Surrogate-Based and One-shot Optimization Methods for PDE-Constrained Problems with an Application in Climate Models.

Slawig, Thomas, Prieß, Malte and Kratzenstein, Claudia (2014) Surrogate-Based and One-shot Optimization Methods for PDE-Constrained Problems with an Application in Climate Models. In: Solving Computationally Expensive Engineering Problems. . Springer Proceedings in Mathematics & Statistics, 97 . Springer International Publishing, 97:1-97:24. ISBN 978-3-319-08984-3 DOI 10.1007/978-3-319-08985-0_1.

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Abstract

We discuss PDE-constrained optimization problems with iterative state solvers. As typical and challenging example, we present an application in climate research, namely a parameter optimization problem for a marine ecosystem model. Therein, a periodic state is obtained via a slowly convergent fixed-point type iteration. We recall the algorithm that results from a direct or black-box optimization of such kind of problems, and discuss ways to obtain derivative information to use in gradient-based methods. Then we describe two optimization approaches, the One-shot and the Surrogate-based Optimization method. Both methods aim to reduce the high computational effort caused by the slow state iteration. The idea of the One-shot approach is to construct a combined iteration for state, adjoint and parameters, thus avoiding expensive forward and reverse computations of a standard adjoint method. In the Surrogate-based Optimization method, the original model is replaced by a surrogate which is here based on a truncated iteration with fewer steps. We compare both approaches, provide implementation details for the presented application, and give some numerical results.

Document Type: Book chapter
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
DOI etc.: 10.1007/978-3-319-08985-0_1
Projects: Future Ocean
Date Deposited: 18 Jan 2017 10:06
Last Modified: 15 Mar 2018 09:52
URI: http://oceanrep.geomar.de/id/eprint/35690

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