Linearization of moment tensor potentials for multicomponent systems with a preliminary assessment for short-range interaction energy in water dimer and trimer

Abstract

Moment tensor potentials have been recently proposed as a promising novel method of polynomial expansion for the systematic approximation of molecular potential energy surfaces. However, its current formulation for multicomponent systems has not been fully linearized and requires nonlinear optimization techniques for parameter estimation. We propose an alternative relaxed formulation of the original potential energy function where parameter optimization is expressed as a linear sparse approximation problem. The main difficulty arising in sparse approximation is finding a suitable subset of predictors in highly multi-collinear variable space where the number of variables largely exceeds the size of the training set. To efficiently reduce the number of descriptors to an optimal size and prevent overfitting, we present a simple heuristic that is based on importance ranking of variables and Bayesian information criterion. For the empirical assessment of our approach, we employed published data on short-range components of water two-body and three-body interaction energies that have previously been used for the comparison of various potential energy representations. Numerical experiments suggest that our proposed methodology allows achieving accuracy that is comparable to other popular interpolation and machine learning techniques and requires significantly less time for model training than nonlinearly parameterized formulation.