Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization

Zahr, Matthew J.; Farhat, Charbel

doi:10.1002/nme.4770

Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization

Journal Article · Mon Dec 22 23:00:00 EST 2014 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.4770· OSTI ID:1400895

Zahr, Matthew J. ^[1]; Farhat, Charbel ^[2]

Institute for Computational and Mathematical Engineering Stanford University Mail Code 4035 Stanford CA 94305 USA
Institute for Computational and Mathematical Engineering Stanford University Mail Code 4035 Stanford CA 94305 USA, Department of Aeronautics and Astronautics Stanford University Mail Code 4035 Stanford CA 94305 USA, Department of Mechanical Engineering Stanford University Mail Code 4035 Stanford CA 94305 USA

Summary

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%. Copyright © 2014 John Wiley & Sons, Ltd.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

OSTI ID:: 1400895

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 5 Vol. 102; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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