Fast general two- and three-body interatomic potential

Abstract

We introduce a new class of machine learning interatomic potentials-fast General Two-and Three-body Potential (GTTP) which are as fast as conventional empirical potentials and require computational time that remains constant with increasing fitting flexibility. GTTP does not contain any assumptions about functional form of two-and three-body interactions. These interactions can be modeled arbitrarily accurately potentially by thousands of parameters not affecting resulting computational cost. Time complexity is O(1) per every considered pair or triple of atoms. The fitting procedure is reduced to simple linear regression on ab initio calculated energies and forces and leads to effective two-and three-body potential which reproduces quantum many-body interactions as accurately as possible. Our potential can be made continuously differentiable any number of times at the expense of increased computational time. We made a number of performance tests on one-, two-and three-component systems. Flexibility of the introduced approach makes the potential transferable in terms of size and type of atomic systems. We show, that trained on randomly generated structures with just 8 atoms in the unit cell, it significantly outperforms common empirical interatomic potentials in the study of large systems, such as grain boundaries in polycrystalline materials.

Physics-Inspired Structural Representations for Molecules and Materials

“…289−291 In fact, when computing a linear model which is explicitly equivalent to a (ν + 1)-body-order potential, the low-order terms can be more efficiently evaluated as a sum over neighbors. 195,292 In line with the general focus of this review, we concentrate in particular on the efficient implementation of atom-density representations. As we shall see, roughly the same considerations apply to both those representations that are usually built on a smooth atom density, 109,125,149 that generalize the construction of the SOAP power spectrum and bispectrum, 29 and those that are usually computed in a way that corresponds to a δ-like density, such as ACE 126,150 and MTP.…”