Surrogate-Based and One-Shot Optimization Methods for PDE-Constrained Problems with an Application in Climate Models
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.
KeywordsOptimization Climate model Marine ecosystem model One-shot method Surrogate-based optimization
The work was supported by DFG in the Cluster “Future Ocean” and the priority program 1253 “Optimization with Partial Differential Equations”, and by the EU in the FP7 project “CarboChange”.
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