Insightful classification of crystal structures using deep learning

Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and analytics. Current methods require a user-specified threshold, and are unable to detect average symmetries for defective structures. Here, we propose a machine-learning-based approach to automatically classify structures by crystal symmetry. First, we represent crystals by calculating a diffraction image, then construct a deep-learning neural-network model for classification. Our approach is able to correctly classify a dataset comprising more than 100 000 simulated crystal structures, including heavily defective ones. The internal operations of the neural network are unraveled through attentive response maps, demonstrating that it uses the same landmarks a materials scientist would use, although never explicitly instructed to do so. Our study paves the way for crystal-structure recognition of - possibly noisy and incomplete - three-dimensional structural data in big-data materials science.Comment: Nature Communications, in press (2018

TCMI: a non-parametric mutual-dependence estimator for multivariate continuous distributions

The identification of relevant features, i.e., the driving variables that determine a process or the property of a system, is an essential part of the analysis of data sets whose entries are described by a large number of variables. The preferred measure for quantifying the relevance of nonlinear statistical dependencies is mutual information, which requires as input probability distributions. Probability distributions cannot be reliably sampled and estimated from limited data, especially for real-valued data samples such as lengths or energies. Here, we introduce total cumulative mutual information (TCMI), a measure of the relevance of mutual dependencies based on cumulative probability distributions. TCMI can be estimated directly from sample data and is a non-parametric, robust and deterministic measure that facilitates comparisons and rankings between feature sets with different cardinality. The ranking induced by TCMI allows for feature selection, i.e., the identification of the set of relevant features that are statistical related to the process or the property of a system, while taking into account the number of data samples as well as the cardinality of the feature subsets. We evaluate the performance of our measure with simulated data, compare its performance with similar multivariate dependence measures, and demonstrate the effectiveness of our feature selection method on a set of standard data sets and a typical scenario in materials science

Bimagnon studies in cuprates with Resonant Inelastic X-ray Scattering at the O K edge. II - The doping effect in La2-xSrxCuO4

We present RIXS data at O K edge from La2-xSrxCuO4 vs. doping between x=0.10 and x=0.22 with attention to the magnetic excitations in the Mid-Infrared region. The sampling done by RIXS is the same as in the undoped cuprates provided the excitation is at the first pre-peak induced by doping. Note that this excitation energy is about 1.5 eV lower than that needed to see bimagnons in the parent compound. This approach allows the study of the upper region of the bimagnon continuum around 450 meV within about one third of the Brilluoin Zone around \Gamma. The results show the presence of damped bimagnons and of higher even order spin excitations with almost constant spectral weight at all the dopings explored here. The implications on high Tc studies are briefly addressed

The NOMAD Artificial-Intelligence Toolkit: Turning materials-science data into knowledge and understanding

We present the Novel-Materials-Discovery (NOMAD) Artificial-Intelligence (AI) Toolkit, a web-browser-based infrastructure for the interactive AI-based analysis of materials-science findable, accessible, interoperable, and reusable (FAIR) data. The AI Toolkit readily operates on the FAIR data stored in the central server of the NOMAD Archive, the largest database of materials-science data worldwide, as well as locally stored, users' owned data. The NOMAD Oasis, a local, stand alone server can be also used to run the AI Toolkit. By using Jupyter notebooks that run in a web-browser, the NOMAD data can be queried and accessed; data mining, machine learning, and other AI techniques can be then applied to analyse them. This infrastructure brings the concept of reproducibility in materials science to the next level, by allowing researchers to share not only the data contributing to their scientific publications, but also all the developed methods and analytics tools. Besides reproducing published results, users of the NOMAD AI toolkit can modify the Jupyter notebooks towards their own research work

SISSO++: A C++ Implementation of the Sure-Independence Screening and Sparisifying Operator Approach

The sure independence screening and sparsifying operator (SISSO) approach (Ouyang et al., 2018) is an algorithm belonging to the field of artificial intelligence and more specifically a combination of symbolic regression and compressed sensing. As a symbolic regression method, SISSO is used to identify mathematical functions, i.e. the descriptors, that best predict the target property of a data set. Furthermore, the compressed sensing aspect of SISSO, allows it to find sparse linear models using tens to thousands of data points. SISSO is introduced for both regression and classification tasks. In practice, SISSO first constructs a large and exhaustive feature space of trillions of potential descriptors by taking in a set of user-provided primary features as a dataframe, and then iteratively applying a set of unary and binary operators, e.g. addition, multiplication, exponentiation, and squaring, according to a user-defined specification. From this exhaustive pool of candidate descriptors, the ones most correlated to a target property are identified via sure-independence screening, from which the low-dimensional linear models with the lowest error are found via an l0 regularization. Because symbolic regression generates an interpretable equation, it has become an increasingly popular concept across scientific disciplines (Neumann et al., 2020; Udrescu & Tegmark, 2020; Wang et al., 2019). A particular advantage of these approaches are their capability to model complex phenomena using relatively simple descriptors. SISSO has been used successfully in the past to model, explore, and predict important material properties, including the stability of different phases (Bartel et al., 2018; Schleder et al., 2020); the catalytic activity and reactivity (Andersen et al., 2019; Andersen & Reuter, 2021; Han et al., 2021; W. Xu et al., 2021); and glass transition temperatures (Pilania et al., 2019). Beyond regression problems, SISSO has also been used successfully to classify materials into different crystal prototypes (Ouyang et al., 2019), or whether a material crystallizes in its ground state as a perovskite (Bartel et al., 2019), or to determine whether a material is a topological insulator or not (Cao et al., 2020). The SISSO++ package is an open-source (Apache-2.0 licence), modular, and extensible C++ implementation of the SISSO method with Python bindings. Specifically, SISSO++ applies this methodology for regression, log regression, and classification problems. Additionally, the library includes multiple Python functions to facilitate the post-processing, analyzing, and visualizing of the resulting models

Ab Initio Approach for Thermodynamic Surface Phases with Full Consideration of Anharmonic Effects: The Example of Hydrogen at Si(100)

A reliable description of surfaces structures in a reactive environment is crucial to understand materials functions. We present a first-principles theory of replica-exchange grand-canonical-ensemble molecular dynamics (REGC-MD) and apply it to evaluate phase equilibria of surfaces in reactive gas-phase environment. We identify the different surface phases and locate phase boundaries including triple and critical points. The approach is demonstrated by addressing open questions for the Si(100) surface in contact with a hydrogen atmosphere. In the range from 300 to 1 000 K, we find 25 distinct thermodynamically stable surface phases, for which we also provide microscopic descriptions. Most of the identified phases, including few order-disorder phase transitions, have not yet been observed experimentally. The REGC-MD-derived phase diagram shows significant, qualitative differences to the description by the state-of-the-art "ab initio atomistic thermodynamics" approach. <br

High-energy magnetic excitations in overdoped La2−x_{2-x}Srx_{x}CuO4_{4} studied by neutron and resonant inelastic X-ray scattering

We have performed neutron inelastic scattering and resonant inelastic X-ray scattering (RIXS) at the Cu-$L_3$ edge to study high-energy magnetic excitations at energy transfers of more than 100 meV for overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.25$ ($T_c=15$ K) and $x=0.30$ (non-superconducting) using identical single crystal samples for the two techniques. From constant-energy slices of neutron scattering cross-sections, we have identified magnetic excitations up to ~250 meV for $x=0.25$. Although the width in the momentum direction is large, the peak positions along the (pi, pi) direction agree with the dispersion relation of the spin-wave in the non-doped La$_{2}$CuO$_{4}$ (LCO), which is consistent with the previous RIXS results of cuprate superconductors. Using RIXS at the Cu-$L_3$ edge, we have measured the dispersion relations of the so-called paramagnon mode along both (pi, pi) and (pi, 0) directions. Although in both directions the neutron and RIXS data connect with each other and the paramagnon along (pi, 0) agrees well with the LCO spin-wave dispersion, the paramagnon in the (pi, pi) direction probed by RIXS appears to be less dispersive and the excitation energy is lower than the spin-wave of LCO near (pi/2, pi/2). Thus, our results indicate consistency between neutron inelastic scattering and RIXS, and elucidate the entire magnetic excitation in the (pi, pi) direction by the complementary use of two probes. The polarization dependence of the RIXS profiles indicates that appreciable charge excitations exist in the same energy range of magnetic excitations, reflecting the itinerant character of the overdoped sample. A possible anisotropy in the charge excitation intensity might explain the apparent differences in the paramagnon dispersion in the (pi, pi) direction as detected by the X-ray scattering.Comment: 7 pages, 7 figure

Interacting electrons, spin statistics, and information theory

We consider a nearly (or quasi) uniform gas of interacting electrons for which spin statistics play a crucial role. A previously developed procedure, based on the extension of the Levy–Lieb constrained search principle and Monte Carlo sampling of electron configurations in space, allows us to approximate the form of the kinetic-energy functional. For a spinless electron gas, this procedure led to a correlation term, which had the form of the Shannon entropy, but the resulting kinetic-energy functional does not satisfy the Lieb–Thirring inequality, which is rigorous and one of the most general relations regarding the kinetic energy. In this paper, we show that when the fermionic character of the electrons is included via a statistical spin approach, our procedure leads to correlation terms, which also have the form of the Shannon entropy and the resulting kinetic-energy functional does satisfy the Lieb–Thirring inequality. In this way we further strengthen the connection between Shannon entropy and electron correlation and, more generally, between information theory and quantum mechanics