TY - JOUR

T1 - MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals

AU - Fischer, Hendrik

AU - Roth, Julian

AU - Wick, Thomas

AU - Chamoin, Ludovic

AU - Fau, Amelie

N1 - 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.

PY - 2024/5/1

Y1 - 2024/5/1

N2 - 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.

AB - 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.

KW - Dual-weighted residual method

KW - Goal-oriented error control

KW - Incremental proper orthogonal decomposition

KW - Tensor-product space-time reduced-order modeling

UR - http://www.scopus.com/inward/record.url?scp=85185832719&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2024.112863

DO - 10.1016/j.jcp.2024.112863

M3 - Article

AN - SCOPUS:85185832719

VL - 504

JO - Journal of computational physics

JF - Journal of computational physics

SN - 0021-9991

M1 - 112863

ER -