Abstract
Bicontinuous multiscale structures, commonly observed in nature, comprise two interpenetrating networks that are solid and void phases forming a continuous and interconnected system. These unique architectures exhibit superior multi-physical performances and multifunctionalities; however, their design has been limited by the lack of analytical expressions and the computational challenges in multiscale optimization. This study presents a 3D Large-range, Boundary-identical, Bicontinuous, and Open-cell Microstructure (L-BOM) datasets for the fast data-driven inverse design of multifunctional bicontinuous multiscale structures. Each dataset features identical boundaries, bicontinuous open-cell structures, and broad property coverage for performance explora…
Abstract
Bicontinuous multiscale structures, commonly observed in nature, comprise two interpenetrating networks that are solid and void phases forming a continuous and interconnected system. These unique architectures exhibit superior multi-physical performances and multifunctionalities; however, their design has been limited by the lack of analytical expressions and the computational challenges in multiscale optimization. This study presents a 3D Large-range, Boundary-identical, Bicontinuous, and Open-cell Microstructure (L-BOM) datasets for the fast data-driven inverse design of multifunctional bicontinuous multiscale structures. Each dataset features identical boundaries, bicontinuous open-cell structures, and broad property coverage for performance exploration. These properties are satisfied by active learning techniques developed with a generative artificial intelligence model. The datasets hold significant promise for advancing the design of bicontinuous multiscale structures with a large-range property space, without additional post-processing to ensure the connectivity. This work further demonstrates the potential of the datasets in devising bone implants, chair components, and multifunctional materials with tunable elasticity and permeability.
Data availability
The tables of physical properties for the microstructures in the four datasets, as well as those for the microstructures shown in each figure of the main text and supplementary materials, are available on Zenodo66 (https://doi.org/10.5281/zenodo.17662421). Additionally, the aforementioned Zenodo repository also includes selected example data and the corresponding visualization scripts. Source data are provided with this paper.
Code availability
The code for the microstructure generation network and the corresponding training dataset are available at Zenodo67 (https://doi.org/10.5281/zenodo.17475876). The repository link for the LIVE3D framework is https://github.com/lavenklau/homo3d, and the Git commit version is 608f473.
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Acknowledgements
This work is supported by the National Key R&D Program of China (No. 2024YFA1016300, X.Z.), the National Natural Science Foundation of China (No. 62402467, X.Z., No. 92570201, X.F., No. 12494555, X.Z., No. 62025207, L.L.), the Youth Innovation Key Research Funds for the Central Universities, China (No. YD0010002010, X.Z.), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB0640000, X.Z.), the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2025D01B75, L.W.), the University of Science and Technology of China-Xinjiang Normal University Cooperative Development Joint Fund (No. XJNULH2502, L.W.), Xiaoya Zhai is USTC Tang Scholar.
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Author notes
These authors contributed equally: Lili Wang, Jingxuan Feng.
Authors and Affiliations
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China
Lili Wang, Jingxuan Feng, Xiaoya Zhai, Jiacheng Han, Ligang Liu & Xiao-Ming Fu 1.
School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, China
Lili Wang 1.
Zhongguancun Institute of Artificial Intelligence, Beijing, China
Kai Chen 1.
Department of Mechanical Engineering, Hong Kong Polytechnic University, Hong Kong, China
Winston Wai Shing Ma
Authors
- Lili Wang
- Jingxuan Feng
- Xiaoya Zhai
- Jiacheng Han
- Kai Chen
- Winston Wai Shing Ma
- Ligang Liu
- Xiao-Ming Fu
Contributions
L.W., J.F., X.Z., L.L., and X.F. conceived and designed the research; L.W. constructed the 3D L-BOM dataset, implemented the numerical simulations, and performed the data analysis; L.W. and X.Z. printed the metamaterial samples; J.F. and K.C. designed the machine learning framework; L.W., J.F., and J.H. wrote the relevant code and conducted the experiments; L.W., X.Z., and X.F. drafted the manuscript; L.W., J.F., X.Z., J.H., W.W.S.M., and X.F. revised the manuscript; X.Z., L.L., and X.F. supervised the project; X.Z., L.L., X.F., and L.W. provided funding support and resources. All authors participated in the discussion of the results.
Corresponding author
Correspondence to Xiaoya Zhai.
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Wang, L., Feng, J., Zhai, X. et al. Data-driven inverse design of multifunctional bicontinuous multiscale structures. Nat Commun (2026). https://doi.org/10.1038/s41467-025-68089-2
Received: 05 December 2024
Accepted: 26 November 2025
Published: 08 January 2026
DOI: https://doi.org/10.1038/s41467-025-68089-2