Globally approximate Gaussian processes for big data with application to data-driven metamaterials design

Ramin Bostanabad, Yu Chin Chan, Liwei Wang, Ping Zhu, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globally approximate Gaussian process (GAGP). Unlike most large-scale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build a collection of independent GPs that use the same hyperparameters but randomly distribute the entire training dataset among themselves. This is based on our observation that the GP hyperparameter approximations change negligibly as the size of the training data exceeds a certain level, which can be estimated systematically. For inference, the predictions from all GPs in the collection are pooled, allowing the entire training dataset to be efficiently exploited for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power matching (and in some cases exceeding) that of state-of-the-art supervised learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials, using it to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then achieved by employing GAGP in inverse optimization.

Original languageEnglish (US)
Article numbere4044257
JournalJournal of Mechanical Design, Transactions of the ASME
Volume141
Issue number11
DOIs
StatePublished - Nov 1 2019

Keywords

  • Big data
  • Design automation
  • Design optimization
  • Design representation
  • Gaussian processes
  • Metamaterials
  • Metamodeling
  • Supervised learning

ASJC Scopus subject areas

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

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