The discretization process of the cotinuous differential issue (with the initial-border conditions) leads to obtaining the linear set of algebraic equations. To resolve such a set of equations, the knowledge about the inverted form of system matrix is required. One-directional neural networks can be effectively used in matrix algebra to conduct lots of standard matrix operations, including matrix inversion. The neural models listed above during exploitation let to obtain a great functional speed (nearly real time work). The basic problem, in mentioned context, is the proper definition of an energetic function, minimalization of which lets to design, generate and learn the proper neural network topology. The aim of work was analysis of the possibilities of using modern techniques of artificial neural networks to generate the inverted matrix form.