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

Linear models, such as force constant (FC) and cluster expansions, play a key role in physics and materials science and can be parametrized using regression and feature selection approaches. The convergence behavior of these techniques, in particular with respect to thermodynamic properties is, however, not well understood. In this presentation, we analyze the efficacy and efficiency of several state-of-the-art regression and feature selection methods in the context of FC extraction and the prediction of different thermodynamic properties. Generic feature selection algorithms such as RFE-OLS, ARDR, ad-LASSO can yield physically sound models for systems with a modest number of degrees of freedom. For complex systems or high-order expansions they can, however, be more than two orders of magnitude more expansive to construct than OLS. While regression techniques are thus very powerful, they require well-tuned protocols. To this end, we will provide general guidelines for the design of such protocols that are readily usable, e.g., in high-throughput and materials discovery schemes. We hope that the general conclusions drawn here also have a bearing on the construction of other linear models in physics and materials science.