# Bayesian optimization for tuning and selecting hybrid-density functionals

## TL;DR

This paper demonstrates that Bayesian optimization can efficiently tune parameters and select the best hybrid-density functional models, significantly reducing computational effort compared to traditional grid search methods.

## Contribution

It introduces the application of Bayesian optimization for tuning and selecting density functional models, including joint optimization of parameters and functional form, in material science.

## Key findings

- BO requires approximately 55 evaluations for optimal parameter tuning.
- BO can identify the most suitable exchange-correlation functional without prior info.
- Joint optimization with BO improves accuracy in predicting atomization energies.

## Abstract

The accuracy of some density functional (DF) models, widely used in material science, depends on empirical or free parameters which are commonly tuned using reference physical properties. The optimal value of the free parameters is regularly found using grid search algorithms, which computational complexity scales with the number of points in the grid. In this report, we illustrate that Bayesian optimization (BO), a sample-efficient machine learning algorithm, can efficiently calibrate different density functional models, e.g., hybrid-exchange-correlation and range-separated density functionals. We present that, BO can optimize the free parameters of hybrid-exchange-correlation functionals, with approximately 55 evaluations of the root-mean-square or mean-absolute error functions of the atomization energies and the bond length of the Gaussian-1 (G1) database. We also illustrate that BO can identify, without any prior information, the most appropriate exchange-correlation functional by navigating through the space of density functional models. We optimize and select the free parameters and the exchange-correlation functional form jointly by also minimizing the root-mean-square error function with respect to the atomization energies of the G1 database using BO.