Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression
(2023) In Computers and Mathematics with Applications 149. p.1-23- Abstract
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... (More)
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.
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- author
- Cicci, Ludovica ; Fresca, Stefania ; Guo, Mengwu LU ; Manzoni, Andrea and Zunino, Paolo
- publishing date
- 2023-11-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Gaussian process regression, Nonlinear solid mechanics, Parameter estimation, Reduced order modeling, Sensitivity analysis, Uncertainty quantification
- in
- Computers and Mathematics with Applications
- volume
- 149
- pages
- 23 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85169901566
- ISSN
- 0898-1221
- DOI
- 10.1016/j.camwa.2023.08.016
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2023 The Author(s)
- id
- c36d9d70-eeb4-461e-8ab0-05269ce261d4
- date added to LUP
- 2024-03-18 23:04:27
- date last changed
- 2024-04-17 08:51:19
@article{c36d9d70-eeb4-461e-8ab0-05269ce261d4,
abstract = {{<p>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.</p>}},
author = {{Cicci, Ludovica and Fresca, Stefania and Guo, Mengwu and Manzoni, Andrea and Zunino, Paolo}},
issn = {{0898-1221}},
keywords = {{Gaussian process regression; Nonlinear solid mechanics; Parameter estimation; Reduced order modeling; Sensitivity analysis; Uncertainty quantification}},
language = {{eng}},
month = {{11}},
pages = {{1--23}},
publisher = {{Elsevier}},
series = {{Computers and Mathematics with Applications}},
title = {{Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression}},
url = {{http://dx.doi.org/10.1016/j.camwa.2023.08.016}},
doi = {{10.1016/j.camwa.2023.08.016}},
volume = {{149}},
year = {{2023}},
}