Data-driven topology optimization with multiclass microstructures using latent variable Gaussian process

Liwei Wang, Siyu Tao, Ping Zhu*, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or “distance” measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.

Original languageEnglish (US)
Article number031708
JournalJournal of Mechanical Design - Transactions of the ASME
Issue number3
StatePublished - Mar 2021


  • Data-driven design
  • Gaussian process
  • Mixed variables
  • Multiclass
  • Multiscale topology optimization

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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