Force fields developed with machine learning methods in tandem with quantum mechanics are beginning to find merit, given their (i) low cost, (ii) accuracy, and (iii) versatility. Recently, we proposed one such approach, wherein, the vectorial force on an atom is computed directly from its environment. Here, we discuss the multi-step workflow required for their construction, which begins with generating diverse reference atomic environments and force data, choosing a numerical representation for the atomic environments, down selecting a representative training set, and lastly the learning method itself, for the case of Al. The constructed force field is then validated by simulating complex materials phenomena such as surface melting and stressstrain behavior -that truly go beyond the realm of ab initio methods both in length and time scales. To make such force fields truly versatile an attempt to estimate the uncertainty in force predictions is put forth, allowing one to identify areas of poor performance and paving the way for their continual improvement.

We analyze orbital solutions for 48 massive multiple-star systems in the Cygnus OB2 association, 23 of which are newly presented here, to find that the observed distribution of orbital periods is approximately uniform in log P for P < 45 days, but it is not scale-free. Inflections in the cumulative distribution near 6 days, 14 days, and 45 days suggest key physical scales of 0.2, 0.4, and 1 A.U. where yet-to-be-identified phenomena create distinct features. No single power law provides a statistically compelling prescription, but if features are ignored, a power law with exponent β −0.22 provides a crude approximation over P = 1.4-2000 days, as does a piece-wise linear function with a break near 45 days. The cumulative period distribution flattens at P > 45 days, even after correction for completeness, indicating either a lower binary fraction or a shift toward low-mass companions. A high degree of similarity (91% likelihood) between the Cyg OB2 period distribution and that of other surveys suggests that the binary properties at P 25 days are determined by local physics of disk/clump fragmentation and are relatively insensitive to environmental and evolutionary factors. Fully 30% of the unbiased parent sample is a binary with period P < 45 days. Completeness corrections imply a binary fraction near 55% for P < 5000 days. The observed distribution of mass ratios 0.2 < q < 1 is consistent with uniform, while the observed distribution of eccentricities 0.1 < e < 0.6 is consistent with uniform plus an excess of e 0 systems. We identify six stars, all supergiants, that exhibit aperiodic velocity variations of ∼30 km s −1 attributed to atmospheric fluctuations.

Emerging machine learning (ML)-based approaches provide powerful and novel tools to study a variety of physical and chemical problems. In this contribution, we outline a universal strategy to create ML-based atomistic force fields, which can be used to perform high-fidelity molecular dynamics simulations. This scheme involves (1) preparing a big reference dataset of atomic environments and forces with sufficiently low noise, e.g., using density functional theory or higher-level methods, (2) utilizing a generalizable class of structural fingerprints for representing atomic environments, (3) optimally selecting diverse and non-redundant training datasets from the reference data, and (4) proposing various learning approaches to predict atomic forces directly (and rapidly) from atomic configurations. From the atomistic forces, accurate potential energies can then be obtained by appropriate integration along a reaction coordinate or along a molecular dynamics trajectory. Based on this strategy, we have created model ML force fields for six elemental bulk solids, including Al, Cu, Ti, W, Si, and C, and show that all of them can reach chemical accuracy. The proposed procedure is general and universal, in that it can potentially be used to generate ML force fields for any material using the same unified workflow with little human intervention. Moreover, the force fields can be systematically improved by adding new training data progressively to represent atomic environments not encountered previously.

To facilitate chemical space exploration for material screening or to accelerate computationally expensive first-principles simulations, inexpensive surrogate models that capture electronic, atomistic, or macroscopic materials properties have become an increasingly popular tool over the last decade. The most fundamental quantity common across all such machine learning (ML)-based methods is the f ingerprint used to numerically represent a material or its structure. To increase the learning capability of the ML methods, the common practice is to construct fingerprints that satisfy the same symmetry relations as displayed by the target material property of interest (for which the ML model is being developed). Thus, in this work, we present a general, simple, and elegant fingerprint that can be used to learn different electronic/atomistic/structural properties, irrespective of their scalar, vector, or tensorial nature. This fingerprint is based on the concept of multipole terms and can be systematically increased in sophistication to achieve a desired level of accuracy. Using the examples of Al, C, and hafnia (HfO 2 ), we demonstrate the applicability of this fingerprint to easily classify different atomistic environments, such as phases, surfaces, point defects, and so forth. Furthermore, we demonstrate the generality and effectiveness of this fingerprint by building an accurate, yet inexpensive, ML-based potential energy model for the case of Al using a reference data set that is obtained from density functional theory computations. Finally, we note that the fingerprint definition presented here has applications in fields beyond materials informatics, such as structure prediction, identification of defects, and detection of new crystal phases.