Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 23, 2014
- Source ID
- 10.1002/nme.4770
Entities
People
- Charbel Farhat
- Matthew J. Zahr
Organizations
- Office of Naval Research
- Stanford University
- United States Army Research Laboratory
- United States Department of Energy