Xiang Liu

About Me

I am a postdoctoral scholar in the Department of Mathematics at Michigan State University, working in Prof. Guo-Wei Wei's group. I received my Ph.D. in Applied Topology from the Chern Institute of Mathematics at Nankai University, supervised by Prof. Kelin Xia and Prof. Huitao Feng.

My research connects topology, geometry, and artificial intelligence. I develop mathematically grounded learning methods and apply them to biomedical imaging, molecular science, protein function, drug design, and complex networks.

Research Interests

My research focuses on mathematical and computational methods for learning from complex structured data. Current topics include:

• Topological Data Analysis: Persistent homology, hypergraph topology, graph complexes, sheaves
• Topological Deep Learning: Simplicial neural networks, copresheaf topological neural network, path complex neural networks
• Mathematical AI: Interpretable and geometry-aware machine learning
• AI for Science: Molecular representation, protein function prediction, biomedical data, and drug design

Research Experience

• 2024–Present   Postdoctoral Scholar, Department of Mathematics, Michigan State University.
  In Prof. Guo-Wei Wei's group.
• 2023–2024   Joint Ph.D. Student, School of Physical and Mathematical Sciences, Nanyang Technological University.
  In Prof. Kelin Xia's group.
• 2022–2023   Visiting Scholar, Beijing Institute of Mathematical Sciences and Applications (BIMSA).
  In Prof. Jie Wu's group.

Education

• 2024   Ph.D. in Applied Topology, Nankai University.
  Advisors: Prof. Kelin Xia and Prof. Huitao Feng.
• 2020   M.S. in Algebraic Topology, Nankai University.
  Advisor: Prof. Xiangjun Wang.
• 2017   B.E. in Software Engineering, Jilin University.

Publications

• Xinyu You, Xiang Liu, Chuan-Shen Hu, Kelin Xia, Tze Chien Sum. “Quotient Complex Transformer (QCformer) for Perovskite Data Analysis.” Cell Reports Physical Science, 2026.
• Xiang Liu, Zhe Su, Yongyi Shi, Yiying Tong, Ge Wang, Guo-Wei Wei. “Manifold Topological Deep Learning for Biomedical Data.” Nature Communications, 2026.
• Zhe Su, Xiang Liu, Layal Bou Hamdan, Vasileios Maroulas, Jie Wu, Gunnar Carlsson, Guo-Wei Wei. “Topological data analysis and topological deep learning beyond persistent homology—a review.” Artificial Intelligence Review, 2025.
• Xiang Liu, Junjie Wee, Guo-Wei Wei. “Topological Machine Learning for Protein–Nucleic Acid Binding Affinity Changes Upon Mutation.” Machine Learning: Science and Technology, 2025.
• Xiang Liu, Xuefei Huang, Guo-Wei Wei. “Topological Learning Prediction of Virus-like Particle Stoichiometry and Stability.” Biophysical Journal, 2025.
• Cong Shen, Xiang Liu, Jiawei Luo, Kelin Xia. “Torsion Graph Neural Networks.” IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025.
• Li Feng, Dengcheng Yang, Sinan Wu, Chengwen Xue, Mengmeng Sang, Xiang Liu, Jincan Che, Jie Wu, Claudia Gragnoli, Christopher Griffin, Chen Wang, Shing-Tung Yau, Rongling Wu. “Network modeling and topology of aging.” Physics Reports, 2025.
• Li Feng, Huiying Gong, Shen Zhang, Xiang Liu, Yu Wang, Jincan Che, Ang Dong, Christopher H. Griffin, Claudia Gragnoli, Jie Wu, Shing-Tung Yau, Rongling Wu. “Hypernetwork modeling and topology of high-order interactions for complex systems.” Proceedings of the National Academy of Sciences, 2024.
• Huiying Gong, Hongxing Wang, Yu Wang, Shen Zhang, Xiang Liu, Jincan Che, Shuang Wu, Jie Wu, Xiaomei Sun, Shougong Zhang, Shing-Tung Yau, Rongling Wu. “Topological change of soil microbiota networks for forest resilience under global warming.” Physics of Life Reviews, 2024.
• Xiang Liu, Huitao Feng, Jie Wu, Kelin Xia. “Computing hypergraph homology.” Foundations of Data Science, 2024.
• Shuang Wu, Xiang Liu, Ang Dong, Claudia Gragnoli, Christopher Griffin, Jie Wu, Shing-Tung Yau, Rongling Wu. “The metabolomic physics of complex diseases.” Proceedings of the National Academy of Sciences, 2023.
• Xiang Liu, Huitao Feng, Zhi Lü, Kelin Xia. “Persistent Tor-algebra for protein–protein interaction analysis.” Briefings in Bioinformatics, 2023.
• Ran Liu, Xiang Liu, Jie Wu. “Persistent Path-Spectral Based Machine Learning for Protein–Ligand Binding Affinity Prediction.” Journal of Chemical Information and Modeling, 2023.
• Xiang Liu, Huitao Feng, Jie Wu, Kelin Xia. “Dowker complex based machine learning models for protein-ligand binding affinity prediction.” PLOS Computational Biology, 2022.
• Xiang Liu, Huitao Feng, Jie Wu, Kelin Xia. “Persistent spectral hypergraph based machine learning for protein-ligand binding affinity prediction.” Briefings in Bioinformatics, 2021.
• Xiang Liu, Xiangjun Wang, Jie Wu, Kelin Xia. “Hypergraph based persistent cohomology for molecular representations in drug design.” Briefings in Bioinformatics, 2021.

For the complete and current list, see [ Google Scholar ] or [ Curriculum Vitae ].

Services

Journal Reviewer