  The Chirikov standard map and the 2D Froeschl\'e map are investigated. A few
thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent
(mLE) are plotted in a mixed space of the nonlinear parameter versus the
initial condition. Both characteristic exponents reveal remarkably similar
structures in this space. A tight correlation between the HEs and mLEs is
found, with the Spearman rank $\rho=0.83$ and $\rho=0.75$ for the Chirikov and
2D Froeschl\'e maps, respectively. Based on this relation, a machine learning
(ML) procedure, using the nearest neighbor algorithm, is performed to reproduce
the HE distribution based on the mLE distribution alone. A few thousand HE and
mLE values from the mixed spaces were used for training, and then using
$2-2.4\times 10^5$ mLEs, the HEs were retrieved. The ML procedure allowed to
reproduce the structure of the mixed spaces in great detail.
