  Approximation of entropies of various types using machine learning (ML)
regression methods are shown for the first time. The ML models presented in
this study define the complexity of the short time series by approximating
dissimilar entropy techniques such as Singular value decomposition entropy
(SvdEn), Permutation entropy (PermEn), Sample entropy (SampEn) and Neural
Network entropy (NNetEn) and their 2D analogies. A new method for calculating
SvdEn2D, PermEn2D and SampEn2D for 2D images was tested using the technique of
circular kernels. Training and testing datasets on the basis of Sentinel-2
images are presented (two training images and one hundred and ninety-eight
testing images). The results of entropy approximation are demonstrated using
the example of calculating the 2D entropy of Sentinel-2 images and R^2 metric
evaluation. The applicability of the method for the short time series with a
length from N = 5 to N = 113 elements is shown. A tendency for the R^2 metric
to decrease with an increase in the length of the time series was found. For
SvdEn entropy, the regression accuracy is R^2 > 0.99 for N = 5 and R^2 > 0.82
for N = 113. The best metrics were observed for the ML_SvdEn2D and ML_NNetEn2D
models. The results of the study can be used for fundamental research of
entropy approximations of various types using ML regression, as well as for
accelerating entropy calculations in remote sensing. The versatility of the
model is shown on a synthetic chaotic time series using Planck map and logistic
map.
