Kriging atomic properties with a variable number of inputs

A new force field called FFLUX uses the machine learning technique kriging to capture the link between the properties (energies and multipole moments) of topological atoms (i.e., output) and the coordinates of the surrounding atoms (i.e., input). Here we present a novel, general method of applying kriging to chemical systems that do not possess a fixed number of (geometrical) inputs. Unlike traditional kriging methods, which require an input system to be of fixed dimensionality, the method presented here can be readily applied to molecular simulation, where an interaction cutoff radius is commonly used and the number of atoms or molecules within the cutoff radius is not constant. The method described here is general and can be applied to any machine learning technique that normally operates under a fixed number of inputs. In particular, the method described here is also useful for interpolating methods other than kriging, which may suffer from difficulties stemming from identical sets of inputs correspond...