Bayesian Optimization for Calibrating and Selecting Hybrid-Density Functional Models

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 exchangecorrelation 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.

Magnetism variation of the compressed antiferromagnetic topological insulator EuSn2As2

“…We calculated the vibrational properties of EuSn 2 As 2 at atmospheric pressure and 15.6 GPa. The structural optimization and calculations of the electronic properties were conducted using DFT implemented in the Vienna Ab initio Simulation Package (VASP) [22,23]. The electron-core interactions were assessed using the projector augmented wave (PAW) approximation [24].…”

“…Our first-principles calculations for the magnetic exchange interactions were carried out separately based on DFT. The VASP with GGA was employed [22,23]. We adopted PAW pseudopotentials to describe the core-valence interaction and an energy cutoff of 400 eV for basis expansion [24,27].…”

Effects of quarantine disobedience and mobility restrictions on COVID-19 pandemic waves in dynamical networks

“…Bayesian optimization is a sequential search algorithm designed to find the global minimizer or maximizer of an unknown non-analytic or oracle function whose gradient is also analytically unknown BO requires two components: a model that approximates and an acquisition function, that quantifies the informational gain [60] , [61] . Here, we use Gaussian process (GP) models as the probabilistic models in order to approximate the average number of deaths.…”

Bayesian machine learning for quantum molecular dynamics

“…It has thus become possible to combine traditional quantum dynamics calculations, molecular dynamics simulations and chemistry experimentation with ML. While ML is already used extensively to assist molecular dynamics simulations for a variety of applications [2][3][4], density functional theory [5][6][7][8][9][10][11], the design of chemistry experiments [12][13][14][15], new materials discovery [16][17][18][19] and the prediction of molecular properties [20,21], it is only beginning to have an impact on the research field of quantum reaction dynamics of molecules. The purpose of this article is to describe what can be gained from combining ML with quantum dynamics calculations aimed at understanding the microscopic reactions of molecules.…”