Bayesian optimization in atomic structure calculations for collisional problems

The computation of collisional rates demands an accurate description of the ions involved in the processes. However, determining an adequate atomic structure can signify lots of time and computational resources. The optimization of the target wavefunctions relies on considering a configuration interaction (CI) expansion, in which additional levels are added to improve the accuracy of the calculations. The radial wavefunctions are often obtained with model potentials containing scaling parameters, which are varied. Designing an intuitive way to optimize these parameters can be challenging in this framework. The number of configurations included in the CI and the direction in which the scaling parameters are varied lead to erratic oscillations in the results. This behavior implies the lack of a systematic and logical prescription for this procedure.

In this contribution, we implemented the Bayesian method via Gaussian processes (GP) to optimize the atomic structure of the ions. This optimization is an excellent machine learning methodology to minimize scalar-valued error functions. To illustrate the procedure, we considered the neutral beryllium atom. An accurate description of the target has proven to be necessary for obtaining accurate electron impact excitation and electron impact ionization cross-sections [1, 2].

The atomic structure of Be and various transition metals is calculated with the autostructure code [3]. The scaling parameters of the model potentials used define the parameters of the atomic structure calculation. These parameters are then optimized within the Bayesian approach. The energy and oscillator strengths values of the most low-lying terms obtained generally agree with experimental values within 1% and 10%, respectively.

[1] Zatsarinny O et al 2016 J. Phys. B 49 235701

[2] Ballance C P et al 2003 Phys. Rev. A 68 062705

[3] Badnell N R 2011 Comput. Phys. Commun. 7 1528