Chiral effective field theory with machine learning

Abstract

Machine learning is a method to develop computational algorithms for making predictions based on a limited set of observations or data. By training on a well selected set of data points it is in principle possible to emulate the underlying processes and make reliable predictions. In this thesis we explore the possibility of replacing computationally expensive solutions of the Schrödinger equation for atomic nuclei with a so-called Gaussian process (GP) that we train on a selected set of exact solutions. A GP represents a continuous distribution of functions defined by a mean and a covariance function. These processes are often used in machine learning since they can be made to emulate a wide range of data by choosing a suitable covariance function. This thesis aims to present a pilot study on how to use GPs to emulate the calculation of nuclear observables at low energies. The governing theory of the strong interaction, quantum chromodynamics, becomes non-perturbative at such energy-scales. Therefore an effective field theory, called chiral effective field theory (EFT), is used to describe the nucleon-nucleon interactions. The training points are selected using different sampling methods and the exact solutions for these points are calculated using the research code nsopt. After training at these points, GPs are used to mimic the behavior of nsopt for a new set of points called prediction points. In this way, results are generated for various cross sections for two-nucleon scattering and boundstate observables for light nuclei. We find that it is possible to reach a small relative error (sub-percent) between the simulator, i.e. nsopt, and the emulator, i.e. the GP, using relatively few training points. Although there seems to be no obvious problem for taking this method further, e.g. emulating heavier nuclei, we discuss some areas that need more critical attention. For example some observables were difficult to emulate with the current choice of covariance function. Therefore a more thorough study of different covariance functions is needed.