Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

Atomic-scale representation and statistical learning of tensorial properties

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

Hypersexuality, gender, and sexual orientation: a large-scale psychometric survey study

Criteria for Hypersexual Disorder (HD) were proposed for consideration in the DSM-5 but ultimately excluded for a variety of reasons. Regardless, research continues to investigate hypersexual behavior (HB). The Hypersexual Behavior Inventory (HBI) is one of the most robust scales assessing HB, but further examination is needed to explore its psychometric properties among different groups. Therefore, the aim of the present study was to examine the generalizability of the HBI in a large, diverse, nonclinical sample (N = 18,034 participants; females = 6132; 34.0%; Mage = 33.6 years, SDage = 11.1) across both gender and sexual orientation. Measurement invariance testing was carried out to ensure gender- and sexual-orintation based comparisons were meaningful. Results demonstrated when both gender and sexual-orientation were considered (i.e., heterosexual males vs. LGBTQ males vs. heterosexual females vs. LGBTQ females), LGBTQ males had significantly higher latent means on the HBI factors. Results also demonstrated LGBTQ males had the highest scores on other possible indicators of hypersexuality (e.g., frequency of masturbation, number of sexual partners, or frequency of pornography viewing). These findings suggest LGBTQ males may be a group most at risk of engaging in hypersexual behavior and LGBTQ females are at a higher risk of engaging in hypersexual activities due to coping problems. Given the largescale nature of the study, the findings significantly contribute to the currently growing body of literature on hypersexuality

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered

Insight into liquid polymorphism from the complex phase behavior of a simple model

We systematically explored the phase behavior of the hard-core two-scale ramp model suggested by Jagla [Phys. Rev. E 63, 061501 (2001)] using a combination of the nested sampling and free energy methods. The sampling revealed that the phase diagram of the Jagla potential is significantly richer than previously anticipated, and we identified a family of new crystalline structures, which is stable over vast regions in the phase diagram. We showed that the new melting line is located at considerably higher temperature than the boundary between the low- and high-density liquid phases, which was previously suggested to lie in a thermodynamically stable region. The newly identified crystalline phases show unexpectedly complex structural features, some of which are shared with the high-pressure ice VI phase

A collinear-spin machine learned interatomic potential for Fe\textsubscript{7}Cr\textsubscript{2}Ni alloy

We have developed a new machine learned interatomic potential for the prototypical austenitic steel Fe$_{7}$Cr$_{2}$Ni, using the Gaussian approximation potential (GAP) framework. This new GAP can model the alloy's properties with higher accuracy than classical interatomic potentials like embedded atom models (EAM), while also allowing us to collect much more statistics than expensive first-principles methods like density functional theory (DFT). We also extended the GAP input descriptors to approximate the effects of collinear spins (Spin GAP), and demonstrate how this extended model successfully predicts low temperature structural distortions due to the antiferromagnetic spin state. We demonstrate the application of the Spin GAP model for bulk properties and vacancies and validate against DFT. These results are a step towards modelling ageing in austenitic steels with close to DFT accuracy but at a fraction of its cost