Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression

Ludovica Cicci, Stefania Fresca, Mengwu Guo*, Andrea Manzoni, Paolo Zunino

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
19 Downloads (Pure)


Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of the need to query expensive numerical solvers repeatedly. Projection-based reduced order models (ROMs), such as the Galerkin-reduced basis (RB) method, have been extensively developed in the last decades to overcome the computational complexity of high fidelity full order models (FOMs), providing remarkable speed-ups when addressing UQ tasks related with parameterized differential problems. Nonetheless, constructing a projection-based ROM that can be efficiently queried usually requires extensive modifications to the original code, a task which is non-trivial for nonlinear problems, or even not possible at all when proprietary software is used. Non-intrusive ROMs – which rely on the FOM as a black box – have been recently developed to overcome this issue. In this work, we consider ROMs exploiting proper orthogonal decomposition to construct a reduced basis from a set of FOM snapshots, and Gaussian process regression (GPR) to approximate the RB projection coefficients. Two different approaches, namely a global GPR and a tensor-decomposition-based GPR, are explored on a set of 3D time-dependent solid mechanics examples. Finally, the non-intrusive ROM is exploited to perform global sensitivity analysis (relying on both screening and variance-based methods) and parameter estimation (through Markov chain Monte Carlo methods), showing remarkable computational speed-ups and very good accuracy compared to high-fidelity FOMs.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalComputers and Mathematics with Applications
Early online date6 Sept 2023
Publication statusPublished - 1 Nov 2023


  • Gaussian process regression
  • Nonlinear solid mechanics
  • Parameter estimation
  • Reduced order modeling
  • Sensitivity analysis
  • Uncertainty quantification
  • UT-Hybrid-D


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