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

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.