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Bi-fidelity fitting and optimization
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Image of FIG. 1.
FIG. 1.

The contours in the top panel show a potential surface calculated as described in the text. The dots on the panel show a maximin LHC design as described in Sec. II. Using the Gaussian process model of Sec. II, with the LHC design, results in the set of dotted contours in the bottom panel, which lie on top of the solid contour lines from the top panel, repeated in the bottom plot.

Image of FIG. 2.
FIG. 2.

The top panel shows a 1D slice of the potential surface at two levels of accuracy, as described in the text. The expensive CASPT2 surface in the middle panel (black line) is interpolated with only 4 points, using the GPM, resulting in a significant error (blue curve in the bottom panel). The bottom panel also shows the difference in the two potentials from the top panel (red curve) and the error in the fit using the 11 points from the top panel and the 4 points from the middle panel (black curve).

Image of FIG. 3.
FIG. 3.

Schematic diagrams of (a) a periodic array of (2D) slits in a silver film and (b) a periodic array of holes in a gold film on a glass substrate.

Image of FIG. 4.
FIG. 4.

(a) FDTD simulation results for an identical system, calculated with high and low spatial grid resolution. The 11 low fidelity samples are also shown. (b) The co-kriging predictor constructed from the 11 low-fidelity and an additional 4 high-fidelity points. The high-fidelity function is also shown. (c) The co-kriging predictor enhanced by 2 expected improvement points is shown.

Image of FIG. 5.
FIG. 5.

(a) Electric field intensity spectrum corresponding to system with a low FOM, t = 80 nm, r = 41 nm, p = 303 nm. (b) Electric field intensity corresponding to a system with a large FOM, t = 11.7 nm, r = 147 nm, p = 463 nm.


Generic image for table
Table I.

Co-kriging results. The low-fidelity kriging results are incorporated into a model that includes 6 high-fidelity samples and 10 high-fidelity iterations.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Bi-fidelity fitting and optimization