Machine learning of atomic-scale properties is revolutionizing molecular modeling, 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, depend 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.

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Ice is one of the most extensively studied condensed matter systems. Yet, both experimentally and theoretically several new phases have been discovered over the last years. Here we report a large-scale density-functional-theory study of the configuration space of water ice. We geometry optimise 74,963 ice structures, which are selected and constructed from over five million tetrahedral networks listed in the databases of Treacy, Deem, and the International Zeolite Association. All prior knowledge of ice is set aside and we introduce “generalised convex hulls” to identify configurations stabilised by appropriate thermodynamic constraints. We thereby rediscover all known phases (I–XVII, i, 0 and the quartz phase) except the metastable ice IV. Crucially, we also find promising candidates for ices XVIII through LI. Using the “sketch-map” dimensionality-reduction algorithm we construct an a priori, navigable map of configuration space, which reproduces similarity relations between structures and highlights the novel candidates. By relating the known phases to the tractably small, yet structurally diverse set of synthesisable candidate structures, we provide an excellent starting point for identifying formation pathways.

Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well-suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical error in the electronic structure methods. We also extend the recently-developed ShiftML machine-learning model, including the evaluation of the uncertainty of its predictions. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the of similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated 13 C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use 13 C shifts to improve the accuracy of structure determinations.

Searching for novel materials involves identifying potential candidates and selecting those that have desirable properties and facile synthesis. It is relatively easy to generate large numbers of potential candidates, for instance by computational searches or elemental substitution. The identification of synthesizable compounds, however, is a needle-in-a-haystack problem. Conventionally, the screening is based on a convex hull construction, which identifies structures stabilized by a particular thermodynamic constraint, such as pressure, chosen based on prior experimental evidence or intuition. We introduce a generalized convex hull framework that instead relies on data-driven coordinates, and represents the full structural diversity of the candidate compounds in an unbiased way. Its probabilistic construction addresses the inevitable uncertainty in input structure data and provides a superior measure of stability compared to the input (free) energies, that can for instance also be used to assist experimental crystal structure determination. It efficiently identifies candidates with high probabilities of being synthesizable and suggests the relevant experimentally realizable constraints, thereby providing a much needed starting point for the determination of viable synthetic pathways.arXiv:1803.01932v2 [cond-mat.mtrl-sci]

The Norian in the Western Tethys is characterised by the deposition of early-dolomitised inner platform facies (Dolomia Principale/Hauptdolomit, DP/HD), bordered on the landward side by terrigenous coastal deposits (Keuper) and on the seaward side by calcareous backreef and reefal facies (Dachstein Limestone) passing basinward to open-sea sediments (Hallstatt facies). The inner carbonate platform is locally (Lombardy Basin, Carnic Alps, Central Austroalpine) dissected by normal faults leading to the development of intraplatform troughs. Close to the Norian-Rhaetian boundary, sedimentation records an abrupt environmental change both on platform top and basins all over the Western Tethys (e.g. Western Carpathians, Transdanubian Range, Alps, Central Apennine). The top of the Dolomia Principale locally emerged, reflecting a major eustatic sea-level fall. Emersion is recorded in favourable settings by the development of polycyclic paleosols up to 30 m thick. In the Norian intraplatform basins, the succession is capped by 4 to 8 meters of thin-bedded, fine-grained limestones yielding abundant remnants of fishes and terrestrial reptiles. Fossil concentration as well as sedimentological features are indicative of reduced sedimentation rates due to decreased carbonate production, induced by the emersion of the platform top. The sea-level fall was followed by deposition of mixed fine-grained siliciclasticcarbonate successions (e.g. Riva di Solto Shale, Kössen beds, "Rhaetavicula contorta beds", Fatra Formation). Stratigraphic evidence indicates a dry climate in the Western Tethys during the Norian, as indicated by the presence of evaporites (Burano, Apennine) and arid to semi-arid coastal to playa settings (Upper Keuper, Germany). In contrast, the basal layers of the basinal shales show evidence of wet climate.

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