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@article{zahr2015progressive,
abstract = {An adaptive approach to using reduced-order models (ROMs) as surrogates in partial differential equations (PDE)-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given ROM is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the high-dimensional model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust-region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a reduced-order basis is also presented, along with a methodology for computing sensitivities of the ROM that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm.
The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4-5, compared with the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1\%.},
arxiv = {https://arxiv.org/abs/1407.7618},
author = {Zahr, Matthew J. and Farhat, Charbel},
contribution = {conceptualization, methodology, software, formal analysis, investigation, writing - original (MJZ); resources, writing - edit/review, supervision (CF)},
corauthor = {Zahr, Matthew J.},
date-modified = {2020-12-31 15:01:59 -0500},
doi = {10.1002/nme.4770},
journal = {International Journal for Numerical Methods in Engineering},
keywords = {model order reduction, PDE-constrained optimization, optimization, proper orthogonal decomposition (POD), reduced-order model (ROM), singular value decomposition (SVD)},
link = {http://onlinelibrary.wiley.com/doi/10.1002/nme.4770/abstract?userIsAuthenticated=false&deniedAccessCustomisedMessage=},
number = {5},
pages = {1111--1135},
project = {trammo},
publisher = {Wiley Online Library},
title = {Progressive construction of a parametric reduced-order model for {PDE}-constrained optimization},
volume = {102},
year = {2015},
bdsk-url-1 = {https://dx.doi.org/10.1002/nme.4770}
}
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