Methodology study of machine learning for the neutron star equation of state

We discuss a methodology of machine learning to deduce the neutron star equation of state from a set of mass-radius observational data. We propose an efficient procedure to deal with a mapping from finite data points with observational errors onto an equation of state. We generate training data and optimize the neural network. Using independent validation data (mock observational data) we confirm that the equation of state is correctly reconstructed with precision surpassing observational errors. We finally discuss the relation between our method and Bayesian analysis with an emphasis put on generality of our method for underdetermined problems.