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Register a new userGeneralized convex hull construction for materials discovery
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High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull construction, which identifies structures stabilized by manipulation of a particular thermodynamic constraint (for example pressure or composition) chosen based on prior experimental evidence or intuition. To address the biased nature of this procedure we introduce a generalized convex hull framework. Convex hulls are constructed on data-driven principal coordinates, which represent the full structural diversity of the database. Their coupling to experimentally-realizable constraints hints at the conditions that are most likely to stabilize a given configuration. The probabilistic nature of our framework also addresses the uncertainty stemming from the use of approximate models during database construction, and eliminates redundant structures. The remaining small set of candidates that have a high probability of being synthesizable provide a much needed starting point for the determination of viable synthetic pathways.
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The traditional paradigm for materials discovery has been recently expanded to incorporate substantial data driven research. With the intent to accelerate the development and the deployment of new technologies, the AFLOW Fleet for computational materials design automates high-throughput first principles calculations, and provides tools for data verification and dissemination for a broad community of users. AFLOW incorporates different computational modules to robustly determine thermodynamic stability, electronic band structures, vibrational dispersions, thermo-mechanical properties and more. The AFLOW data repository is publicly accessible online at aflow.org, with more than 1.7 million materials entries and a panoply of queryable computed properties. Tools to programmatically search and process the data, as well as to perform online machine learning predictions, are also available.
Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata.
Recent application of neural networks (NNs) to modeling interatomic interactions has shown the learning machines encouragingly accurate performance for select elemental and multicomponent systems. In this study, we explore the possibility of building a library of NN-based models by introducing a hierarchical NN training. In such a stratified procedure NNs for multicomponent systems are obtained by sequential training from the bottom up: first unaries, then binaries, and so on. Advantages of constructing NN sets with shared parameters include acceleration of the training process and intact description of the constituent systems. We use an automated generation of diverse structure sets for NN training on density functional theory-level reference energies. In the test case of Cu, Pd, Ag, Cu-Pd, Cu-Ag, Pd-Ag, and Cu-Pd-Ag systems, NNs trained in the traditional and stratified fashions are found to have essentially identical accuracy for defect energies, phonon dispersions, formation energies, etc. The models robustness is further illustrated via unconstrained evolutionary structure searches in which the NN is used for the local optimization of crystal unit cells.
Assessing the synthesizability of inorganic materials is a grand challenge for accelerating their discovery using computations. Synthesis of a material is a complex process that depends not only on its thermodynamic stability with respect to others, but also on factors from kinetics, to advances in synthesis techniques, to the availability of precursors. This complexity makes the development of a general theory or first-principles approach to synthesizability currently impractical. Here we show how an alternative pathway to predicting synthesizability emerges from the dynamics of the materials stability network: a scale-free network constructed by combining the convex free-energy surface of inorganic materials computed by high-throughput density functional theory and their experimental discovery timelines extracted from citations. The time-evolution of the underlying network properties allows us to use machine-learning to predict the likelihood that hypothetical, computer-generated materials will be amenable to successful experimental synthesis.
Given a finite set of points $P subseteq mathbb{R}^d$, we would like to find a small subset $S subseteq P$ such that the convex hull of $S$ approximately contains $P$. More formally, every point in $P$ is within distance $epsilon$ from the convex hull of $S$. Such a subset $S$ is called an $epsilon$-hull. Computing an $epsilon$-hull is an important problem in computational geometry, machine learning, and approximation algorithms. In many real world applications, the set $P$ is too large to fit in memory. We consider the streaming model where the algorithm receives the points of $P$ sequentially and strives to use a minimal amount of memory. Existing streaming algorithms for computing an $epsilon$-hull require $O(epsilon^{-(d-1)/2})$ space, which is optimal for a worst-case input. However, this ignores the structure of the data. The minimal size of an $epsilon$-hull of $P$, which we denote by $text{OPT}$, can be much smaller. A natural question is whether a streaming algorithm can compute an $epsilon$-hull using only $O(text{OPT})$ space. We begin with lower bounds that show that it is not possible to have a single-pass streaming algorithm that computes an $epsilon$-hull with $O(text{OPT})$ space. We instead propose three relaxations of the problem for which we can compute $epsilon$-hulls using space near-linear to the optimal size. Our first algorithm for points in $mathbb{R}^2$ that arrive in random-order uses $O(log ncdot text{OPT})$ space. Our second algorithm for points in $mathbb{R}^2$ makes $O(log(frac{1}{epsilon}))$ passes before outputting the $epsilon$-hull and requires $O(text{OPT})$ space. Our third algorithm for points in $mathbb{R}^d$ for any fixed dimension $d$ outputs an $epsilon$-hull for all but $delta$-fraction of directions and requires $O(text{OPT} cdot log text{OPT})$ space.
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