Bayesian Optimization for Calibrating and Selecting Hybrid-Density Functional Models.

Area of Science:

• Computational chemistry
• Materials science
• Machine learning

Background:

• Density functional (DF) models are crucial in material science but rely on empirical parameters.
• Optimizing these parameters typically uses computationally expensive grid-search methods.
• Accurate DF models are essential for predicting material properties.

Purpose of the Study:

• To demonstrate Bayesian optimization (BO) as a sample-efficient alternative for calibrating DF models.
• To compare BO's performance against standard grid-search methods for parameter optimization.
• To explore BO's capability in selecting optimal exchange-correlation functionals.

Main Methods:

• Bayesian optimization (BO) was employed to calibrate DF models, including hybrid and range-separated functionals.
• The optimization process utilized atomization energies and bond lengths from the Gaussian-1 (G1) and Gaussian-2 (G2) databases.
• Root-mean-square error functions were minimized to jointly optimize and select functionals and parameters.

Main Results:

• BO optimized DF parameters with approximately 55 error function evaluations, significantly fewer than grid-search.
• BO successfully selected appropriate exchange-correlation functionals for various physical systems.
• The calibrated DF models showed improved accuracy compared to standard methods like PBE0 and B3LYP.

Conclusions:

• Bayesian optimization offers a computationally efficient and effective method for calibrating density functional models.
• BO enhances the accuracy of material property predictions by optimizing functional parameters.
• This approach facilitates both the selection and optimization of density functionals for specific applications.