Inverting the structure–property map of truss metamaterials by deep learning

Jan Hendrik Bastek, Siddhant Kumar, Bastian Telgen, Raphaël N. Glaesener, Dennis M. Kochmann*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
6 Downloads (Pure)


Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While predicting effective truss properties is now commonplace, efficiently identifying architectures that have homogeneous or spatially varying target properties has remained a roadblock to applications from lightweight structures to biomimetic implants. To overcome this gap, we propose a deep-learning framework, which combines neural networks with enforced physical constraints, to predict truss architectures with fully tailored anisotropic stiffness. Trained on millions of unit cells, it covers an enormous design space of topologically distinct truss lattices and accurately identifies architectures matching previously unseen stiffness responses. We demonstrate the application to patient-specific bone implants matching clinical stiffness data, and we discuss the extension to spatially graded cellular structures with locally optimal properties.

Original languageEnglish
Article numbere2111505119
Number of pages8
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number1
Publication statusPublished - 2022


  • Deep learning
  • Inverse design
  • Metamaterial
  • Stiffness
  • Truss


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