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We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Inorganic lead halide perovskite nanostructures show promise as the active layers in photovoltaics, light emitting diodes, and other optoelectronic devices. They are robust in the presence of oxygen and water, and the electronic structure and dynamics of these nanostructures can be tuned through quantum confinement. Here we create aligned bundles of CsPbBr 3 nanowires with widths resulting in quantum confinement of the electronic wave functions and subject them to ultrafast microscopy. We directly image rapid one-dimensional exciton diffusion along the nanowires, and we measure an exciton trap density of roughly one per nanowire. Using transient absorption microscopy, we observe a polarization-dependent splitting of the band edge exciton line, and from the polarized fluorescence of nanowires in solution, we determine that the exciton transition dipole moments are anisotropic in strength. Our observations are consistent with a model in which splitting is driven by shape anisotropy in conjunction with long-range exchange.

The phase-change material, Ge 2 Sb 2 Te 5 , is the canonical material ingredient for next-generation storage-class memory devices used in novel computing architectures, but fundamental questions remain regarding its atomic structure and physicochemical properties. Here, we introduce a machine-learning (ML)-based interatomic potential that enables large-scale atomistic simulations of liquid, amorphous, and crystalline Ge 2 Sb 2 Te 5 with an unprecedented combination of speed and density functional theory (DFT) level of accuracy. Two applications exemplify the usefulness of such an ML-driven approach: we generate a 7200-atom structural model, hitherto inaccessible with DFT simulations, that affords new insight into the medium-range structural order and we create an ensemble of uncorrelated, smaller structures, for studies of their chemical bonding with statistical significance. Our work opens the way for new atomistic insights into the fascinating and chemically complex class of phase-change materials that are used in real nonvolatile memory devices.

Coarse-grained (CG) polymer simulations can access longer times and larger lengths than all-atom (AA) molecular dynamics simulations; however, not all CG models correctly reproduce polymer properties on all length scales. Here we coarse-grain atomistic position data from polyethylene (PE) and polytetrafluoroethylene (PTFE) melt simulations by combining λ backbone carbon atoms in a single CG bead. Resulting CG variables have correlations along the chain backbone that depend on the coarse-graining scale λ and are generally not reproduced by independent bond-length, bond-angle and torsion-angle distributions. By constructing distributions of CG variables equivalent to those from simulated CG potentials we are able to evaluate the bond-orientation correlation for different CG models at reduced computational cost. CG models and potentials that include only nonbonded, bond-length, and bond-angle interactions computed by Boltzmann inversion correctly reproduce the CG variable distributions but do not necessarily reproduce the chain stiffness, overestimating the persistence length L p and end-to-end distance ⟨ R 2 ⟩ 1/2 with increasing λ. While CG models that include an independent torsion angle match the bond-orientation correlation and ⟨ R 2 ⟩ 1/2 better, only approximate models that include correlations between bond and torsion angles match the true bond-orientation correlation.

Practical free energy reconstruction algorithms involve three separate tasks: biasing, measuring some observable, and finally reconstructing the free energy surface from those measurements. In more than one dimension, adaptive schemes make it possible to explore only relatively low lying regions of the landscape by progressively building up the bias toward the negative of the free energy surface so that free energy barriers are eliminated. Most schemes use the final bias as their best estimate of the free energy surface. We show that large gains in computational efficiency, as measured by the reduction of time to solution, can be obtained by separating the bias used for dynamics from the final free energy reconstruction itself. We find that biasing with metadynamics, measuring a free energy gradient estimator, and reconstructing using Gaussian process regression can give an order of magnitude reduction in computational cost.

Adsorption-induced deformation is expansion or contraction of a solid due to adsorption on its surface. This phenomenon is important for a wide range of applications, from chemomechanical sensors to methane recovery from geological formations. The strain of the solid is driven by the change of the surface stress due to adsorption. Using ab initio molecular dynamics, we calculate the surface stresses for the dry α-quartz surfaces, and investigate how these stresses change when the surfaces are exposed to water. We find that the nonhydroxylated surface shows small and approximately isotropic changes in stress, while the hydroxylated surface, which interacts more strongly with the polar water molecules, shows larger and qualitatively anisotropic (opposite sign in xx and yy) surface stress changes. All of these changes are several times larger than the surface tension of water itself. The anisotropy and possibility of positive surface stress change can explain experimentally observed surface area contraction due to adsorption.

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org .