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

Using the machine learning method kriging, we predict the energies of atoms in ion-water clusters, consisting of either Cl or Na surrounded by a number of water molecules (i.e., without NaCl interaction).

Geometry Optimization with Machine Trained Topological Atoms.

The geometry optimization of a water molecule with a novel type of energy function called FFLUX is presented, which bypasses the traditional bonded potentials. Instead, topologically-partitioned atomic energies are trained by the machine learning method kriging to predict their IQA atomic energies for a previously unseen molecular geometry. Proof-of-concept that FFLUX's architecture is suitable for geometry optimization is rigorously demonstrated.

The long-range convergence of the energetic properties of the water monomer in bulk water at room temperature.

The Interacting Quantum Atoms (IQA) energy partitioning scheme has been applied to a set of liquid water largely spherical clusters (henceforth called spheres) of up to 9 Å radius, with a maximum cluster size of 113 molecules. This constitutes half of the commonly used 216 molecules in a typical simulation box of a liquid water box, and to our knowledge is the largest analysis of this kind ever undertaken. As well as demonstrating the topological analysis of large systems, which has only recently become computationally feasible, important long range properties of liquid water are obtained.

FEREBUS: Highly parallelized engine for kriging training.

FFLUX is a novel force field based on quantum topological atoms, combining multipolar electrostatics with IQA intraatomic and interatomic energy terms. The program FEREBUS calculates the hyperparameters of models produced by the machine learning method kriging. Calculation of kriging hyperparameters (θ and p) requires the optimization of the concentrated log-likelihood L̂(θ,p).

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.

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer.

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra-atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster.

Optimization Algorithms in Optimal Predictions of Atomistic Properties by Kriging.

The machine learning method kriging is an attractive tool to construct next-generation force fields. Kriging can accurately predict atomistic properties, which involves optimization of the so-called concentrated log-likelihood function (i.e.

Prediction of Intramolecular Polarization of Aromatic Amino Acids Using Kriging Machine Learning.

Present computing power enables novel ways of modeling polarization. Here we show that the machine learning method kriging accurately captures the way the electron density of a topological atom responds to a change in the positions of the surrounding atoms. The success of this method is demonstrated on the four aromatic amino acids histidine, phenylalanine, tryptophan, and tyrosine.

Free Energy Calculations with Reduced Potential Cutoff Radii.

The Jarzynski Equality, the Crooks Fluctuation Theorem, and the Maximum Likelihood Estimator use a nonequilibrium approach for the determination of free energy differences due to a change in the state of a system. Here, this approach is used in combination with a novel transformation algorithm to increase computational efficiency in simulations with interacting particles, without losing accuracy. The algorithm is shown to work well for a Lennard-Jones fluid undergoing a change in density over three very different density ranges, and for the systems considered the algorithm demonstrates computational savings of up to approximately 90%.

The free energy of expansion and contraction: treatment of arbitrary systems using the Jarzynski equality.

Thermodynamic integration, free energy perturbation, and slow change techniques have long been utilised in the calculation of free energy differences between two states of a system that has undergone some transformation. With the introduction of the Jarzynski equality and the Crooks relation, new approaches are possible. This paper investigates an important phenomenon - systems undergoing a change in volume/density - and derives both the Jarzynski equality and Crooks relation of such systems using a statistical mechanical approach.