Multidimensional surrogates

Multidimensional surrogates operate typically on input Datasets (see e.g. DynamicalSystems.jl package) and output the same type.

Shuffle dimensions

This surrogate was made to distinguish multidimensional data with structure in the state space from multidimensional noise.

Here is a simple application that shows that the distinction is successful for a system that we know a-priori is deterministic and has structure in the state space.

using DynamicalSystems, TimeseriesSurrogates, CairoMakie

D = 4
lo = Systems.lorenz96(D, range(0; length = D, step = 0.1); F = 24.0)
X = trajectory(lo, 1000; Δt = 0.1, Ttr = 100.0)

e = 10.0 .^ range(-3, 1, length = 10)
CX = correlationsum(X, e; w = 5)

le = log10.(e)
fig, ax = lines(le, log10.(CX))

sg = surrogenerator(X, ShuffleDimensions())
for i in 1:10
    Z = sg()
    CZ = correlationsum(Z, e)
    lines!(ax, le, log10.(CZ); color = ("black", 0.8))
end
ax.xlabel = "log(e)"; ax.ylabel = "log(C)"
fig