Efficient Classification Method for Topological Quantum Materials Based on Graph Neural Networks and Persistent Homology Theory

Topological quantum materials hold considerable promise for applications in quantum computing and spintronic devices due to their unique electronic properties. However, traditional Density Functional Theory (DFT) methods encounter difficulties in predicting these topological properties, including high computational costs and classification errors. This study proposes a machine learning framework that combines Graph Isomorphism Networks (GIN) with Atomic-Specific Persistent Homology (ASPH) to achieve efficient classification of topological materials by integrating global crystal structure features with local atomic topological descriptors. GIN is used to capture the global graph representation of periodic crystal structures, while ASPH extracts local features of atomic environments through multiscale topological analysis. These two feature sets are integrated following dimensionality reduction and subsequently classified using XGBoost. Principal Component Analysis (PCA) was employed to reduce the dimensionality of the high-dimensional ASPH feature vectors, thereby enhancing both model efficiency and accuracy. Experimental results indicate that this method performs exceptionally well in binary classification (topologically trivial/non-trivial), achieving an accuracy of 87.32%, which is significantly better than models based on a single feature. However, performance in ternary classification (trivial, semi-metal, topological insulator) declines to 75.04% due to class imbalance and feature overlap. The study validates the feasibility of combining graph neural networks with topological data analysis, providing an efficient computational framework for high-throughput screening of topological materials and offering new ideas for the application of multimodal feature fusion in materials science.