Tensor product function

The tensor product function is defined as: $f(x) = \prod_{i=1}^d \cos(a\pi x_i)$

Let's import Surrogates and Plots:

using Surrogates
using Plots

Define the 1D objective function:

function f(x)
    a = 0.5
    return cos(a * pi * x)
end

f (generic function with 1 method)

n = 100
lb = -5.0
ub = 5.0
a = 0.5
x = sample(n, lb, ub, SobolSample())
y = f.(x)
xs = lb:0.001:ub
scatter(x, y, label = "Sampled points", xlims = (lb, ub), ylims = (-1, 1), legend = :top)
plot!(xs, f.(xs), label = "True function", legend = :top)

Fitting and plotting different surrogates:

loba_1 = LobachevskySurrogate(x, y, lb, ub)
krig = Kriging(x, y, lb, ub)
scatter(
    x, y, label = "Sampled points", xlims = (lb, ub), ylims = (-2.5, 2.5), legend = :bottom)
plot!(xs, f.(xs), label = "True function", legend = :top)
plot!(xs, loba_1.(xs), label = "Lobachevsky", legend = :top)
plot!(xs, krig.(xs), label = "Kriging", legend = :top)