) is empty, and outputting the simplified tetrahedral mesh model.

[0006] Further, in the (1), the determination method of the geometric features of the grid edge is: The geometric properties of the two end points of each grid edge in the tetrahedral mesh unit are defined in advance, including the location of each end point in the geometric vertex, geometric edge or geometric face of the three-dimensional entity, or the geometric internal point belonging to the three-dimensional entity, then the geometric property matrix of the two end points of the grid edge is constructed, and is taken as the geometric features of the grid edge.

[0007] Further, in the (1), the determination method of the topological features of the grid edge is: (1.2.1) Calculate the number of tetrahedral mesh units sharing at least one end point with the two end points of the grid edge, and determine the number as the number n of tetrahedral mesh units adjacent to the grid edge; (1.2.2) Determine the initial topological quality T of the grid edge local : ; Wherein: V e The degree of the grid edge e, that is, the number of adjacent grid faces, VI e Indicates the ideal degree of the grid edge e; (1.2.3) Determine the change value of the local topological quality after the deletion of the grid edge, and take it as the topological features of the grid edge: Delete the grid edge e and combine its adjacent grid edges to obtain a new grid edge The local topological quality , of the grid edge e after deletion, The degree of the new grid edge , ideal degree of the grid edge e the change value of the local topological quality after deletion .

[0008] Further, in the (1), the determination method of the quality feature of the grid edge is: (1.3.1), determining the set of adjacent tetrahedral mesh elements before and after the deletion of the grid edge e: the set S of tetrahedral mesh elements sharing at least one endpoint with the two endpoints of the grid edge e before the deletion of the grid edge e A is denoted as: S A ={S A1 ,S A2 ,…,S An}, n is the number of tetrahedral mesh elements sharing an endpoint with the grid edge e; deleting the grid edge e and obtaining a new grid vertex v, the set S of tetrahedral mesh elements sharing an endpoint with the new grid vertex v B is denoted as: S B ={SB1,SB2,…,S Bm}, m is the number of tetrahedral mesh elements sharing an endpoint with the new grid vertex v; (1.3.2), calculating the local volume average value, the volume distortion value, the collapse value, the edge length ratio, and the scaled Jacobian value of the five quality indicators of the sets S A and S B respectively, and calculating the minimum dihedral angle, the volume edge length ratio, the minimum internal angle value, and the grid edge length of the set S A , and the results are taken as the quality features of the grid edge.

[0009] Further, in the (1), the determination method of the spatial feature of the grid edge is: A spatial position encoding module is constructed through two fully connected layers, and the output dimensions of the two fully connected layers are set as NPE1=64 and NPE2=18 respectively, the three-dimensional coordinates of the midpoint of the grid edge e are input into the spatial position encoding module, and the three-dimensional coordinates of the midpoint of the grid edge e are mapped to a high-dimensional feature space through the two fully connected layers in the spatial position encoding module, to obtain the spatial feature of the grid edge.

[0010] Further, in the (1), the determination method of the physical feature of the grid edge is: The strain values of each endpoint of the grid edge e are determined, the average strain value and the maximum strain value representing the physical feature of the grid edge are calculated, the strain values of the two endpoints of the grid edge e are denoted as: U a , U b , the average strain value of the grid edge e is: , and the maximum strain value is: .

[0011] Further, the specific implementation method of step (2) is: (2.1), taking the grid edge as the graph node, constructing the topological graph structure of the tetrahedral mesh model according to the adjacent relationship between the edges, obtaining the adjacency matrix of the tetrahedral mesh model, and then assigning the multi-dimensional features of the grid edges extracted in step (1) to the graph nodes to obtain the original feature matrix of all grid edges; (2.2), inputting the original feature matrix into the graph convolution network, obtaining a new feature matrix through at least two graph convolutions, and then adding the original feature matrix and the new feature matrix to obtain the final feature matrix of the graph convolution; (2.3), inputting the original feature matrix into the graph attention network, obtaining a new feature matrix through at least two feature updates of the graph attention network, and then adding the original matrix and the new feature matrix to obtain the final feature matrix of the graph attention; (2.4), constructing a node prediction module through two fully connected layers, setting the output dimensions of the two fully connected layers as NPE1=36 and NPE2=18 respectively, inputting the sum of the final feature matrix of the graph convolution and the final feature matrix of the graph attention into the fully connected layer of the node prediction module, performing batch normalization and ReLU activation function operation on the output of each fully connected layer, and finally predicting the deletion probability of each grid edge through the output layer of the node prediction module using the Sigmoid activation function; (2.5), comparing the deletion probability of each grid edge with the pre-set deletion threshold, if the deletion probability is greater than the deletion threshold, the grid edge is identified as a grid edge to be deleted.

[0012] Further, the specific standard for judging the geometric invalidity of the grid edge to be deleted in step (3) is: When the two end points of the grid edge to be deleted are located on different geometric vertices, different geometric edges or different geometric faces of the three-dimensional entity, the grid edge to be deleted cannot be deleted; When one of the two end points of the grid edge to be deleted is located at a geometric vertex of the three-dimensional entity, and the other end point is located at a geometric edge or a geometric face of the three-dimensional entity, and the geometric vertex and the geometric edge are not connected or the geometric vertex and the geometric face are not connected, the grid edge to be deleted cannot be deleted; When one of the two end points of the grid edge to be deleted is located on a geometric edge of the three-dimensional entity, and the other end point is located on a geometric face of the three-dimensional entity, and the geometric edge and the geometric face are not connected, the grid edge to be deleted cannot be deleted.

[0013] Further, the quality pre-judgment method of the grid unit after deleting the grid edge to be deleted in step (3) is: The new grid vertex is obtained after deleting the grid edge to be deleted, a scaled Jacobian value is calculated for a set of tetrahedral grid cells sharing an end point with the new grid vertex, and if the scaled Jacobian value is a positive value, the grid edge to be deleted can be deleted; otherwise, the grid edge to be deleted cannot be deleted.

[0014] Further, the step (3) is a method for judging the interference of the grid edge to be deleted with the adjacent structure of the grid edge, and the method comprises the following steps: The grid edges sharing one end point with the grid edge to be deleted are put into the same set to obtain an adjacent edge set N(e), and if one or more grid edges to be deleted exist in the adjacent edge set N(e) The one or more grid edges to be deleted cannot be deleted.

[0015] Compared with the prior art, the method has the following advantages: (1) The method extracts features of the grid edge from multiple dimensions such as geometry, topology, quality, physics and space, so that the graph neural network (including the graph convolution network and the graph attention network) can comprehensively perceive the structural features of the tetrahedral grid, evaluate the importance (i.e. the deletion probability) of each grid edge from multiple angles, and thus realize a reliable edge deletion strategy and improve the generalization of the model. (2) By introducing the graph neural network technology, the relationship between the grid edge structure and the simulation analysis accuracy can be automatically learned, the influence (i.e. the deletion probability of the grid edge) of the grid edge to be deleted on the overall grid analysis accuracy can be predicted, and the intelligent grid simplification oriented by the analysis accuracy can be realized. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The flowchart of the present application is shown in the figure. Figure 2 The simplified effect comparison chart of the present application is shown in the figure. DETAILED DESCRIPTION

[0017] The present application will be further described in detail below with reference to the embodiments of the drawings.

[0018] As shown in the figure, a tetrahedral grid simplification method based on a graph neural network comprises the following specific steps: (1) The features of each grid edge e of each tetrahedral grid cell in the tetrahedral grid model are extracted, including geometric features, topological features, quality features, spatial features and physical features, and the specific steps are as follows: (1.1) The determination method of the geometric features of the grid edge e is as follows: ​The geometric properties of two end points of each grid edge e in the tetrahedral mesh unit are predefined, including the location of each end point at a geometric vertex, a geometric edge or a geometric face of the three-dimensional entity, or a geometric interior point belonging to the three-dimensional entity, and then a geometric property matrix of the two end points of the grid edge is constructed and used as the geometric feature of the grid edge; (1.2), the determination method of the topological feature of the grid edge e is: (1.2.1), the number of tetrahedral mesh units sharing at least one end point with the two end points of the grid edge e is calculated, and the number is determined as the number n of tetrahedral mesh units adjacent to the grid edge e; (1.2.2), the initial topological quality T of the grid edge e is determined local : ; Wherein: the topological quality of the grid edge is defined based on the degree of the grid edge, V e , which represents the degree of the grid edge e, i.e. the number of adjacent grid faces, the adjacent (or adjacent) grid face refers to the grid face sharing the two end points of the grid edge e; VI e , which represents the ideal degree of the grid edge e; The ideal degree of the grid edge is affected by its geometric properties: if the grid edge e is an internal grid edge of the three-dimensional entity, its ideal degree is VI e =6; if the grid edge e is located on a geometric face of the three-dimensional entity, its ideal degree is VI e =4; if the grid edge e is located on a geometric edge of the three-dimensional entity, its ideal degree is determined according to the dihedral angle of the geometric edge , wherein: is the dihedral angle of the geometric edge; (1.2.3), the change value D of the local topological quality after the grid edge e is deleted is determined and used as the topological feature of the grid edge e: The grid edge e is deleted and its adjacent grid edge pairs are merged to obtain a new grid edge , the local topological quality after the grid edge e is deleted , , which represents the degree of the new grid edge , i.e. the number of grid faces adjacent to the new grid edge , , which represents the ideal degree of the new grid edge , , the value determination method of VI e is the same as e , the change value D of the local topological quality after the grid edge is pre-judged; (1.3), the method for determining the quality characteristics of the mesh edge e is: (1.3.1), determine the set of adjacent tetrahedral mesh elements before and after the mesh edge e is deleted: the set S of tetrahedral mesh elements sharing at least one of the two endpoints of the mesh edge e before the mesh edge e is deleted A denoted as: S A ={S A1 ,S A2 ,…,S An}, n is the number of tetrahedral mesh elements sharing an endpoint with the mesh edge e; delete the mesh edge e and get a new mesh vertex v, the set S of tetrahedral mesh elements sharing an endpoint with the new mesh vertex v B denoted as: S B ={SB1,SB2,…,S Bm}, m is the number of tetrahedral mesh elements sharing an endpoint with the new mesh vertex v; the position of the new mesh vertex v can be determined by the following table, where A and B represent the two endpoints of the mesh edge e respectively: VI Description Position of new mesh vertex v At a geometric vertex, belonging to a geometric interior point At At a geometric vertex, at a geometric edge, and the geometric vertex is connected to the geometric edge At At a geometric vertex, at a geometric face, and the geometric vertex is connected to the geometric face At At a geometric edge, belonging to a geometric interior point At At the same geometric edge At the midpoint between two points At a geometric edge, at a geometric face, and the geometric edge is connected to the geometric face At At a geometric face, belonging to a geometric interior point At At the same geometric face At the midpoint between two points Belongs to an interior point (1.3.2), calculate the local volume average, volume distortion value, collapse value, edge length ratio, and scaling Jacobian value of the five quality indicators for the sets S A and S B respectively, and calculate the minimum dihedral angle, volume edge length ratio, minimum internal angle value, and mesh edge length for the set S A , and the results are taken as the quality characteristics of the mesh edge e; Local volume average: represents the average volume of adjacent tetrahedral mesh elements, that is, the average volume of tetrahedral mesh elements in the sets S A and S B is calculated respectively; Volume distortion value: represents the minimum volume distortion value of adjacent tetrahedral mesh elements, which is used to measure the geometric preservation of tetrahedral mesh during deformation; Collapse value: represents the minimum collapse value of adjacent tetrahedral mesh elements, which is used to evaluate the stability of the mesh during local deformation; both the volume distortion value and the collapse value can be calculated using the corresponding method in [LI H. 2012 Finite Element Mesh Generation and Decision Criteria of Mesh Quality]; Edge length ratio: represents the ratio of the current mesh edge length to the average edge length of its adjacent mesh edges, which is used to detect flat or sharp elements in the tetrahedral mesh, thereby enhancing the overall uniformity and stability of the mesh structure; adjacent mesh edges refer to mesh edges sharing one endpoint with the current mesh edge; scaled jacobian value: this index is the minimum scaled jacobian value of the adjacent tetrahedral mesh element; minimum dihedral angle: this index is used to evaluate the minimum angle between two mesh faces adjacent to the mesh edge e and located in the same tetrahedral mesh element; volume edge length ratio: it refers to the relationship between the volume of the tetrahedral mesh element and its corresponding edge length by the minimum volume edge length ratio value; the calculation of the scaled jacobian value, the minimum dihedral angle and the volume edge length ratio can be calculated by the corresponding method in [Chen et al. 2013 SVM-based topological optimization of tetrahedral meshes]; minimum internal angle value: it refers to the minimum internal angle value of the mesh face adjacent to the mesh edge e (i.e. the minimum internal angle of the triangle), which is mainly used to identify and avoid sharp tetrahedral mesh elements, thereby improving the stability of the mesh; mesh edge length: edge length is a key index to evaluate the degree of mesh detail, and shorter mesh edge length corresponds to finer mesh detail and better geometric representation, while longer mesh edge length indicates that the mesh is coarser and has lower geometric fidelity; The above nine quality indexes are known calculation parameters in tetrahedral mesh, which can be calculated by the corresponding method disclosed in the prior art, and will not be repeated here; (1.4), the determination method of the spatial feature of the mesh edge e is: A spatial position encoding module (PE) is constructed through two fully connected layers, and the output dimensions of the two fully connected layers are set as NPE1=64 and NPE2=18 respectively. The three-dimensional coordinates of the midpoint of the mesh edge e are input into the spatial position encoding module, and the three-dimensional coordinates of the midpoint of the mesh edge e are mapped to a high-dimensional feature space through the two fully connected layers in the spatial position encoding module to obtain the spatial feature of the mesh edge; (1.5), the determination method of the physical feature of the mesh edge e is: The strain values of each end point of the mesh edge e are determined, and the average strain value and the maximum strain value representing the physical feature of the mesh edge are calculated. The strain values of the two end points of the mesh edge e are denoted as: a , b The average strain value of the mesh edge e is: , and the maximum strain value is: ; (2), the original feature matrix is constructed based on the multi-dimensional features of the mesh edge, and the original feature matrix is input into the graph neural network to obtain the final feature matrix of the mesh edge, and then the node prediction module is used to predict the deletion probability P i , (2.1), constructing a topological graph structure of the tetrahedral mesh model according to the adjacent relationship between edges and edges, obtaining an adjacency matrix of the tetrahedral mesh model, and then assigning the multi-dimensional features (including geometric features, topological features, quality features, spatial features and physical features) of the mesh edges extracted in step (1) to the graph nodes to obtain an original feature matrix of all mesh edges; (2.2), inputting the original feature matrix into a graph convolution network (GCN), obtaining a new feature matrix through at least two times of graph convolution, and then adding the original feature matrix and the new feature matrix to obtain a final feature matrix of the graph convolution; (2.3), inputting the original feature matrix into a graph attention network (GAT), obtaining a new feature matrix through at least two times of feature updating of the graph attention network, and then adding the original matrix and the new feature matrix to obtain a final feature matrix of the graph attention; (2.4), constructing a node prediction module through two fully connected layers, setting the output dimensions of the two fully connected layers as NPE1=36 and NPE2=18 respectively, inputting the sum of the final feature matrix of the graph convolution and the final feature matrix of the graph attention into the fully connected layers of the node prediction module, performing batch normalization and ReLU activation function operation on the output of each fully connected layer, and finally predicting the deletion probability P i of each mesh edge e through the output layer of the node prediction module using a Sigmoid activation function; (2.5), comparing the deletion probability P i of each mesh edge e with a pre-set deletion threshold P, if the deletion probability P i is greater than the deletion threshold P, the mesh edge is identified as a mesh edge to be deleted; (3), performing geometric invalidity judgment, quality pre-judgment of the mesh unit after deletion and interference judgment of the adjacent structure of the mesh edge on the mesh edge to be deleted to realize the deletion effectiveness check of the mesh edge to be deleted, removing the mesh edge to be deleted which meets any one of the three judgment conditions, and then putting the remaining mesh edge to be deleted into a same set to obtain a mesh edge to be deleted set; the three judgment conditions are: (3.1), in the simplification process of tetrahedral mesh, the incorrect mesh edge deletion operation can cause the invalidity of geometric structure, and further cause the instability of simulation, the increase of numerical error, and even the failure of simulation, which seriously affects the accuracy and reliability of subsequent finite element analysis. Therefore, when performing the mesh edge simplification operation, the geometric consistency constraint must be introduced to ensure that the tetrahedral mesh structure remains valid at the geometric level; geometric invalidity is usually manifested as illegal vertex merging or local deformation that is too large, which destroys the geometric integrity of the tetrahedral mesh element. Whether the deletion of a mesh edge will cause geometric invalidity can be realized by analyzing whether the geometric properties of the two endpoints of the mesh edge meet the preset consistency condition, so the specific standard for judging the geometric invalidity of the mesh edge to be deleted is: When the two endpoints of the mesh edge to be deleted are located on different geometric vertices, different geometric edges or different geometric faces of the three-dimensional entity, the mesh edge to be deleted cannot be deleted; When one of the two endpoints of the mesh edge to be deleted is located on a geometric vertex of the three-dimensional entity, and the other endpoint is located on a geometric edge or a geometric face of the three-dimensional entity, and the geometric vertex and the geometric edge are not connected or the geometric vertex and the geometric face are not connected, the mesh edge to be deleted cannot be deleted; When one of the two endpoints of the mesh edge to be deleted is located on a geometric edge of the three-dimensional entity, and the other endpoint is located on a geometric face of the three-dimensional entity, and the geometric edge and the geometric face are not connected, the mesh edge to be deleted cannot be deleted; (3.2), the quality pre-judgment method of the mesh element after deleting the mesh edge to be deleted is: After deleting the mesh edge to be deleted, a new mesh vertex is obtained, the scaled Jacobian value of the set of tetrahedral mesh elements sharing the new mesh vertex is calculated, if the scaled Jacobian value is positive, the mesh edge to be deleted can be deleted; otherwise, it cannot be deleted; (3.3), the interference judgment method of the mesh edge for the adjacency structure of the mesh edge to be deleted is: Put the mesh edges sharing one of the endpoints of the mesh edge to be deleted into the same set to obtain the adjacent edge set N(e), if one or more mesh edges to be deleted exist in the adjacent edge set N(e) , the one or more mesh edges to be deleted cannot be deleted; (4), the batch deletion is performed on the set of mesh edges to be deleted, and then steps (1)-(4) are repeated until the set of mesh edges to be deleted established in step (3) is empty, and finally the simplified tetrahedral mesh model is output.

[0019] The tetrahedral mesh simplification method of the application is verified by simulation analysis of a three-dimensional entity, and the results are as follows: The three-dimensional entity is divided by high-density tetrahedral mesh to obtain a high-density tetrahedral mesh model as shown in At the midpoint between two points (a), the number of tetrahedral mesh units is 17990, the number of mesh edges is 25866, and the maximum strain value is 3.132. Figure 2 The high-density tetrahedral mesh model of (a) is simplified by the method to obtain a simplified mesh model as shown in Figure 2 (b), the number of tetrahedral mesh units is 11684, the number of mesh edges is 16602, the simplification rate of the number of tetrahedral mesh units is 35.05%, and the maximum strain value is 3.061, which does not change obviously compared with the maximum strain value before simplification, thereby ensuring the simulation analysis precision after simplification. Figure 2 For the same three-dimensional entity, a low-density tetrahedral mesh is used for division to obtain a low-density tetrahedral mesh model as shown in Figure 2 Figure 2 (c), the number of tetrahedral mesh units is 11241, the number of mesh edges is 16481, and the number of tetrahedral mesh units is close to that of the mesh model after simplification of (b), but the maximum strain value is only 2.742, and the simulation analysis precision is greatly reduced.

[0020] The protection scope of the present application includes but is not limited to the above embodiments, and the protection scope is subject to the claims, and any replacement, deformation, improvement of the present technology easily thought by those skilled in the art falls within the protection scope of the present application.

Claims

1. A method for simplifying a tetrahedral mesh based on a graph neural network, characterized in that The method comprises the following specific steps: (1) feature extraction is performed on each mesh edge of each tetrahedral mesh unit in the tetrahedral mesh model, including geometric features, topological features, quality features, spatial features and physical features; (2) an original feature matrix is constructed based on the multi-dimensional features of the mesh edge, the original feature matrix is input into a graph neural network to obtain a final feature matrix of the mesh edge, the deletion probability of each mesh edge is predicted through a node prediction module, and the deletion probability is compared with a pre-set deletion threshold value; if the deletion probability is greater than the deletion threshold value, the mesh edge is identified as a mesh edge to be deleted; (3) geometric invalidity judgment, quality pre-judgment of the mesh unit after deletion and interference judgment of the adjacent structure of the mesh edge are performed on the mesh edge to be deleted to realize deletion effectiveness checking of the mesh edge to be deleted; the mesh edge to be deleted that meets any one of the judgment conditions is removed, and the remaining mesh edge to be deleted is put into a same set to obtain a mesh edge to be deleted set; (4) batch deletion is performed on the mesh edge to be deleted set, and then steps (1)-(4) are repeated until the mesh edge to be deleted set established in step (3) is empty, and a simplified tetrahedral mesh model is output.

2. The tetrahedral mesh simplification method based on graph neural network of claim 1, wherein: In the step (1), the geometric feature of the mesh edge is determined by: defining the geometric properties of the two end points of each mesh edge in the tetrahedral mesh unit in advance, including the positions of each end point at the geometric vertex, geometric edge or geometric face of the three-dimensional entity, or the geometric internal point belonging to the three-dimensional entity, then constructing a geometric property matrix of the two end points of the mesh edge, and taking the geometric property matrix as the geometric feature of the mesh edge.

3. The method of claim 1, wherein: In the step (1), the topological feature of the mesh edge is determined by: (1.2.1) calculating the number of tetrahedral mesh units sharing at least one end point with the two end points of the mesh edge, and taking the number as the number n of tetrahedral mesh units adjacent to the mesh edge; (1.2.2), determining an initial topology quality T of the grid edges local : ; wherein: V e denotes the degree of a grid edge e, i.e. the number of adjacent grid faces, VI e denotes the ideal degree of a grid edge e; (1.2.3) determining the change value of the local topological quality after the mesh edge is deleted, and taking the change value as the topological feature of the mesh edge: Delete mesh edge e and merge its adjacent mesh edge pairs to obtain a new mesh edge. Local topology quality after mesh edge e is deleted , Indicates the new grid edge The degree, Indicates the new grid edge Ideal degree, predict grid edge e Change in local topology quality after deletion .

4. The method of claim 1, wherein: In the step (1), the quality feature of the mesh edge is determined by: (1.3.1) Determine the set of adjacent tetrahedral mesh elements before and after the deletion of mesh edge e: Before the deletion of mesh edge e, the set S of tetrahedral mesh elements that share at least one of the two endpoints of mesh edge e. A Noted as: S A ={S A1 ,S A2 ,…,S An }, where n is the number of tetrahedral mesh elements that share an endpoint with mesh edge e; deleting mesh edge e results in a new mesh vertex v, and the set S of tetrahedral mesh elements that share an endpoint with the new mesh vertex v is... B Noted as: S B ={SB1,SB2,…,S Bm }, where m is the number of tetrahedral mesh cells that share an endpoint with the new mesh vertex v; (1.3.2), respectively, the set S A and S B are calculated with five quality indicators of local volume average, volume twist, collapse, edge length ratio, scaled Jacobian, and the set S A are calculated with four quality indicators of minimum dihedral angle, volume edge length ratio, minimum internal angle value, mesh edge length, and the results are taken as the quality characteristics of the mesh edge.

5. The method of claim 1, wherein: In the step (1), the spatial feature of the mesh edge is determined by: a spatial position coding module is constructed through two fully connected layers, the output dimensions of the two fully connected layers are set as NPE1=64 and NPE2=18 respectively, the three-dimensional coordinates of the midpoint of the mesh edge e are input into the spatial position coding module, the three-dimensional coordinates of the midpoint of the mesh edge e are mapped to a high-dimensional feature space through the two fully connected layers in the spatial position coding module, and the spatial feature of the mesh edge is obtained.

6. The method of claim 1, wherein: In the step (1), the physical feature of the mesh edge is determined by: determining strain values for each end point of the mesh edge e, calculating an average strain value and a maximum strain value representative of the physical characteristics of the mesh edge e, denoting the strain values for the two end points of the mesh edge e as: U a , U b The average strain value for the mesh edge e is then: , and the maximum strain value is: .

7. The method of claim 1, wherein: The specific implementation method of the step (2) is: (2.1) taking the mesh edge as a graph node, constructing a topological graph structure of the tetrahedral mesh model according to the adjacent relationship between edges, obtaining an adjacency matrix of the tetrahedral mesh model, and assigning the multi-dimensional features of the mesh edge extracted in the step (1) to the graph node to obtain an original feature matrix of all mesh edges; (2.2), inputting the original feature matrix into a graph convolution network, obtaining a new feature matrix through at least two times of graph convolution, and adding the original feature matrix and the new feature matrix to obtain a final feature matrix of the graph convolution; (2.3), inputting the original feature matrix into a graph attention network, obtaining a new feature matrix through at least two times of feature updating of the graph attention network, and adding the original matrix and the new feature matrix to obtain a final feature matrix of the graph attention; (2.4), constructing a node prediction module through two fully connected layers, setting the output dimensions of the two fully connected layers as NPE1=36 and NPE2=18 respectively, inputting the sum of the final feature matrix of the graph convolution and the final feature matrix of the graph attention into the fully connected layers of the node prediction module, performing batch normalization and ReLU activation function operation on the output of each fully connected layer, and finally predicting the deletion probability of each grid edge through the output layer of the node prediction module using a Sigmoid activation function; (2.5), comparing the deletion probability of each grid edge with a pre-set deletion threshold, if the deletion probability is greater than the deletion threshold, the grid edge is identified as a to-be-deleted grid edge.

8. The method of claim 1, wherein: The specific criteria for the geometric invalidity judgment of the to-be-deleted grid edge in step (3) are: when the two end points of the to-be-deleted grid edge are located on different geometric vertices, different geometric edges or different geometric faces of the three-dimensional entity, the to-be-deleted grid edge cannot be deleted; when one of the two end points of the to-be-deleted grid edge is located on a geometric vertex of the three-dimensional entity, and the other end point is located on a geometric edge or a geometric face of the three-dimensional entity, and the geometric vertex and the geometric edge are not connected or the geometric vertex and the geometric face are not connected, the to-be-deleted grid edge cannot be deleted; when one of the two end points of the to-be-deleted grid edge is located on a geometric edge of the three-dimensional entity, and the other end point is located on a geometric face of the three-dimensional entity, and the geometric edge and the geometric face are not connected, the to-be-deleted grid edge cannot be deleted.

9. The method of claim 1, wherein: The quality pre-judgment method of the grid unit after deleting the to-be-deleted grid edge in step (3) is: after deleting the to-be-deleted grid edge, a new grid vertex is obtained, the scaled Jacobian value of the set of tetrahedral grid units sharing the new grid vertex is calculated, if the scaled Jacobian value is positive, the to-be-deleted grid edge can be deleted; otherwise, it cannot be deleted.

10. The method of claim 1, wherein: The interference judgment method of the adjacent structure of the grid edge for the to-be-deleted grid edge in step (3) is: putting the grid edges sharing one of the end points of the grid edge to be deleted into the same set, obtaining an adjacent edge set N(e), if one or more of the remaining grid edges to be deleted exist in the adjacent edge set N(e), then the one or more of the grid edges to be deleted cannot be deleted.

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