The Neutron Star Outer Crust Equation of State: A Machine Learning approach

Constructing the outer crust of the neutron stars requires the knowledge of the Binding Energy (BE) of the atomic nuclei. Although the BE of a lot of the nuclei is experimentally determined and can be obtained from the AME data table, for the others we need to depend on theoretical models. There exist a lot of physical theories to predict the BE, each with its own strengths and weaknesses. In this paper, we apply Machine Learning (ML) algorithms on AME2016 data set to predict the Binding Energy {of atomic nuclei}. The novel feature of our work is that it is model independent. We do not assume or use any nuclear physics model but use only ML algorithms directly on the AME2016 data set. Our results are further refined by using another ML algorithm to train the errors of the first algorithm, and repeating this process iteratively. Our best algorithm gives $\sigma_{\rm rms} \approx 0.58$ MeV for Binding Energy on randomized testing sets. This is comparable to all physics models or ML improved physics models studied in literature till date. Using the predictions of our Machine Learning algorithm, we construct the outer crust equation of state (EoS) of a neutron star and show that our model is comparable to existing models. This work also demonstrates the use of various ML algorithms and a detailed analysis on how we arrived at our best algorithm. It will help the physics community in understanding how to choose an ML algorithm which would be suited for their data set. Our algorithms and best fit model is also made publicly available for the use of the community.