From masses and radii of neutron stars to EOS of nuclear matter through neural network

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.