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

Abstract

Linear models, such as force constant (FC) and cluster expansions, play a key role in physics and materials science. While they can in principle be parametrized using regression and feature selection approaches, the convergence behavior of these techniques, in particular with respect to thermodynamic properties is not well understood. Here, we therefore analyze the efficacy and efficiency of several state-of-the-art regression and feature selection methods, in particular in the context of FC extraction and the prediction of different thermodynamic properties. Generic feature selection algorithms such as recursive feature elimination with ordinary least-squares (OLS), automatic relevance determination regression, and the adaptive least absolute shrinkage and selection operator can yield physically sound models for systems with a modest number of degrees of freedom. For large unit cells with low symmetry and/or high-order expansions they come, however, with a non-negligible computational cost that can be more than two orders of magnitude higher than that of OLS. In such cases, OLS with cutoff selection provides a viable route as demonstrated here for both second-order FCs in large low-symmetry unit cells and high-order FCs in low-symmetry systems. While regression techniques are thus very powerful, they require well-tuned protocols. Here, the present work establishes guidelines for the design of protocols that are readily usable, e.g., in high-throughput and materials discovery schemes. Since the underlying algorithms are not specific to FC construction, the general conclusions drawn here also have a bearing on the construction of other linear models in physics and materials science.

Efficient Calculation of the Lattice Thermal Conductivity by Atomistic Simulations with Ab Initio Accuracy

“…In fact, the temperature dependence of the LTC follows very closely the $$1/T$$ dependence observed for most crystalline thermal conductors, whereas for Ba 8 Ga 16 Ge 30 one obtains a relation closer to $$1/\sqrt {T}$$. [ 22,35 ]…”

“…[22], using the ShengBTE code [ 15 ] with a $$9\times 9\times 9$$ q ‐point mesh and a smearing parameter of 0.01, with the IFCs taken from ref. [35] as described above (Section 2.3).…”

“…For the specific purpose of analyzing the dynamics of materials and in particular the LTC, high‐order force constant potentials (FCPs) can now be routinely constructed even for materials with large unit cells, low symmetry, and soft interactions. [ 21,30–37 ]…”

Investigating the Chemical Ordering in Quaternary Clathrate Ba8AlxGa16–xGe30

“…To estimate the quality of the CEs, cross-validation (CV) scores were calculated, using 90% of the available structures for training and the rest for validation, based on three different fitting methods, namely, least absolute shrinkage and selection operator (LASSO) and automatic relevance detection regression (ARDR), as well as ordinary least-squares (OLS) with recursive feature elimination (RFE). As has been reported elsewhere, 41 , 42 the latter method gave consistently better results, both in terms of the root-mean-square error (RMSE) and the sparsity, and it was therefore used to construct the final CE. After fitting, the number of nonzero parameters had been reduced to 35, 23 of which corresponded to pairs and just 5 corresponded to triplets.…”

dynasor—A Tool for Extracting Dynamical Structure Factors and Current Correlation Functions from Molecular Dynamics Simulations

“…All of the latter limitations can in principle be overcome by analyzing correlation functions, such as the dynamical structure factor, from MD simulations using forces from density‐functional theory (DFT) calculations, empirical potentials [ 23 ] or high‐order force constants. [ 24 ] To take full advantage of this approach it is desirable to obtain the dispersion relations as a function of not only the magnitude but also the direction of the momentum transfer vector. While this information is in principle present whenever analyzing trajectories from periodic systems, this is not the primary focus of the aforementioned tools.…”