Application of Machine Training Methods to Design of New Inorganic Compounds

Statement Of The Problem Of Designing New Inorganic Compounds

The problem of designing new inorganic compounds can be formulated as the search for combination of chemical elements and their ratio (i.e., determining qualitative and quantitative compositions) for the synthesis (under given conditions) of the predefined space molecular or crystal structure of a compound that possesses the required functional properties. It is the knowledge of the properties of chemical elements and data about other compounds already investigated that constitute initial information for the calculations. The problem of designing new inorganic compounds can be reduced to discovering the relationships between the properties of chemical systems (for example, properties of inorganic compounds) and the properties of elements that form these systems (Burkhanov & Kiselyova, 2009; Kiselyova, 2005).

The methods of pattern recognition are one of the most effective means of search for regularities in the large arrays of chemical data. In this case, the problem can be defined as follows (Zhuravlev, Kiselyova, Ryazanov, Senko, & Dokukin, 2011). Suppose that every inorganic substance is described by a vector x = (x₁⁽¹⁾, x₂⁽¹⁾,..x_M⁽¹⁾, x₁⁽²⁾, x₂⁽²⁾,.., x_M⁽²⁾,…, x₁^(L), x₂^(L),.., x_M^(L)), where L is the number of chemical elements that form a compound and M is the number of parameters of chemical elements. Each substance is also characterized by a class membership parameter: a(x) ∈ {1, 2,…, K}, where K is the number of classes. The training sample consists of N objects: S = {x_i, i = 1, …, N}. We denote a subset of objects of the training sample from class a_j, j = 1, 2, …, K, by S_aj = {x: a(x) = a_j}. The aim of training is to construct a classification rule that distinguishes not only between objects of different classes in the training sample but also preserve prognostic ability to generate new combinations of chemical elements that were not used for training. Thus, we deal with the classical statement of a precedent-based pattern recognition problem. The peculiarity of the subject field manifests itself only via the formation of attribute description possessing a composite structure: the set of parameters of chemical elements (the components of an inorganic substance) is repeated as many times as there are elements included into the compound.