  The equation of state (EOS) of dense nuclear matter is a key factor to
determine the internal structure and properties of neutron stars. However, the
EOS of high-density nuclear matter has great uncertainty mainly because the
terrestrial nuclear experiments cannot reproduce matter as dense as that in the
inner core of a neutron star. Fortunately, continuous improvements in
astronomical observations of neutron stars provide the opportunity to inversely
constrain the EOS of high-density nuclear matter. A number of methods have been
proposed to implement this inverse constraint, such as the Bayesian analysis
algorithm, the Lindblom's approach, and so on. Neural network algorithm is an
effective new method developed in recent years. By employing a set of
isospin-dependent parametric EOSs as the training sample of neural network
algorithm, we set up an effective way to reconstruct the EOS with relative
accuracy through a few mass-radius data. Based on the obtained neural network
algorithms and according to the NICER observations on masses and radii of
neutron stars with assumed precision, we get the inversely constrained EOS and
further calculate the corresponding macroscopic properties of the neutron star.
The results are basically consistent with the constraint on EOS from the Huth
$et~ al.$ based on Bayesian analysis. Moreover, the results show that even
though the neural network algorithm was obtained by using the finite
parameterized EOS as the training set, it is valid for any rational parameter
combination of the parameterized EOS model.
