  In this study, we present the original method for reconstructing the
potential of interparticle interaction from statistically averaged structural
data, namely, the radial distribution function of particles in many-particle
system. This method belongs to a family of machine learning methods and is
implemented through the differential evolution algorithm. As demonstrated for
the case of the Lennard-Jones liquid taken as an example, there is no
one-to-one correspondence between structure and potential of interparticle
interaction of a many-particle disordered system at a certain thermodynamic
state. Namely, a whole family of the Mie potentials determined by two
parameters $p_{ 1 }$ and $p_{ 2 }$ related to each other according to a certain
rule can reproduce properly a unique structure of the Lennard-Jones liquid at a
given thermodynamic state. It is noteworthy that this family of the potentials
quite correctly reproduces for the Lennard-Jones liquid the transport
properties (in particular, the self-diffusion coefficient) over a temperature
range as well as the dynamic structure factor, which is one of the key
characteristics of the collective dynamics of particles.
