Reduced order modeling for nonlinear structural analysis using Gaussian process regression

Mengwu Guo*, Jan S. Hesthaven*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

135 Citations (Scopus)


A non-intrusive reduced basis (RB) method is proposed for parametrized nonlinear structural analysis undergoing large deformations and with elasto-plastic constitutive relations. In this method, a reduced basis is constructed from a set of full-order snapshots by the proper orthogonal decomposition (POD), and the Gaussian process regression (GPR) is used to approximate the projection coefficients. The GPR is carried out in the offline stage with active data selection, and the outputs for new parameter values can be obtained rapidly as probabilistic distributions during the online stage. Due to the complete decoupling of the offline and online stages, the proposed non-intrusive RB method provides a powerful tool to efficiently solve parametrized nonlinear problems with various engineering applications requiring multi-query or real-time evaluations. With both geometric and material nonlinearities taken into account, numerical results are presented for typical 1D and 3D examples, illustrating the accuracy and efficiency of the proposed method.
Original languageEnglish
Pages (from-to)807-826
JournalComputer methods in applied mechanics and engineering
Publication statusPublished - Nov 2018
Externally publishedYes


  • Reduced basis method
  • Nonlinear structural analysis
  • Proper orthogonal decomposition
  • Gaussian process regression
  • Machine learning

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