Hessian-based model reduction for large-scale systems with initial-condition inputs

• Published in: International journal for numerical methods in engineering 2008-02, Vol.73 (6), p.844-868
• Main Authors: Bashir, O., Willcox, K., Ghattas, O., van Bloemen Waanders, B., Hill, J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Exact sciences and technology; initial-condition problems; model reduction; Modelling and identification; Optimal control; optimization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2100

Reduced‐order models that are able to approximate output quantities of interest of high‐fidelity computational models over a wide range of input parameters play an important role in making tractable large‐scale optimal design, optimal control, and inverse problem applications. We consider the problem of determining a reduced model of an initial value problem that spans all important initial conditions, and pose the task of determining appropriate training sets for reduced‐basis construction as a sequence of optimization problems. We show that, under certain assumptions, these optimization problems have an explicit solution in the form of an eigenvalue problem, yielding an efficient model reduction algorithm that scales well to systems with states of high dimension. Furthermore, tight upper bounds are given for the error in the outputs of the reduced models. The reduction methodology is demonstrated for a large‐scale contaminant transport problem. Copyright © 2007 John Wiley & Sons, Ltd.