MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals

authored by: Hendrik Fischer, Julian Roth, Thomas Wick, Ludovic Chamoin, Amelie Fau
Abstract: In this work, the dual-weighted residual (DWR) method is applied to obtain an error-controlled incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with time slabbing and an incremental POD basis generation with goal-oriented error control based on dual-weighted residual estimates. The error in the goal functional is being estimated during the simulation and the POD basis is being updated if the estimate exceeds a given threshold. This allows an adaptive enrichment of the POD basis in case of unforeseen changes in the solution behavior. Consequently, the offline phase can be skipped, the reduced-order model is being solved directly with the POD basis extracted from the solution on the first time slab and –if necessary– the POD basis is being enriched on-the-fly during the simulation with high-fidelity finite element solutions. Therefore, the full-order model solves can be reduced to a minimum, which is demonstrated on numerical tests for the heat equation and elastodynamics using time-averaged quantities of interest.
Organisation(s): Institute of Applied Mathematics
External Organisation(s): Université Paris-Saclay
Type: Article
Journal: Journal of computational physics
Volume: 504
ISSN: 0021-9991
Publication date: 01.05.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Modelling and Simulation, Physics and Astronomy (miscellaneous), General Physics and Astronomy, Computer Science Applications, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.jcp.2024.112863 (Access: Open)

BibTeX

@article{ab2a60267d184bc39faa991f96b8eb8d,
title = "MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals",
abstract = "In this work, the dual-weighted residual (DWR) method is applied to obtain an error-controlled incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with time slabbing and an incremental POD basis generation with goal-oriented error control based on dual-weighted residual estimates. The error in the goal functional is being estimated during the simulation and the POD basis is being updated if the estimate exceeds a given threshold. This allows an adaptive enrichment of the POD basis in case of unforeseen changes in the solution behavior. Consequently, the offline phase can be skipped, the reduced-order model is being solved directly with the POD basis extracted from the solution on the first time slab and –if necessary– the POD basis is being enriched on-the-fly during the simulation with high-fidelity finite element solutions. Therefore, the full-order model solves can be reduced to a minimum, which is demonstrated on numerical tests for the heat equation and elastodynamics using time-averaged quantities of interest.",
keywords = "Dual-weighted residual method, Goal-oriented error control, Incremental proper orthogonal decomposition, Tensor-product space-time reduced-order modeling",
author = "Hendrik Fischer and Julian Roth and Thomas Wick and Ludovic Chamoin and Amelie Fau",
note = "Funding Information: The authors acknowledge the funding of the German Research Foundation (DFG) within the framework of the International Research Training Group on Computational Mechanics Techniques in High Dimensions GRK 2657 under Grant Number 433082294 . In addition, we thank Hendrik Geisler (Leibniz University Hannover, GRK 2657) for fruitful discussions and comments. The support of the French-German University through the French-German Doctoral college “Sophisticated Numerical and Testing Approaches” ( CDFA-DFDK 19-04 ) is also acknowledged. We thank the anonymous reviewers for their extensive questions that helped to improve the manuscript. ",
year = "2024",
month = may,
day = "1",
doi = "10.1016/j.jcp.2024.112863",
language = "English",
volume = "504",
journal = "Journal of computational physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
}