Data-driven reduced order modeling for time-dependent problems
(2019) In Computer Methods in Applied Mechanics and Engineering 345. p.75-99- Abstract
A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order data, a reduced basis is constructed by the proper orthogonal decomposition (POD), and the maps between the time/parameter values and the projection coefficients onto the RB are approximated as a regression model. With a natural tensor grid between the time and the parameters in the database, a singular-value decomposition (SVD) is used to extract the principal components in the data of projection coefficients. The regression functions are represented as the linear combinations of... (More)
A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order data, a reduced basis is constructed by the proper orthogonal decomposition (POD), and the maps between the time/parameter values and the projection coefficients onto the RB are approximated as a regression model. With a natural tensor grid between the time and the parameters in the database, a singular-value decomposition (SVD) is used to extract the principal components in the data of projection coefficients. The regression functions are represented as the linear combinations of several tensor products of two Gaussian processes, one of time and the other of parameters. During the online stage, the solutions at new time/parameter locations in the domain of interest can be recovered rapidly as outputs from the regression models. Featuring a non-intrusive nature and the complete decoupling of the offline and online stages, the proposed approach provides a reliable and efficient tool for approximating parametrized time-dependent problems, and its effectiveness is illustrated by non-trivial numerical examples.
(Less)
- author
- Guo, Mengwu LU and Hesthaven, Jan S.
- publishing date
- 2019-03-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Data-driven, Gaussian process regression, Low-rank approximation, Machine learning, Non-intrusive reduced order modeling, Time-dependent problem
- in
- Computer Methods in Applied Mechanics and Engineering
- volume
- 345
- pages
- 25 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85056770924
- ISSN
- 0045-7825
- DOI
- 10.1016/j.cma.2018.10.029
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2018 Elsevier B.V.
- id
- 8103aa72-670e-4ae5-93b8-749376965ffe
- date added to LUP
- 2024-03-19 12:21:13
- date last changed
- 2024-04-17 15:20:08
@article{8103aa72-670e-4ae5-93b8-749376965ffe,
abstract = {{<p>A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order data, a reduced basis is constructed by the proper orthogonal decomposition (POD), and the maps between the time/parameter values and the projection coefficients onto the RB are approximated as a regression model. With a natural tensor grid between the time and the parameters in the database, a singular-value decomposition (SVD) is used to extract the principal components in the data of projection coefficients. The regression functions are represented as the linear combinations of several tensor products of two Gaussian processes, one of time and the other of parameters. During the online stage, the solutions at new time/parameter locations in the domain of interest can be recovered rapidly as outputs from the regression models. Featuring a non-intrusive nature and the complete decoupling of the offline and online stages, the proposed approach provides a reliable and efficient tool for approximating parametrized time-dependent problems, and its effectiveness is illustrated by non-trivial numerical examples.</p>}},
author = {{Guo, Mengwu and Hesthaven, Jan S.}},
issn = {{0045-7825}},
keywords = {{Data-driven; Gaussian process regression; Low-rank approximation; Machine learning; Non-intrusive reduced order modeling; Time-dependent problem}},
language = {{eng}},
month = {{03}},
pages = {{75--99}},
publisher = {{Elsevier}},
series = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{Data-driven reduced order modeling for time-dependent problems}},
url = {{http://dx.doi.org/10.1016/j.cma.2018.10.029}},
doi = {{10.1016/j.cma.2018.10.029}},
volume = {{345}},
year = {{2019}},
}