Despite the huge number of possible materials (e.g. GaAs, Al2O3, etc.), we note that “the chemical compound space” is sparsely populated when the focus is on selected properties or functions (e.g. structure: rock salt vs. zinkblende, electrical conductivity, etc.). NOMAD offers big-data analytics tools that will help to sort all of the available materials data to identify trends and anomalies. For more information click the "INTRODUCTION TO" button above.

The following tutorials are designed to get started with the Analytics Toolkit (click title to show/hide details of the selected tutorial):

*created by:* Regler, Benjamin | Sastre, Alfonso | Mohamed, Fawzi | Ghiringhelli, Luca

A tutorial introduction on how to perform a query over the NOMAD Archive, by means of a light and intuitive GUI, and browse the results

*Method:* ElasticSearch

*Language(s):* python | javascript

*created by:* Regler, Benjamin | Ghiringhelli, Luca | Scheffler, Matthias

In this notebook, we use the Nomad infrastructure to query a limited number of atomic data collections and to visualize them in the periodic table of elements. There are several filters that can be applied to atomic data collections and a field to select which atomic property should be visualized in the periodic table of elements.

*Keywords:* Atomic species

*Language(s):* python | javascript

*created by:* Christopher Bartel | Christopher Sutton | Bryan Goldsmith | Runhai Ouyang | Charles Musgrave | Luca Ghiringhelli | Matthias Scheffler

A tool for predicting the probability that a given chemical formula will crystallize in a perovskite structure. This prediction is made using a newly developed tolerance factor (descriptor) which makes predictions based on automatically assigned ionic radii and oxidation states. Within this notebook, you can also visualize the probability of forming perovskite for any single or double perovskite formula as a function of the cationic radii.

*Keywords:* perovskites | stability | classification

*Method:* SISSO

*Language(s):* python | javascript

*created by:* Ziletti, Angelo | Kariryaa, Ankit | Mohamed, Fawzi | Ghiringhelli, Luca | Scheffler, Matthias

This Notebook allows to retrieve your query results from the NOMAD Archive, and subsequently perform state-of-the-art machine learning analysis on this dataset. Given a user-specified query, the structures of the top-5 space groups (for crystals) or point groups (for molecules) within this dataset are returned, and then a structural-similarity model is built on-the-fly.

*Keywords:* Query usage

*Method:* SOAP | Global Similarity | Glosim | Kernel Principal-Component Analysis | Kernel PCA | MultiDimensional Scaling | MDS

*Language(s):* python | javascript

*created by:* Ziletti, Angelo | Ahmetcik, Emre | Ouyang, Runhai | Kariryaa, Ankit | Mohamed, Fawzi | Ghiringhelli, Luca | Scheffler, Matthias

A tool for predicting the difference in the total energy between different polymorphs for 82 octet binary compounds, which gives an indication of the stability of the material. This is accomplished by identifying a set of descriptive parameters (a descriptor) from the free-atom data for the binary atomic species comprising the material using the Sure Independent Screening (SIS) + l0-norm minimization approach.

*Keywords:* Octet binaries

*Method:* Compressed Sensing | SISSO

*Language(s):* python | javascript

*created by:* Ahmetcik, Emre | Ziletti, Angelo | Ouyang, Runhai | Ghiringhelli, Luca | Scheffler, Matthias

This tutorial introduces from scratch and step by step: Compressed sensing, LASSO, and SISSO for materials property prediction

*Keywords:* Octet binaries

*Method:* Compressed Sensing | LASSO+l0 | SISSO

*Language(s):* python | javascript

*created by:* Boley, Mario | Goldsmith, Bryan | Kariryaa, Ankit | Ghiringhelli, Luca

In this tutorial, Subgroup Discovery (SGD) is used to identify simple descriptors for predicting whether an octet binary material crystallizes in rock-salt or zinc-blende crystal structures. SGD is a data-mining technique that is used to identify and describe local patterns (subgroups) in complex data. SGD will mine the data for subgroups that optimize the utility functions and at the same time cover (contain) as many materials as possible. The groups are described by combining one or more Boolean statements on the features (e.g., “the electron affinity of atom A (the cation) is smaller than 1.00”).

*Method:* Subgroup Discovery

*created by:* Poelking, Carl | Ziletti, Angelo | Ghiringhelli, Luca | Csányi, Gábor

A tool for mapping and visualizing materials databases using generic kernel- and graph-based similarity measures together with the powerful Smooth Overlap of Atomic Positions (SOAP) descriptor for atomic environments.

*Keywords:* Octet binaries | GDB molecular database

*Method:* SOAP | Global Similarity | Glosim | Kernel Principal-Component Analysis | Kernel PCA | MultiDimensional Scaling | MDS

*Language(s):* python | javascript

*created by:* Ziletti, Angelo | Kariryaa, Ankit | Mohamed, Fawzi | Ghiringhelli, Luca | Scheffler, Matthias

A tool that produces two-dimensional structure maps for octet binary compounds, starting from a high-dimensional set of coordinates (features) that identify each material (data point), based on free-atom data of the atomic species constituting the binary material.

*Keywords:* Octet binaries

*Method:* Dimensionality Reduction | Principal-Component Analysis | PCA | MultiDimensional Scaling | MDS | t-Distributed Stochastic Neighbor Embedding | t-SNE

*Language(s):* python | javascript

*created by:* Ziletti, Angelo | Ahmetcik, Emre | Ouyang, Runhai | Kariryaa, Ankit | Mohamed, Fawzi | Ghiringhelli, Luca | Scheffler, Matthias

A tool for predicting the difference in the total energy between different polymorphs for 82 octet binary compounds, which gives an indication of the stability of the material. This is accomplished by identifying a set of descriptive parameters (a descriptor) from the free-atom data for the binary atomic species comprising the material using LASSO + l0-norm minimization approach.

*Keywords:* Octet binaries

*Method:* Compressed Sensing | LASSO+l0

*Language(s):* python | javascript

*created by:* Himanen, Lauri | Huhs, Georg | Hurtado, Iker | Kuban, Martin | Vancea, Ioan | Draxl, Claudia

This tutorial deals mainly with accessing the NOMAD Encyclopedia API (searching for materials, extracting data for specific materials and calculations). It also shows how code developed for the Encyclopedia GUI can be embedded into client applications.

*Language(s):* python | javascript

*created by:* Bieniek, Björn | Strange, Mikkel | Carbogno, Christian

A set of tools to analyze the error in electronic structure calculations due to the choice of numerical settings. We use the NOMAD infrastructure to systematically investigate the deviances in total and relative energies as function of typical settings for basis sets, k-grids, etc. for 71 elemental and 81 binary solids in four different electronic-structure codes.

*Keywords:* Binaries | Elemental solids

*Method:* Linear Least-squares Regression

*Language(s):* python | javascript

*created by:* Ahmetcik, Emre | Ziletti, Angelo | Ouyang, Runhai | Ghiringhelli, Luca | Scheffler, Matthias

This tutorial shows how to find descriptive parameters (short formulas) for the classification of materials properties. As an example, we address the classification of elemental and binary systems AxBy into metals and non metals using experimental data extracted from the SpringerMaterials data base. The method is based on the algorithm sure independence screening and sparsifying operator (SISSO), which enables to search for optimal descriptors by scanning huge feature spaces.

*Keywords:* Binaries | Metal/insulator | Classification

*Method:* Compressed Sensing | SISSO

*Language(s):* python | javascript

*created by:* Fekete, Adam | Glielmo, Aldo | Stella, Martina | De Vita, Alessandro

This tutorial makes use of Gaussian process (GP) regression in order to assess the complexity of a given system. This can be defined as the data set size necessary to the GP to predict a target property (eg. atomic forces, total energy of a configuration). The currently available data is the atomic forces in the mono-crystalline silicon at 300K, 1200K and 3000K.

*Keywords:* Elemental solids

*Method:* Gaussian-Process Regression | GPR

*Language(s):* python | javascript

*created by:* Fekete, Ádám | Stella, Martina | Lambert, Henry | De Vita, Alessandro | Csányi, Gábor

In this tutorial we will be using a machine learning method (clustering) to analyse results of Grain Boundary (GB) calculations of alpha-iron. Along the way we will learn about different methods to describe local atomic environment in order to calculate properties of GBs. We will use these properties to separate the different regions of the GB using clustering methods. Finally we will determine how the energy of the GB is changing according to the angle difference of the regions.

*Keywords:* Grain boundaries

*Method:* Clustering

*created by:* Mera Acosta, Carlos | Ahmetcik, Emre | Carbogno, Christian | Ouyang, Runhai | Fazzio, Adalberto | Ghiringhelli, Luca | Scheffler, Matthias

This tutorial shows how to find descriptive parameters (short formulas) for the prediction of topological phase transitions. As an example, we address the topological classification of two-dimensional functionalized honeycomb-lattice materials, which are formally described by the Z2 topological invariant, i.e., Z2=0 for trivial (normal) insulators and Z2=1 for two-dimensional topological insulators (quantum spin Hall insulators). Using a recently developed machine learning based on compressed sensing, we then derive a map of these materials, in which metals, trivial insulators, and quantum spin Hall insulators are separated in different spatial domains. The axes of this map are given by a physically meaningful descriptor, i.e., a non-linear analytic function that only depends on the properties of the material's constituent atoms, but not on the properties of the material itself. The method is based on the algorithm sure independence screening and sparsifying operator (SISSO), which enables to search for optimal descriptors by scanning huge feature spaces.

*Keywords:* Qunatum Phase | Topological insulator | Classification

*Method:* Compressed Sensing | SISSO

*Language(s):* python | javascript

*created by:* Csányi, Gábor | Kermode, James R.

In this tutorial, we will use Gaussian process regression, GPR (or equivalently, Kernel Ridge Regression, KRR) to train and predict charges of atoms in small organic molecules.

*Keywords:* GDB molecular database

*Method:* Gaussian-Process Regression | GPR | Kernel Ridge Regression | KRR

*created by:* Rigamonti, Santiago | Troppenz, Maria | Draxl, Claudia

A tool for predicting ground state configurations of binary alloys. In this tutorial, the ground state configurations of a AlNa surface alloy are found. Starting from a set of ab initio data for random configurations of the alloy, a cluster expansion is performed and the ground states are found through a configurational sampling.

*Method:* Cluster Expansion

*Language(s):* python

*created by:* Rigamonti, Santiago | Troppenz, Maria | Draxl, Claudia

A tool for predicting ground state configurations of binary alloys. In this tutorial, the ground state configurations of a SiGe binary alloy are found. Starting from a set of ab initio data for random configurations of the alloy, a cluster expansion is performed and the ground states are found through a configurational sampling.

*Keywords:* Alloys

*Method:* Cluster Expansion

*Language(s):* python

*created by:* Strange, Mikkel | Thygesen, Kristian S.

Developed by .A tool that produces compositional phase diagrams. As an example we consider materials made of Li-Fe-P-O. Phase diagrams are generally useful to determine if a given material is thermodynamically stable under certain conditions such as temperature, pressure etc. In this tutorial, we consider only a compositional phase diagram at zero temperature and pressure.

*Keywords:* Alloys

*Language(s):* python | javascript

*created by:* Ziletti, Angelo | Kumar, Devinder | Scheffler, Matthias | Ghiringhelli, Luca

In this notebook, we use a machine learning-based approach to automatically classify structures by crystal symmetry; first, we represent crystals by a diffraction image, then use a neural network for classification. The notebook allows to reproduce the main results of: A. Ziletti, D. Kumar, M. Scheffler and L. M. Ghiringhelli, Nature Communications 9, 2775 (2018)

*Keywords:* Crystals | Structure

*Method:* Neural networks | Deep learning

*Language(s):* python | javascript

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