First-principles interatomic potentials for ten elemental metals via compressed sensing

Abstract

Interatomic potentials have been widely used in atomistic simulations such as molecular dynamics. Recently, frameworks to construct accurate interatomic potentials that combine a systematic set of density functional theory (DFT) calculations with machine learning techniques have been proposed. One of these methods is to use compressed sensing to derive a sparse representation for the interatomic potential. This facilitates the control of the accuracy of interatomic potentials. In this study, we demonstrate the applicability of compressed sensing to deriving the interatomic potential of ten elemental metals, namely, Ag, Al, Au, Ca, Cu, Ga, In, K, Li and Zn. For each elemental metal, the interatomic potential is obtained from DFT calculations using elastic net regression. The interatomic potentials are found to have prediction errors of less than 3.5 meV/atom, 0.03 eV/Å and 0.15 GPa for the energy, force and the stress tensor, respectively, which enable the accurate prediction of physical properties such as lattice constants and the phonon dispersion relationship. PACS numbers: 71.15.Pd,31.50.Bc,

Machine learning based interatomic potential for amorphous carbon

“…If training is successful, this makes atomistic simulations close to quantummechanical accuracy accessible but requires less computational effort by many orders of magnitude. Recent implementations use high-dimensional artificial neural networks, [30][31][32] compressed sensing, 33 or Gaussian process regression. 34 Interatomic ML-based potentials have been developed for several prototypical solids [30][31][32][33][34][35][36][37][38][39] and applied, e.g., in studies of phase transitions.…”

Compressive sensing lattice dynamics. I. General formalism

“…54 The CS technique has also been used to fit interatomic potentials. 55 Here, we lay out the general theory and computational techniques of lattice dynamics specifically adapted for a (possibly underdetermined) linear problem in Section II. The numerical CS method for the lattice dynamics is described in Section III, and select examples of the efficacy of CSLD are presented in Section IV.…”

Descriptors for Machine Learning of Materials Data

“…In this section, we demonstrate the applicability of the Lasso regression to derive the IPs of 12 elemental metals (Na, Mg, Ag, Al, Au, Ca, Cu, Ga, In, K, Li, and Zn) [11,12]. The features of linear modeling of the atomic energy and descriptors using the Lasso regression include the following.…”

“…The vector w composed of all the regression coefficients can be estimated by a regression, which is a machine-learning method to estimate the relationship between the predictor and observation variables using a training dataset. For the training data, the energy, forces acting on atoms, and stress tensor computed by DFT calculations can be used as the observations in the regression process since they all are expressed by linear equations with the same regression coefficients [12]. A simple procedure to estimate the regression coefficients employs a linear ridge regression [13].…”