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Big data has ushered in a new wave of predictive power using machine learning models. In this work, we assess what {\it big} means in the context of typical materials-science machine-learning problems. This concerns not only data volume, but also data quality and veracity as much as infrastructure issues. With selected examples, we ask (i) how models generalize to similar datasets, (ii) how high-quality datasets can be gathered from heterogenous sources, (iii) how the feature set and complexity of a model can affect expressivity, and (iv) what infrastructure requirements are needed to create larger datasets and train models on them. In sum, we find that big data present unique challenges along very different aspects that should serve to motivate further work.

Computational materials science produces large quantities of data, both in terms of high-throughput calculations and individual studies. Extracting knowledge from this large and heterogeneous pool of data is challenging due to the wide variety of computational methods and approximations, resulting in significant veracity in the sheer amount of available data. Here, we present MADAS, a Python framework for computing similarity relations between material properties. It can be used to automate the download of data from various sources, compute descriptors and similarities between materials, analyze the relationship between materials through their properties, and can incorporate a variety of existing machine learning methods. We explain the design of the package and demonstrate its power with representative examples.

We present the Python package CELL, which provides a modular approach to the cluster expansion (CE) method. CELL can treat a wide variety of substitutional systems, including one-, two-, and three-dimensional alloys, in a general multi-component and multi-sublattice framework. It is capable of dealing with complex materials comprising several atoms in their parent lattice. CELL uses state-of-the-art techniques for the construction of training data sets, model selection, and finite-temperature simulations. The user interface consists of well-documented Python classes and modules (http://sol.physik.hu-berlin.de/cell/). CELL also provides visualization utilities and can be interfaced with virtually any ab initio package, total-energy codes based on interatomic potentials, and more. The usage and capabilities of CELL are illustrated by a number of examples, comprising a Cu-Pt surface alloy with oxygen adsorption, featuring two coupled binary sublattices, and the thermodynamic analysis of its order-disorder transition; the demixing transition and lattice-constant bowing of the Si-Ge alloy; and an iterative CE approach for a complex clathrate compound with a parent lattice consisting of 54 atoms.

The widely used linear-response (LR) theory of thermal conduction in the quantum regime rests on the yet unproven assumption, that the thermal conductivity is invariant with respect to the gauge of the energy density of the system. This assumption manifests itself clearly in, e.g., Hardy's formulation of the heat-flux operator [Phys. Rev. 132, 168 (1963)]. In this work, we rigorously prove this assumption. Our proof, being valid for the nuclear and electronic subsystems, not only puts the state-of-the-art theory on solid grounds, but also enables going beyond the scope of the widely-used Boltzmann transport equation (BTE) within the LR framework for many-body systems., Comment: 5 pages

A main goal of data-driven materials research is to find optimal low-dimensional descriptors, allowing us to predict a physical property, and to interpret them in a human-understandable way. In this work, we advance methods to identify descriptors out of a large pool of candidate features by means of compressed sensing. To this extent, we develop schemes for engineering appropriate candidate features that are based on simple basic properties of building blocks that constitute the materials and that are able to represent a multi-component system by scalar numbers. Cross-validation based feature-selection methods are developed for identifying the most relevant features, thereby focusing on high generalizability. We apply our approaches to an \textit{ab initio} dataset of ternary group-IV compounds to obtain a set of descriptors for predicting lattice constants and energies of mixing. In particular, we introduce simple complexity measures in terms of involved algebraic operations as well as the amount of utilized basic properties.

Identifying similar materials, i.e., those sharing a certain property or feature, requires interoperable data of high quality. It also requires means to measure similarity. We demonstrate how a spectral fingerprint as a descriptor, combined with a similarity metric, can be used for establishing quantitative relationships between materials data, thereby serving multiple purposes. This concerns, for instance, the identification of materials exhibiting electronic properties similar to a chosen one. The same approach can be used for assessing uncertainty in data that potentially come from different sources. Selected examples show how to quantify differences between measured optical spectra or the impact of methodology and computational parameters on calculated properties, like the the density of states or excitonic spectra. Moreover, combining the same fingerprint with a clustering approach allows us to explore materials spaces in view of finding (un)expected trends or patterns. In all cases, we provide physical reasoning behind the findings of the automatized assessment of data.

We develop a materials descriptor based on the electronic density of states and investigate the similarity of materials based on it. As an application example, we study the Computational 2D Materials Database that hosts thousands of two-dimensional materials with their properties calculated by density-functional theory. Combining our descriptor with a clustering algorithm, we identify groups of materials with similar electronic structure. We characterize these clusters in terms of their crystal structure, their atomic composition, and the respective electronic configurations to rationalize the found (dis)similarities.

We derive a formula for the electrical conductivity of solids that includes relaxation, dissipation, and quantum coherence. The derivation is based on the Kubo formula, with a Mori memory function approach to include dissipation effects at all orders in the relaxation interaction. It offers a practical method to evaluate the conductivity with electronic-structure codes and avoids the complications and limitations of the Kubo formula in the thermodynamic limit. The derivation of our formula provides a method applicable to other transport coefficients and correlation functions.

On the quest for efficient thermoelectrics, semiconducting behavior is a targeted property. Yet, this is often difficult to achieve due to the complex interplay between electronic structure, temperature, and disorder. We find this to be the case for the thermoelectric clathrate Ba$_8$Al$_{16}$Si$_{30}$: Although this material exhibits a band gap in its groundstate, a temperature-driven partial order-disorder transition leads to its effective closing. This finding is enabled by a novel approach to calculate the temperature-dependent effective band structure of alloys. Our method fully accounts for the effects of short-range order and can be applied to complex alloys with many atoms in the primitive cell, without relying on effective medium approximations., Comment: 5 pages, 3 figures

To gain insight into the peculiar temperature dependence of the thermoelectric material SnSe, we employ many-body perturbation theory and explore the influence of the electron-phonon interaction on its electronic and transport properties. We show that a lattice dynamics characterized by soft highly-polar phonons induces a large thermal enhancement of the Fr\"ohlich interaction. We account for these phenomena in ab-initio calculations of the photoemission spectrum and electrical conductivity at finite temperature, unraveling the mechanisms behind recent experimental data. Our results reveal a complex interplay between lattice thermal expansion and Fr\"ohlich coupling, providing a new rationale for the in-silico prediction of transport coefficients of high-performance thermoelectrics., Comment: 6 pages, 3 figures

The structural and electronic properties of the clathrate compounds Ba$_{8}$Al$_{x}$Si$_{46-x}$ and Sr$_{8}$Al$_{x}$Si$_{46-x}$ are studied from first principles, considering an Al content $x$ between 6 and 16. Due to the large number of possible substitutional configurations we make use of a special iterative cluster-expansion approach, to predict ground states and quasi-degenerate structures in a highly efficient way. These are found from a simulated annealing technique where millions of configurations are sampled. For both compounds, we find a linear increase of the lattice constant with the number of Al substituents, confirming experimental observations for Ba$_{8}$Al$_{x}$Si$_{46-x}$. Also the calculated bond distances between high-symmetry sites agree well with experiment for the full compositional range. For $x$ being below 16, all configurations are metallic for both materials. At the charge-balanced composition ($x=16$), the substitutional ordering leads to a metal-semiconductor transition, and the ground states of Ba$_{8}$Al$_{16}$Si$_{30}$ and Sr$_{8}$Al$_{16}$Si$_{30}$ exhibit indirect Kohn-Sham band gaps of 0.36 and 0.30 eV, respectively, while configurations higher in energy are metals. The finding of semiconducting behavior is a promising result in view of exploiting these materials in thermoelectric applications., Comment: 9 figures

Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of non-linear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Green's function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Green's function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction., Comment: 5 pages, 3 figures plus supplemental material

A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density-functional theory. We show that the trustful prediction of strongly bound electron-hole pairs within this framework using simple approximations is still a challenge and that available promising results have to be revisited. Deriving a set of analytical formula we analyze and explain the difficulties. We deduce an alternative approximation from an iterative scheme guided by previously available knowledge, significantly improving the description of exciton binding energies. Finally, we show how one can "read" exciton binding energies from spectra determined in the random phase approximation, without any further calculation., Comment: 5 pages, 2 figures plus supplemental material