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Register a new userIncorporating long-range physics in atomic-scale machine learning
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The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that depend on the configurations within finite atom-centered environments. The obvious downside of this approach is that it cannot capture non-local, non-additive effects such as those arising due to long-range electrostatics or quantum interference. We propose a solution to this problem by introducing non-local representations of the system that are remapped as feature vectors that are defined locally and are equivariant in O(3). We consider in particular one form that has the same asymptotic behavior as the electrostatic potential. We demonstrate that this framework can capture non-local, long-range physics by building a model for the electrostatic energy of randomly distributed point-charges, for the unrelaxed binding curves of charged organic molecular dimers, and for the electronic dielectric response of liquid water. By combining a representation of the system that is sensitive to long-range correlations with the transferability of an atom-centered additive model, this method outperforms current state-of-the-art machine-learning schemes, and provides a conceptual framework to incorporate non-local physics into atomistic machine learning.
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Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of molecules and condensed-phase systems. This short review summarizes recent progress in the field, focusing in particular on the problem of representing an atomic configuration in a mathematically robust and computationally efficient way. We also discuss some of the regression algorithms that have been used to construct surrogate models of atomic-scale properties. We then show examples of how the optimization of the machine-learning models can both incorporate and reveal insights onto the physical phenomena that underlie structure-property relations.
We investigate theoretically the long-range electrostatic interactions between a ground-state homonuclear alkali-metal dimer and an excited alkali-metal atom taking into account its fine-structure. The interaction involves the combination of first-order quadrupole-quadrupole and second-order dipole-dipole effects. Depending on the considered species, the atomic spin-orbit may be comparable to the atom-molecule electrostatic energy and to the dimer rotational structure. Here we extend our general description in the framework of the second-order degenerate perturbation theory [M. Lepers and O. Dulieu, Eur. Phys. J. D, 2011] to various regimes induced by the magnitude of the atomic spin-orbit. A complex dynamics of the atom-molecule may take place at large distances, which may have consequences for the search for an universal model of ultracold inelastic collisions as proposed for instance in [Z. Idziaszek and P. S. Julienne, Phys. Rev. Lett. textbf{104}, 113202 (2010)].
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule.
We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for the atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.
Atomic scale simulations are a key element of modern science in that they allow to understand, and even predict, complex physical or chemical phenomena on the basis of the fundamental laws of nature. Among the different existing atomic scale simulation approaches, molecular dynamics (MD) has imposed itself as the method of choice to model the behavior of the structure of materials under the action of external stimuli, say temperature, strain or stress, irradiation, etc. Despite the widespread use of MD in condensed matter science, some basic material characteristics remain difficult to determine. This is for instance the case of the long-range strain tensor in heavily disordered materials, or the quantification of rotated crystalline domains lacking clearly defined boundaries. In this work, we introduce computational diffraction as a fast and reliable structural characterization tool of atomic scale simulation cells. As compared to usual direct-space methods, computational diffraction operates in the reciprocal-space and is therefore highly sensitive to long-range spatial correlations. With the example of defective UO2, it is demonstrated that the homogeneous strain tensor, the heterogeneous strain tensor, the disorder, as well as rotated crystallites are straightforwardly and unambiguously determined. Computational diffraction can be applied to any type of atomic scale simulation and can be performed in real time, in parallel with other analysis tools. In experimental workflows, diffraction and microscopy are almost systematically used together in order to benefit from their complementarity. Computational diffraction, used together with computational microscopy, can potentially play a major role in the future of atomic scale simulations.
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