Topological material classification model TopoGNN based on graph neural network

Abstract

The invention relates to the field of topological material classification, and discloses a topological material classification model TopoGNN based on a graph neural network, the classification model TopoGNN comprises five layers of TopoGNN Layer, the input of the TopoGNN comprises an atom type alpha i, a Weikov position wi, a space group sg and side information # imgabs0 #, after all category information is digitalized, the atom type alpha i, the Weikov position wi, the space group sg and the side information # imgabs0 # are input into the TopoGNN, and the Weikov position wi, the space group sg and the side information # imgabs0 # are input into the TopoGNN; the atom type is processed by an embedding module which is the same as that of the CGCNN and a linear layer and then is connected with embedding of a View position and a space group to form each node input of the TopoGNN Layer, and side information is processed into a vector mode by an RBF core and then is processed by using two linear layers to form another input of the TopoGNN Layer; the output contents of the two modules are summed and processed by using a residual error to serve as the final output result of each layer, and finally the outputs of the five layers of models are summed, so that the model can effectively perform the classification process of topological materials, and the classification effect is better.

Description

Technical Field

[0001] The present invention relates to the field of topological material classification, specifically a topological material classification model TopoGNN based on a graph neural network. Background Art

[0002] Topological materials, including topological insulators and topological semimetals, can exhibit robust boundary states, quantized bulk responses, and exotic transport properties, which are characterized by topologically non-trivial electronic wave functions. Generally speaking, the boundary states of topological materials have characteristics such as "backscattering channel confinement", which can be used to fabricate ultra-low energy-consuming electronic components. For example, spin electronic devices can be designed by utilizing the "momentum-spin locking" characteristics of electrons in the boundary states of topological materials, and qubits can be designed by using the "Majorana zero modes" at the boundaries of topological superconductors. Therefore, studying topological materials has double significance in basic science and applied technology.

[0003] The establishment of a large-scale topological material database has enabled researchers to start using machine learning methods developed in recent years to determine the topological properties and types of materials. For example, Nina Andrejevic et al. calculated the X-ray absorption edge structure (XANES) spectra of more than 10,000 inorganic materials to train a neural network classifier. This classifier directly predicts the topological type from the XANES features, achieving accuracies of 89% and 93% in classifying topological and trivial types respectively. In addition, Andrew Ma and Yang Zhang et al. proposed a heuristic chemical rule called "Topogivity" to determine the topological type of a material from its chemical formula and discovered 56 new topological materials using this method. However, these methods all have certain drawbacks. In determining the topological type of materials, computational methods are costly, while machine learning-based methods do not consider the structural and symmetry information of materials, making it difficult to distinguish topological materials with the same chemical formula but different structures. In addition to manually constructing feature vectors, another method called graph neural network can predict the properties of materials based on their crystal structures. This method is expected to solve the problem that machine learning methods have difficulty in distinguishing topological materials with the same chemical formula but different structures. In 2017, Xie et al. first proposed that the crystal structure can be represented by a crystal graph encoding atomic information and interatomic bonding interactions, and then a convolutional neural network can be constructed on the graph. After training, this method achieved high-precision prediction of 8 different density functional theory calculated properties of crystals with different structural types and compositions. Subsequently, researchers have made varying degrees of improvements to the graph neural network in terms of the crystal graph representation method and model architecture, further improving the prediction accuracy of the network for material properties. Currently, in the field of materials science, graph neural networks have been used in areas such as predicting the stability of disordered materials, defect analysis and design, and surface reaction simulation. However, in the prior art, the classification technology for topological materials needs to be improved. Based on the above, this application proposes a topological material classification model TopoGNN based on graph neural networks for classifying topological materials. Summary of the Invention

[0004] An object of the present invention is to provide a topological material classification model TopoGNN based on graph neural networks to solve the problems raised in the above background art.

[0005] To achieve the above object, the present invention provides the following technical solution: A topological material classification model TopoGNN based on graph neural networks, the classification model TopoGNN includes 5 layers of TopoGNN Layer, and the input of the TopoGNN includes atomic type α i , Wyckoff position w i , space group sg and edge information After digitizing all category information, the atomic types are processed by the same embedding module as CGCNN and a linear layer, and then connected to the embeddings of Wyckoff positions and space groups to form the input for each node of the TopoGNN Layer. The edge information is processed into a vector pattern by the RBF kernel and then processed by two linear layers to form another input of the TopoGNN Layer. The outputs of these two modules are summed and processed with a residual connection as the final output of each layer. Finally, the outputs of these 5-layer models are summed.

[0006] Furthermore: Each TopoGNN Layer of the TopoGNN respectively uses a self-attention mechanism to process the node input.

[0007] Furthermore: Each TopoGNN Layer of the TopoGNN respectively uses a message passing network to process the inputs of nodes and edges.

[0008] Furthermore: After summing the outputs of the 5-layer TopoGNN Layer of the TopoGNN, an average pooling and two linear layers are used for processing to output the final classification result.

[0009] The beneficial effects of the present invention compared with the prior art are as follows:

[0010] The classification effect of the Wyckoff position and space group is added to the model of the present invention. The addition of symmetry information can improve the classification ability of the model of the present invention for topological materials to a certain extent. The present invention changes the way the model processes the input. In the original architecture, the space group is connected to the embeddings of atomic types and Wyckoff positions after passing through the embedding layer. Processing the space group information together with the edge information is more suitable for the model to classify topological materials. The present invention uses different message passing networks, and adopting a reasonable architecture can further improve the classification accuracy of the TopoGNN. Brief Description of the Drawings

[0011] Figure 1 It is the model architecture diagram of the present invention;

[0012] Figure 2 It is the structural diagram of the embodiment of the present invention. Detailed Embodiments

[0013] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0014] Example 1

[0015] Please refer to Figure 1 - Figure 2 , in the figure, the topological material classification model TopoGNN based on the graph neural network. The classification model TopoGNN includes 5 TopoGNN Layers. The input of TopoGNN includes atomic type α i , Wyckoff position w i , space group sg and edge information After digitizing all the category information, the atomic type is processed by the same embedding module as CGCNN and a linear layer, and then connected to the embeddings of the Wyckoff position and the space group to form the input of each node of the TopoGNN Layer. The edge information is processed into a vector pattern by the RBF kernel and then processed by two linear layers to form another input of the TopoGNN Layer. The outputs of these two modules are summed and processed by a residual connection to obtain the final output result of each layer. Finally, the outputs of these 5 layers of the model are summed up.

[0016] In this embodiment, each TopoGNN Layer of TopoGNN processes the node input using the self-attention mechanism respectively. Each TopoGNN Layer of TopoGNN processes the inputs of nodes and edges using the message passing network respectively. After summing the outputs of the 5 TopoGNN Layers of TopoGNN, an average pooling and 2 linear layers are used for processing to output the final classification result.

[0017] Furthermore, in order to verify the classification ability of the model of the present invention for topological materials, the present invention constructs two datasets. The first dataset contains 18,100 trivial topological materials, 13,985 topological semimetals (SM) and 6,109 topological insulators (TI). The present invention abbreviates it as TM. The other dataset contains 6,109 trivial topological materials, 6,109 topological semimetals and 6,109 topological insulators. The present invention abbreviates this dataset as TM_Clean. Subsequently, the present invention randomly uses 90% of the data in the dataset as the training set and 10% of the data as the test set. In terms of evaluating performance, the present invention uses 5-fold cross-validation, trains 100 rounds for each fold, selects the model with the best classification effect on the validation set and calculates its classification accuracy on the test set.

[0018] First, to verify the role of symmetry information, the present invention separately tested the classification effects of the model without adding any features, only adding Wyckoff positions, only adding space groups, and adding Wyckoff positions and space groups. As shown in Tables 1 and 2, after adding the Wyckoff position (wk) feature, the classification accuracy of the model has been improved to a certain extent on both the TM and TM_Clean datasets. Especially on the TM_Clean dataset, the improvement in this accuracy has reached about 10%. The addition of symmetry information can improve the classification ability of the model of the present invention for topological materials to a certain extent.

[0019] Table 1 Classification effects of TopoGNN on the TM dataset under different feature inputs

[0020]

[0021] Table 2 Classification effects of TopoGNN on the TM_Clean dataset under different feature inputs

[0022]

[0023] From the above, the present invention found that improper input of the space group may weaken the classification effect of the model. Therefore, as Figure 2 shown, the present invention changed the way the model processes the input. In the original architecture, after passing through the embedding layer, the space group is connected to the embedding of the atomic type and the embedding of the Wyckoff position. The present invention denoted this processing method as V1. After improvement, the embedding of the space group is connected to the embedding of the edge. The present invention denoted this processing method as V2. Subsequently, on the TM and TM_Clean datasets, the present invention tested the classification effects of the V1 and V2 processing methods. As shown in Tables 3 and 4, in 3 out of 4 comparison experiments, the V2 processing method achieved better classification accuracy, indicating that processing the space group information together with the edge information is more suitable for the model to classify topological materials.

[0024] Table 3 Classification effects of TopoGNN on the TM dataset under different feature processing methods

[0025]

[0026]

[0027] Table 4 Classification effects of TopoGNN on the TM_Clean dataset under different feature processing methods

[0028]

[0029] In addition, the present invention notes that using different message passing networks may also have different impacts on the classification effect of TopoGNN. Therefore, the present invention tested the classification effect of the model without using a message passing network, using GINE, using GatedGCN, and using GAT. As shown in Tables 5 and 6, in the TM and TM_Clean datasets, different message passing networks do have different impacts on the classification effect of the model, and GatedGCN achieved the best classification effect in both datasets. This shows that adopting a reasonable architecture can further improve the classification accuracy of TopoGNN.

[0030] Table 5 Classification Effect of TopoGNN on TM Dataset Using Different Message Passing Networks

[0031]

[0032] Table 6 Classification Effect of TopoGNN on TM_Clean Dataset Using Different Message Passing Networks

[0033]

[0034]

[0035] Finally, in order to compare the classification effects of TopoGNN and other graph neural networks on topological materials, the present invention conducted comparative experiments as shown in Tables 7 and 8. The graph neural networks selected by the present invention are CGCNN, SchNet, MEGNet, GATGNN, and Matformer. It can be seen that whether in the TM dataset or the TM_Clean dataset, TopoGNN achieved the best classification effect. This shows that the classification model designed by the present invention for classifying topological materials is very effective, and the newly added symmetry information can well help TopoGNN obtain the differences at the crystal structure level of different topological materials.

[0036] Table 7 Classification Effect of TopoGNN and Other Graph Neural Networks on TM Dataset

[0037]

[0038] Table 8 Classification Effect of TopoGNN and Other Graph Neural Networks on TM_Clean Dataset

[0039]

[0040] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device.

[0041] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A topological material classification model TopoGNN based on graph neural network, the classification model TopoGNN includes 5 layers of TopoGNN Layer, characterized by: The input of the TopoGNN includes atom type α i , Wyckoff position w i , space group sg and side information After all the category information is digitized, the atom type is processed by the same embedding module and a linear layer as CGCNN, and then connected with the embedding of the Vykoff position and space group to form each node input of the TopoGNN Layer. The edge information is processed into a vector pattern by the RBF kernel and then processed by two linear layers to form another input of the TopoGNN Layer. The output contents of these two modules are summed and processed by a residual connection as the final output result of each layer. Finally, the outputs of the 5-layer model are summed.

2. The topological material classification model TopoGNN based on graph neural network according to claim 1 is characterized by: Each TopoGNN layer of the TopoGNN uses a self-attention mechanism to process node input.

3. The topological material classification model TopoGNN based on graph neural network according to claim 2 is characterized by: Each TopoGNN layer of the TopoGNN uses a message passing network to process the input of nodes and edges respectively.

4. The topological material classification model TopoGNN based on graph neural network according to claim 3 is characterized by: The outputs of the five TopoGNNLayer layers of the TopoGNN are summed, and then an average pooling and two linear layers are used to process and output the final classification result.

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