Nonparametric Bayesian approach to extrapolation problems in configuration interaction methods
S. Yoshida
Abstract
The configuration interaction methods are powerful tools for exploring various properties of nuclei. However, in practice, it is often necessary to truncate the model space and then to extrapolate the results to very large model space to obtain the best estimations of the exact eigenvalues under a given nuclear interaction. In this study, a nonparametric extrapolation method based on constrained Gaussian processes for configuration interaction methods is presented. The proposed method has many advantages: (i) applicability to small data sets such as results of ab initio methods, (ii) flexibility to incorporate constraints, which are guided by physics, into the extrapolation model, (iii) providing predictions with quantified extrapolation uncertainty, etc. An application to the extrapolation problem of ground-state energies in the full configuration interaction method is discussed as an example.