Marine Ecosystem Model Calibration through Enhanced Surrogate-Based Optimization - Simulation and Modeling Methodologies, Technologies and Application - page 196

β
f

y d u d y

Fig. 5. Synthetic target data at optimal parameters and fine model response (down-

u f , u c , u s 1 sampled) for two illustrative tracers and at the uppermost depth layer for the solutions

u s 2 of a direct fine and coarse model optimization as well as of a SBO run exploiting the
original and the improved correction scheme. Solutions

and

u s 1 and u s 2 correspond to points 1 and

2inFigure4

u f with an almost
perfect fit of the target data (cf. Figure 5) and of the optimal parameters

On the other hand, direct fine model optimization yields a solution

u d (cf. Table
1), corresponding to a very low cost function of J ≈· 10 − 2 . However, the optimization
cost is substantially higher: about 980 fine model evaluations.
In [14], we demonstrated that in a exemplary SBO run based on the original response
correction scheme, a reasonably accurate solution

u s 1 could be obtained at the cost of

approximately 60 equivalent fine model evaluations only (point 1 in Figure 4). This
resulted in a significant reduction of the total optimization cost of about 84% when
compared to the direct fine model optimization (correspondingly, 375 evaluations were
required in the fine model optimization to reach this cost function value, cf. Figure 4).
Exploiting the improved scheme, a similarly accurate solution - both in terms of
parameter match and optimal fit of the target data - can be obtained at a remarkably
lower cost of only 17 equivalent fine model evaluations (point 3 in Figure 4). This is
over three times less than for the original response correction scheme corresponding to
a reduction of the total optimization cost of about 96%. Specific parameter values and
model responses of this solution are omitted here, since they are similar to those of the
original solution u s 1 .