The virtually integrated distributed system of databases on the properties of inorganic substances and materials of the A.A. Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences is considered. The information-analytical system for automation of process of new inorganic compounds computer-assisted design based on machine learning methods usage for search for regularities in information of the databases on inorganic substances and materials properties is discussed. The results this system application for compound design that have not yet been synthesized are presented.
Modern information technologies have made it possible to systematize and make
available a huge array of data accumulated by chemistry over the centuries. Chemists and
materials scientists make extensive use of the rich capabilities provided by numerous
databases (DB), including the database on the properties of inorganic substances and
materials (DBs PISM) [
Information service does not limit the capabilities of the developed databases. One
of the ways to make rational use of information on substances is the search for
regularities that connect the properties of substances with the parameters of components. The
objective existence of such regularities is a consequence of the Periodic Law. However,
numerous attempts to present the desired complex regularities in an analytical form, as
a rule, were unsuccessful, especially in the case of multicomponent substances. The
methods for finding such complicated regularities in the data, based on the ideas of
machine learning, were developed. In the mid-sixties, the idea of using machine
learning to find regularities, that relate the properties of inorganic compounds to the
parameters of components, was first proposed in our Institute of Metallurgy and Materials
Science (IMET) [
The source of information for the use of machine learning methods is the DBs PISM.
In contrast to the databases usually used for these purposes, the information systems
developed by the Institute of Metallurgy and Materials Science, Russian Academy of
Sciences [
One of the most important problems in the application of machine learning to inorganic chemistry is the inconsistency of data obtained by different researchers. In this regard, the selection of information for machine learning is carried-ot by qualified experts in this subject area. This procedure is facilitated by providing the experts with the full texts of publications contained in our DBs PISM, from which examples are selected for machine learning, as well as through special programs for detecting sharply distinguished objects (outliers).
Now the integrated system of the DBs PISM includes the information systems
developed in the IMET [
The Phases database on the properties of inorganic compounds currently contains
information on the properties of approximately 54000 ternary compounds and more
than 34000 quaternary compounds, collected using more than 36000 publications. It
includes brief information about the most common properties of inorganic compounds:
crystal chemical (the type of crystal structure with indication of the temperature and
pressure above which this structure is implemented, the crystal system, the space group,
the number of formula units in the unit cell, and the lattice parameters) and
thermophysical (the melting type and temperature, the temperature of decomposition of the
compound in solid or gaseous phases, and the boiling point at atmospheric pressure)
data. In addition, the database contains information on the superconducting properties
of compounds. This database is available on the Internet for registered users [
The Elements database includes information about 90 of the most common
properties of chemical elements: the thermal (the melting and boiling points at 1 atm and the
standard values of thermal conductivity, molar heat capacity, enthalpy of atomization,
entropy, etc.), size (the ionic, covalent, metal, and pseudopotential radii, the atomic
volume, etc.), and other physical properties (the magnetic susceptibility, electrical
conductivity, hardness, density, etc.); etc. The database is available on the Internet [
The Diagram database contains data on phase P,T,x-diagrams of binary and ternary
semiconductor systems and the physicochemical properties of phases formed in them,
collected and evaluated by highly qualified experts. The Diagram database is available
on the Internet for registered users [
The Bandgap database includes information about the band gap of more than 3600
inorganic substances and is available on the Internet [
The Crystal database includes information about the piezoelectric (piezoelectric
coefficients, elastic constants, etc.), nonlinear optical (nonlinear optical coefficients, the
Miller tensor components, etc.), crystal chemical (the type of the crystal structure,
crystal system, space and point groups, the number of formula units per unit cell, and the
crystal lattice parameters), optical (refractive indices, the transparency band, etc.), and
thermal (melting point, specific heat, thermal conductivity, etc.) properties of more than
140 acousto-optical, electro-optical, and nonlinear optical materials, collected and
evaluated by highly qualified experts in the subject area. It has Russian and English versions
available for registered users on the Internet [
The AtomWork Inorganic Material Database (NIMS, Japan) contains information
about more than 82000 crystal structures, 55000 values of the properties of materials,
and 15000 phase diagrams; it is also available on the Internet [
The TKV DB on substances thermal constants contains information, available online from the Internet, on about 27 thousand substances formed by all chemical elements.
The complex integration approach that combines integration at data and user
interfaces level is applied to these database integration [
Machine learning procedure involves several stages: 1. The objects selection for machine learning. 2. The attribute description formation (including the most informative attributes selection and filling attribute values gaps also). 3. The best ML algorithms selection. 4. Machine learning including application of algorithms ensembles and collective solution synthesis in a case of several algorithms usage. 5. ML quality estimation. 6. New objects prediction and results interpretation.
The special information-analytical system (IAS), which, in addition to the information
service for professionals, is designed to search for regularities in big chemical data and
computer design of inorganic compounds was developed in IMET [
In the development of this subsystem, the most important task was the selection of the
most appropriate mathematical methods for searching regularities in chemical data.
Typically, this task is performed by the trial-and-error method. In the selection of
machine learning methods for analysis of chemical information, many years’ experience
in the application of these methods to inorganic compounds design was taken into
account [
As a rule, it is not possible to specify in advance which algorithm would be the most
efficient for solving a particular problem. Therefore, it seems promising to apply the
methods of prediction by algorithms ensembles. In a collective decision creation, the
possible prediction errors of individual algorithms can be compensated in many cases
by correct results of other algorithms. Based on this, we included programs that
implement different strategies for collective decision-making, for example, the Bayesian
method, methods using clustering and selection, decision templates, logical correction,
the method of a convex stabilizer, the Woods dynamic method, committee methods,
etc., [
For the selection of informative properties of the chemical compound’s components,
we included programs based on algorithms [
This subsystem facilitates the results interpretation, which constructs the projections of the points corresponding to the compounds in two-dimensional spaces of the properties of components, including not only the initial parameters but also user-specified algebraic functions of these parameters. 3.4
The knowledge base contains the obtained classifying regularities. The prediction base contains the results of previous computer experiments, as well as links to operation information stored in the knowledge base. Using the prediction base helped to improve the functionality of the databases on the properties of inorganic substances and materials, developed at the IMET, by providing the user with not only known data about already studied substances but also predictions for inorganic compounds not yet synthesized and evaluations of their properties. 3.5
The management subsystem organizes the computing process, ensures interaction between the functional subsystems of the IAS, and provides access to the system on the Internet. In addition, the management subsystem provides the expert with software for data preparation for analysis, outputting reports, and implementation of other service functions. In particular, we developed a special subsystem to retrieve information from the database, which, after evaluation of the expert, is used to learn the computer, and to prepare it for further analysis. It gives the expert the capability to edit the found information and to form training samples for analysis. In the latter case, the expert marks only the selected properties of the components in a special table (menu), and the subsystem for the sample preparation for analysis retrieves the selected property values from the Elements database. If needed, the algebraic functions of the initial properties are formed in the subsystem and the description of the compounds is assembled in the form of an Excel table, which is then input to the prediction subsystem. The subsystem of result delivery is intended to make predictions in a tabular form conventional to chemists and materials scientists. 4
The machine learning application allowed a search for inorganic compounds formation regularities, a prediction of thousands not yet synthesized substances and some their properties evaluation using obtained regularities. This approach efficiency to inorganic compounds design can be illustrated by comparison of the predictions results with newer experimental data obtained after publication of our predictions. 4.1
The equiatomic aluminides are of interest for the search for new magnetic materials.
Thirty years ago, the prediction of new compounds of this type was carried out by us
[
Table 1 is a result of comparing the predictions for each sets of properties and contains the comparison results of our predictions with newer experimental data. The following notations are used: + - prediction of the TiNiSi crystal structure type; - - prediction of the absence of the TiNiSi crystal structure type; - a compound with composition ABAl has the TiNiSi crystal structure type and this fact was used for machine learning; © - prediction of the TiNiSi crystal structure type was confirmed experimentally; O - prediction of the crystal structure type different from TiNiSi was confirmed experimentally; - prediction of the crystal structure type different from TiNiSi was not confirmed experimentally; here and in other Tables the blank spaces correspond to the disagreement of the predictions with the use of different sets of the component’s properties; all data and predictions are given for the substances under ambient conditions. A comparison of our predictions with newer experimental data has shown that the prediction error is lower than 12 %. 4.2
The chalcogenides with composition ABX2 are a class of compounds that is promising
for the search for new semiconducting and nonlinear optical materials. Taking into
account the perspective of these compounds practical use the design of their not yet
synthesized analogues was made [
The task solution was subdivided into to stages: (1) prediction of the formation of compounds with composition ABX2; and (2) prediction of the crystal structure type of these compounds under ambient conditions.
examples of the formation of ABX2 (X = S, Se, or Te) and 504 examples of the absence of this composition compounds in the systems A2X–B2X3 and AX–BX under ambient conditions were used for machine learning. The data were taken from the DB Phases. 84 properties of the elements A, B, and X, whose values were taken from the DB Elements, were used for the compounds representation in the computer memory.
For the data analysis, several machine learning algorithms that are included into IAS
were used. The learning quality was estimated on the basis of examination recognition
in the mode of cross-validation. The analysis of the results using various algorithms has
shown that the best predictions under cross-validation have been obtained for the
decision tree method (DT) [
ples of the formation of ABX2 with the crystal structure under ambient conditions αNaFeO2, 44 compounds with NaCl structure, 47 compounds with chalcopyrite structure, and 24 compounds with TlSe structure were used for machine learning. The same properties were used for the compound’s representation.
The problem was solved in two ways. In the first case, multi-class learning and prediction, where the cumulative information on the four above-mentioned crystal phases has been used, was applied. In the second case, four problems of the dichotomy were solved - division into two classes, e.g., class 1, compounds with chalcopyrite crystal structure, and class 2, compounds with another structure. The results of predictions were compared, and a decision was made if the predictions obtained by multi-class prediction and dichotomies did not contradict each other. The results are summarized in Table 2.
X S Se Te
Pm 1 1 5 1 5 1 1 1 1 1 1 1 1 1 Sm #2 #1 #1 #5 #1 #5 #5 #1 #1 ©1 #5 #1 #6 1 ©1 ©1©1 Gd #2 #1 #1 #5 #1 #5 #5 #1 #1 #1 1 #5 #1 #5 1 #1 1 1 ©1 Tb #2 #1 #1 #5 #1 #5 #5 #1 #1 #1 1 #5 #1 1 #1 1 1 Ho #1 #1 #1 #5 #1 #5 #5 #1 #1 #1 1 Er #1 #1 #1 #5 #1 ©5 #5 #1 #1 #1 1 #1 #5 1 #1 1 1 #1 #5 1 #1 1 1 #1 Tm #1 #1 #1 #5 #1 #5 #5 #1 1 1 1 1 #5 1 #1 1 1 1 ©1 1 1 #1 1 #5 1 #1 1 ©5 1 #1 1 #5 1 #1 1 #5 1 #1 1 #5 1 #1 Yb #1 #1 #1 #5 #1 #5 #5 #1 #1 #1 1 #5 #5 ©1 2 1 1 #5 1 1 Lu #1 #1 #1 #5 #1 #2 #5 #1 1 1 1 #1 #5 1 #1 1 1 1 #5 1 #1 Bi #2 #2 #2 #5 #1 #1 #1 #2 #2 #2 #2 #5 #5 #2 #2 #2 #5 $1 #1
In Table 2, the following notations were used: 1 ⎯ prediction of the structure of the α-NaFeO2 type; 2 ⎯ prediction of the structure of the NaCl type; 3 ⎯ prediction of the structure of the chalcopyrite type; 4 ⎯ prediction of the structure of the TlSe type; 5 ⎯ prediction of the structure different from the ones mentioned above; 6 ⎯ prediction of the absence of ABX2; the symbol # is used for objects for the machine learning; © predictions was confirmed experimentally; $ - predictions was not confirmed experimentally.
40 compositions have been experimentally tested and only in five cases the
predictions turned out to be incorrect, i.e., the prediction error was about 12.5 %. Beyond that
the melting point and bandgap were evaluated for compounds with the chalcopyrite
crystal structure type [
type of compounds A2BCHal6. Searching for and studying halide compounds having the composition A2BCHal6 (Hal = F, Cl, Br, or I) with the elpasolite crystal structure type is related to the development of new luminescent, laser, and magnetic materials.
The set for computer-assisted analysis included information about 289 (A ≠ C)
compounds having the elpasolite structure; 20 compounds with Cs2NaCrF6 type of crystal
structure; 57 compounds with crystal structures another than the ones given above
under ambient conditions; and 81 AHal–BHal3–CHal systems where compounds are not
formed [
The problem of predicting new halo-elpasolites included solving three intermediate tasks. Formation of compounds with composition A2BCHal6 was predicted in the first of them (task 1). The next task included searching for regularities and predicting the formation of compounds with given composition and the most common types of crystal structures (elpasolite or Cs2NaCrF6). The latter task was divided into two smaller ones. When solving the first of them, the multi-class prediction of belonging to four classes (elpasolites, compounds with the Cs2NaCrF6 structure, compounds with the structure different from those shown above, and the systems containing no compounds with composition A2BCHal6 (task 2)) was performed. Next, halide systems were consecutively divided into three classes: the target class, e.g., 1 - elpasolites; class 2 - compounds with non-elpasolite structure; and class 3 - the AHal–BHal3–CHal systems containing no compounds with composition A2BCHal6 (task 3). The final decision regarding the class that a compound being predicted belongs to, was made by comparing the predictions obtained when solving all three tasks. If the results were inconsistent, the prediction was regarded to be uncertain and the prediction table cell was left empty.
The algorithms LoReg, artificial neural network learning (ANN), K-nearest
neighbor (KNN), and support vector machine (SVM) ensure the best accuracy of prediction
of compound formation (task 1) in the cross-validation mode and the collective
decision-making software based on the algorithm of generalized polynomial corrector [
When solving task 2 of multi-class prediction, the set of algorithms including DT,
KNN, SVM, ANN, learning a multilayer perceptron, and the algorithm of the convex
stabilizer [
Some results of comparing the predictions found by solving all three classification tasks are summarized in Table 3. The following notations are used: 1 - prediction of compounds with the elpasolite crystal structure; 2 - prediction of compounds with the Cs2NaCrF6 structure type; 3 - prediction of compounds having crystal structure another than the abovementioned ones; and 4 - prediction of the absence of an compound in the ACl–BCl3–CCl system; the # symbol is used to denote previously studied compounds; the information about them was used for machine learning. C A B Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Tl U Pu During half of the century the predictions of thousands of inorganic compounds in binary, ternary and more complicated chemical systems were obtained and some their properties (melting point, critical temperature of superconductivity, band gap energy, etc.) were estimated in IMET. The obtained predictions usage allows an essential progress provision in a search for new magnetic, semiconductor, superconductor, nonlinear optical, electro-optical, acousto-optical and other materials. Hundreds of predicted compounds were synthesized and our results experimental verification shows that the average prediction accuracy is higher than 80%. Machine learning methods application to search for regularities in big chemical data of DB PISM gives an opportunity for theoretic design of new inorganic compounds that allows substantially reduce the costs for search for new materials with predefined properties, replacing them by computations. It is important to note that only information on components properties (chemical elements or more simple compounds) is used in prediction process.
This work was partially supported by the Russian Foundation for Basic Research (project nos. 17-07-01362 and 18-07-00080) and the State task № 075-00746-19-00. We are grateful to V.V. Ryazanov, O.V. Sen’ko, and A.A. Dokukin for long-term help and collaboration.