Advanced Science
02 April 2026
Unsupervised Hierarchical Symbolic Regression for Interpretable Property Modeling in Complex Multi-Variable Systems
Siyu Lou1,2,†, Chengchun Liu3,†, Dongxiao Zhang2, Yuntian Chen2,*, Fanyang Mo3,4,5
1 School of computer science, Shanghai Jiao Tong University, Shanghai, P.R. China
2 Ningbo Key Laboratory of Advanced Manufacturing Simulation, Eastern Institute of Technology, Ningbo, P.R. China
3 School of Materials Science and Engineering, Peking University, Beijing, P.R. China
4 School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, P.R. China
5 AI for Science (AI4S)-Preferred Program, Peking University Shenzhen Graduate School, Shenzhen, P.R. China
6 Guangdong Provincial Key Laboratory of Nano-Micro Materials Research, Peking University Shenzhen Graduate School, Shenzhen, P.R. China
† Siyu Lou and ChengChun Liu contributed equally to this work.
10.1002/advs.202521200
This paper introduces unsupervised hierarchical symbolic regression, a new framework that transforms black-box machine learning into transparent scientific equations. By uncovering human-interpretable laws from high-dimensional data, it bridges artificial intelligence, chemistry, and physics, enabling trustworthy discovery of structure-property relationships and offering a general paradigm for explainable modeling across complex scientific systems.
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