Kriging atomic properties with a variable number of inputs

Abstract

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 corresponding to different outputs or input biasing. As a demonstration, the new method is used to predict 54 energetic and electrostatic properties of the central water molecule of a set of 5000, 4 Å radius water clusters, with a variable number of water molecules. The results are validated against equivalent models from a set of clusters composed of a fixed number of water molecules (set to ten, i.e., decamers) and against models created by using a naïve method of treating the variable number of inputs problem presented. Results show that the 4 Å water cluster models, utilising the method presented here, return similar or better kriging models than the decamer clusters for all properties considered and perform much better than the truncated models. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

“…The final term, V AB corr is responsible to increase the magnitude of the nucleus-electron potential energy and decrease the electronelectron repulsion. All these terms constitute the so-called fine structure [39] of ρ 2 . Figure 1 summarizes the energy terms arising in Eq.…”

“…Three different types of ML techniques, that is, Random Forest (RF), Support Vector Regression (SVR), and Kriging [39,56,[66][67][68][69], were applied to predict correlation energies of three systems: the water monomer, the H 2 -He complex and the water dimer. In the first system, intramolecular-interatomic correlation energies were investigated, while in the last two, the intermolecular correlation energies are in the spotlight, since they are correlated with intermolecular dispersion forces.…”

The accuracy of ab initio calculations without ab initio calculations for charged systems: Kriging predictions of atomistic properties for ions in aqueous solutions

“…In the second part of this work we present kriging models developed for a more general system containing eight water molecules and both Cland Na + , which will be denoted as ClNa-W8. This system will in turn be the reference system used to demonstrate the Variable Number of Features (VNF) kriging method 16 . The VNF method, which will be described in detail later, is a way to extend kriging models to systems with varying dimensions.…”

“…Following the VNF method 16 we choose a single feature and assign it a value outside the sampled domain for each water molecule, and for the extra ion. The selected feature is always the distance RO for each extra water molecule and RX for the extra ion.…”

“…Next, we assign to the remaining features (eight for each extra water molecule and two for the extra ion) a mean value obtained by averaging the features among the training points we have. A more detailed description can be found in reference 16 . One important matter to remember in the construction of the VNF model for a system is that the extended system must mimic exactly the smaller system it encloses.…”