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Open Access

REVIEW

Topological Materials and Machine Learning: A Comprehensive Review

Jing-Wen Gao1,2, Yunan He1,*, Jian Liu1,*
1 Mathematical Science Research Center, Chongqing University of Technology, Chongqing, China
2 Mathematical Science School, Huazhong University of Science and Technology, Wuhan, China
* Corresponding Author: Yunan He. Email: email; Jian Liu. Email: email
(This article belongs to the Special Issue: Advanced Computational Modeling and Simulations for Engineering Structures and Multifunctional Materials: Bridging Theory and Practice, 2nd Edition)

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.084503

Received 23 April 2026; Accepted 24 June 2026; Published online 20 July 2026

Abstract

The unique topological properties of the electronic band structures in topological materials have increasingly attracted attention in both fundamental research and next-generation technological applications. With the rise of machine learning, the connection between topological materials and machine learning has deepened significantly. This review systematically summarizes the interaction between these two fields, tracing the history of their mutual promotion and synergistic development. We further examine the transformative impact of machine learning across multiple domains of topological materials, with a particular focus on recent progress in inverse design and generation of topological materials, topological superconductivity, and the mapping of topological phase diagrams. This paper also analyzes the data complexity arising from the topological properties of electronic structures and notes that topological deep learning is naturally suited for processing such complex data. In addition, we discuss the current limitations of existing machine learning methods and propose potential strategies to address these challenges. This review aims to provide a fundamental reference for researchers seeking to advance the bidirectional integration of machine learning and topological materials.

Keywords

Topological materials; machine learning; symmetry-based theories; data-driven approaches; topological deep learning

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