Modeling the Ga/As binary system across temperaturesand compositions from first principles

Materials composed of elements from the third and fifth columns of the periodic table display a very rich behavior, with the phase diagram usually containing a metallic liquid phase and a polar semiconducting solid. As a consequence, it is very hard to achieve transferable empirical models of interactions between the atoms that can reliably predict their behavior across the temperature and composition range that is relevant to the study of the synthesis and properties of III/V nanostructures and devices. We present a machine-learning potential trained on density functional theory reference data that provides a general-purpose model for the Ga$_x$As$_{1-x}$ system. We provide a series of stringent tests that showcase the accuracy of the potential, and its applicability across the whole binary phase space, computing with ab initio accuracy a large number of finite-temperature properties as well as the location of phase boundaries. We also show how a committe model can be used to reliably determine the uncertainty induced by the limitations of the ML model on its predictions, to identify regions of phase space that are predicted with insufficient accuracy, and to iteratively refine the training set to achieve consistent, reliable modeling.

Uncertainty estimation for molecular dynamics and sampling

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of these models, the reliability of predictions depends on the position in phase space, and it is crucial to obtain an estimate of the error that derives from the finite number of reference structures included during the training of the model. When using a machine-learning potential to sample a finite-temperature ensemble, the uncertainty on individual configurations translates into an error on thermodynamic averages, and provides an indication for the loss of accuracy when the simulation enters a previously unexplored region. Here we discuss how uncertainty quantification can be used, together with a baseline energy model, or a more robust although less accurate interatomic potential, to obtain more resilient simulations and to support active-learning strategies. Furthermore, we introduce an on-the-fly reweighing scheme that makes it possible to estimate the uncertainty in the thermodynamic averages extracted from long trajectories. We present examples covering different types of structural and thermodynamic properties, and systems as diverse as water and liquid gallium.

The role of feature space in atomistic learning

Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as the fact that each choice of features can lead to very different behavior depending on how they are used, e.g. by introducing non-linear kernels and non-Euclidean metrics to manipulate them, makes it difficult to objectively compare different methods, and to address fundamental questions on how one feature space is related to another. In this work we introduce a framework to compare different sets of descriptors, and different ways of transforming them by means of metrics and kernels, in terms of the structure of the feature space that they induce. We define diagnostic tools to determine whether alternative feature spaces contain equivalent amounts of information, and whether the common information is substantially distorted when going from one feature space to another. We compare, in particular, representations that are built in terms of n-body correlations of the atom density, quantitatively assessing the information loss associated with the use of low-order features. We also investigate the impact of different choices of basis functions and hyperparameters of the widely used SOAP and Behler-Parrinello features, and investigate how the use of non-linear kernels, and of a Wasserstein-type metric, change the structure of the feature space in comparison to a simpler linear feature space.

Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials

Machine learning of atomic-scale properties is revolutionizing molecular modelling, making it possible to evaluate inter-atomic potentials with first-principles accuracy, at a fraction of the costs. The accuracy, speed and reliability of machine-learning potentials, however, depends strongly on the way atomic configurations are represented, i.e. the choice of descriptors used as input for the machine learning method. The raw Cartesian coordinates are typically transformed in fingerprints, or symmetry functions, that are designed to encode, in addition to the structure, important properties of the potential-energy surface like its invariances with respect to rotation, translation and permutation of like atoms. Here we discuss automatic protocols to select a number of fingerprints out of a large pool of candidates, based on the correlations that are intrinsic to the training data. This procedure can greatly simplify the construction of neural network potentials that strike the best balance between accuracy and computational efficiency, and has the potential to accelerate by orders of magnitude the evaluation of Gaussian Approximation Potentials based on the Smooth Overlap of Atomic Positions kernel. We present applications to the construction of neural network potentials for water and for an Al-Mg-Si alloy, and to the prediction of the formation energies of small organic molecules using Gaussian process regression.

Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enable routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, BPNN-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.