The Hiphive Package for the Extraction of High‐Order Force Constants by Machine Learning

Abstract

The efficient extraction of force constants (FCs) is crucial for the analysis of many thermodynamic materials properties. Approaches based on the systematic enumeration of finite differences scale poorly with system size and can rarely extend beyond third order when input data is obtained from first-principles calculations. Methods based on parameter fitting in the spirit of interatomic potentials, on the other hand, can extract FC parameters from semi-random configurations of high information density and advanced regularized regression methods can recover physical solutions from a limited amount of data. Here, the hiphive Python package, that enables the construction of force constant models up to arbitrary order is presented. hiphive exploits crystal symmetries to reduce the number of free parameters and then employs advanced machine learning algorithms to extract the force constants. Depending on the problem at hand, both over and underdetermined systems are handled efficiently. The FCs can be subsequently analyzed directly and or be used to carry out, for example, molecular dynamics simulations. The utility of this approach is demonstrated via several examples including ideal and defective monolayers of MoS 2 as well as bulk nickel.

Bending rigidities and universality of flexural modes in 2D crystals

“…This shows that a strict geometry optimization in ab initio calculations is crucial to obtain quadratic dispersions. It further corroborates the observation that the translational and rotational invariance of the FCs are necessary but not sufficient conditions for finding flexural modes [19,22].…”

“…Further, we theoretically show that all (freestanding) orthotropic 2DMs exhibit a flexural mode provided that the material is free of homogeneous stresses. The derivations emphasize the role of sum rules for the FCs which reflect the underlying fundamental symmetries of the crystals [19,22]. Our findings are corroborated by considering four representative 2DMs for which we calculate the phonon dispersions from first principles using VASP [23] and PHONOPY [24].…”

Thermal conductivity in intermetallic clathrates: A first-principles perspective

“…After discarding the first 1,000 steps for equilibration, about 180 snap shots at a spacing of 25 MD steps were used for training, by least-squares fitting temperature dependent interatomic force constants (TDIFCs) using our in-house hiphive code. 45 Finally, shengBTE was used to calculate the thermal conductivity from the resulting IFCs.…”

Efficient construction of linear models in materials modeling and applications to force constant expansions

“…Depending on material and property of interest the FC expansion must be carried out to different orders. Generally, it is preferable to keep the order as low as possible since the number of independent coefficients quickly increases with expansion order, decreasing symmetry, and number of sites in the unit cell 15 .…”

“…Here, we use the HIPHIVE package 15,23 since it is interfaced with machine-learning libraries such as SCIKIT-LEARN that in turn provide efficient implementations of various optimization techniques. In this paper, we present a comparison of linear regression methods and the direct enumeration approach for the extraction of FCs of different order, including second-order FCs for large systems of low symmetry such as defects, third-order FCs for the prediction of the thermal conductivity, as well as higher-order FCs for bulk and surface (see Supplementary Information) systems.…”