Data-driven inverse design of multifunctional bicontinuous multiscale structures

Lili Wang1,2†, Jingxuan Feng1†, Xiaoya Zhai1*, Jiacheng Han1, Kai Chen3, Winston Wai Shing Ma4, Ligang Liu1, Xiao-Ming Fu1

1 School of Mathematical Sciences, University of Science and Technology of China 2 School of Mathematical Sciences, Xinjiang Normal University 3 Zhongguancun Institute of Artificial Intelligence 4 Department of Mechanical Engineering, Hong Kong Polytechnic University

† Equal contribution   * Corresponding author

Nature Communications 2026

Paper ↗ BibTeX ↓
L-BOM dataset, bicontinuous structures, and femoral implant design

Abstract

Bicontinuous multiscale structures combine mechanical support with continuous pathways for transport, but inverse design is difficult when neighboring microstructures must remain connected. This work introduces L-BOM (Large-range, Boundary-identical, Bicontinuous Open-cell Microstructure): four datasets of three-dimensional microstructures that share prescribed boundary masks while spanning a broad range of properties.

Starting from optimized structures, a boundary-conditioned generative model and active learning expand the datasets while retaining connected solid and void phases. These compatible building blocks can be assembled directly in multiscale designs. The paper demonstrates applications in bone implants, chair components, and multifunctional structures with tunable elasticity and permeability.

Pipeline

The approach begins with bicontinuous open-cell microstructures, builds boundary-compatible datasets through optimization and active learning, and selects building blocks for a target multiscale design.

Bicontinuous structures, connectivity constraints, L-BOM dataset construction, and a bone implant application
Figure 1. Motivation, connectivity challenge, L-BOM dataset, and a femoral implant example. Click the figure for the full-resolution version.

Dataset construction

Four boundary masks define separate microstructure families. A boundary-conditioned diffusion model proposes new structures; finite-element analysis and connectivity checks determine which candidates extend the initial optimization sets. The final datasets contain 404,355 microstructures, each discretized into 1283 elements.

Active-learning workflow and initial and final L-BOM datasets under four boundary masks
Figure 2. Initial optimization sets, active-learning workflow, and the resulting datasets under four boundary masks. Click the figure for the full-resolution version.

Femoral implant design

The paper uses the dataset to match elastic response and pore architecture in a porous femoral implant. Selected cells are assembled into a connected structure and compared with representative IWP, BCC truss, and spinodal architectures.

Femoral implant optimization, microstructure matching, and comparison with reference lattices
Figure 4. Femoral implant case study, including property matching, assembly, and comparison with reference porous architectures. Figure numbering follows the published paper.

BibTeX

@article{wang2026lbom,
  title   = {Data-driven inverse design of multifunctional bicontinuous multiscale structures},
  author  = {Wang, Lili and Feng, Jingxuan and Zhai, Xiaoya and Han, Jiacheng and Chen, Kai and Ma, Winston Wai Shing and Liu, Ligang and Fu, Xiao-Ming},
  journal = {Nature Communications},
  volume  = {17},
  pages   = {1335},
  year    = {2026},
  doi     = {10.1038/s41467-025-68089-2}
}

DOI: 10.1038/s41467-025-68089-2